Welcome back. This is the second of the lectures that introduced multi-level modeling. Creatively, I've named it multi-level models, too. You can imagine in your head that it also says Electric Boogaloo. Anybody remembers that movie? No? Okay.  I think I should give you an update on where we are, and partly because I had to do this this morning to figure out what we're going to get done with. So today is... Let me frame this a bit by saying you've learned a tremendous amount. You have. It probably burns the amount of learning that you have accomplished. That burning sensation means the medicine is working. And you have a tremendous amount of statistical power at your fingertips now. You can fit quite complicated models. And with the introduction of multi-level models, the possibilities are going to open up really rapidly. And what I want to do today in finishing the introduction to multi-level modeling is teach you some of the more technical things about them so you can use them more responsibly and make very good use of it. And we're going to need these tools next week when I crack it open even more and we'll have some more elaborate but routinely useful kinds of models like varying slopes where we extend the adaptive prior approach of varying intercepts to many clusters of parameters at the same time, all co-varying with one another at some hyper level in the model. And this will also let us do things like multi-variate outcome models which we'll use to fit instrumental variables. This is a return to causal inference, something more than the backdoor criterion that lets you get causal inferences. Even in cases where you can't close all the backdoors, if everything else is just right and you believe your dad, you can still get a causal inference using something called an instrumental variable. There's also a frontdoor criterion which I think I'll mention but I won't have an example of just for a second time. And I want to introduce a basic kind of network model called the social relations model which is also, apparently it's a custom varying effect sort of model, but it's custom, the covariance matrix is scientifically informed. We'll see what that means when we get there. But this is all about the responsible conduct and the possibilities that open up from understanding varying effects. And then week 10 is the end and I'll spend the first lecture that we're telling you about Gaussian processes which are, to my mind, an extension of the varying effects approach to an infinite number of categories, which I know sounds scary, but actually some of you know adding infinities makes things easier in math, not harder. It's the opposite of the real world. Infinity solves problems in mathematics. This will be very, very useful for routine kinds of variables like distances, phylogenetic distances, spatial distances, where there's covariance amongst units, but they're not categorically discrete. There's some continuous distance that we need to use to categorize them. Similarities, age is another kind of thing like this, right? And then on Friday, measurement error and missing data, topics that are common to everything that we do in the sciences, whether you do experiments or observational studies, these things happen. So into the material for today. This is the slide we ended on on Monday. We're going to pick up again with the pro-social chimpanzee data set. Very quick summary just to remind you, this is an experiment with a small number of individual chimpanzees, many repeat observations on each, in four different experimental treatments which combine which side of a table, left or right, a pro-social food option is on, pro-social is our interpretation. The question is whether they interpret it that way. So the pro-social side means both individuals get food, the other option, the non-pro-social option, is only the experimental individual gets food. The other kind of treatment is whether there's a partner present. And so in this fantastic piece of art on the slide, there is a partner present, but if the other end of the table were empty, then it isn't. And so remember we're interested in whether chimpanzees pull the pro-social option more often when there's a partner present. And the answer was no, right, at least in this experiment. I want to use this data set again, since you're already familiar with it, there'll be less friction. I want to use it to show you how to build a more complicated types of varying effects model where we've got more than one kind of cluster at the same time. This is a very common type of data structure called a cross-classification model. What's cross-classified here are the individual chimpanzees, which are called actors in this data set, and the experimental block. Experimental block is basically what you get, right? So there are block effects because maybe they were all grumpy, the weather was bad, then they were extra hungry, so they all pulled the pro-social option more in some particular block. It happened, right? Block effects happen. The terror of science is block effects. It's one of the reasons you want to randomize the order you feed your DNA samples through the machine, right? So there aren't block effects, time effects correlated with your treatments, right? You've got to de-correlate the blocks in the treatments. A very common thing. So in this data set, it's everything's balance. You've got all the chimpanzees and all the blocks. It's amazing they pulled this off. Chimpanzees will do anything for a grape, right? So this is something you know. And so we're going to be interested in using both of these types of clusters. That is, actors are a type of cluster because you've got multiple observations in each individual chimpanzee. So you can estimate parameters that are specific to that chimpanzee, like handedness, right? You've also got repeat observations inside blocks.  And that's how we measure the block effects, which are noise that is interfering with inference, right? These kinds of models are called cross-classified, but as you'll see, you can just design them as a very intercept model. There's nothing about the data structure that really distinguishes cross-classified from, say, something that's nested except your interpretation of it. The model looks the same. What does it actually look like? Okay, so here's the multi-level chimpanzee model with both actor and block intercepts. Draw your attention to the linear model part of this slide. You'll see that there's an alpha for each actor. There's a gamma for each block, and then there's a beta for each treatment. So each particular observation is getting an offset from each of these effects. The betas for each treatment are ordinary fixed effects. It's not an adaptive prior. We're regularizing, but it's not adaptive. There are four treatments. The alphas are the bearing intercepts on actor. These are just like the tank effects in the tadpole example for Monday. You remember that. Yeah? It's the same sort of thing. This is the handedness, right? This is the handedness of the individual because the outcome is pulling the left lever. There are seven actors. This is an adaptive prior. As you see, there's an alpha bar, and there's a sigma alpha, which is the variation. So the model is going to learn this prior from the data just like with tanks. And then we've got another adaptive prior in here. This one is the gammas. There's a gamma for each block. There are six blocks in the dataset. This is an adaptive prior because there's a sigma in it. This prior is conditional on a parameter. So we recognize that it's adaptive. There's a parameter inside of it. There is no gamma bar. Why? You could put it there, but it would be redundant because then you'd be adding alpha bar and gamma bar inside the linear model, essentially. So you just have some two things, like the left leg and the right leg, that you couldn't distinguish. Remember that from some chapter way in the past. If you don't destroy the model, it's just a redundancy that's unnecessary. It'll still run, but it'll run less efficiently and it won't help you at all. So we can just put a zero there. It's still an adaptive prior because the width of this prior is being learned from the data through this sigma sub gamma, which is a different standard deviation than the others. And then we've got hyper priors at the bottom for each of these. The bits that apply to the block variant effects. Does this make sense? How the definition works? You can extend the strategy to have as many different cluster types as you like in principle. Since you're using stand as your market chain engine, in principle extends a very long way. You can have tens of thousands of parameters if you like in these things and you can often sample them very efficiently. What does the code look like? I'm going to walk through this slowly. So, hang on and I'll highlight bits of it. This is the Ulan code version of the model on the previous slide. Just a logistic regression with a bunch of stuff. Right? That's all you think about. We've got a logistic regression up top. We've got a linear model with a vector of actor parameters, a vector of block parameters and treatment parameters. And then the section in the middle with adaptive priors. The vector affects. So, in the linear model, there's this A for each actor. And then we've got a vector of those. They get each actor parameter has this common prior which itself has two parameters inside of it. It's conditional. That's what makes it adaptive. It's conditional on other parameters. And then down at the bottom in the hyper priors, you see those two parameters that are learned from the data that give the shape to the priors for the actors. This is what creates shrinkage. You're going to see you're going to get shrinkage here just like with the tanks. Yeah? And then the same thing for blocks now shown in green. We've got block up in the linear model. We've got the block adaptive prior. And then there's the sigma down at the bottom for blocks as well. Make sense? Easy, right? You just keep on. You have to manage it. But the strategy grows naturally from there. Okay. You should run this model at home. Remember, you always go home and draw the owl. Finish drawing the owl. You won't encounter any major problems with this. And you summarize the plot the precy output on the left. I'm showing you the B parameters are the treatment parameters. There's no new story here. Remember chimpanzees on average are attracted to the pro-social option, but not more when the partner is present. So there's more food on the side of the table. They tend to pull that lever more, but they seem to be almost entirely insensitive, if at all, sensitive to the presence of a conspecific. The alpha parameters that come just next, these are the handedness ones. And you recognize sweet, sweet individual number two there, right? Lefty. Lefty has got a really big bearing intercept. Yeah. Remember, pulled out. Number four on the horizontal axis means basically always. Why is there such a wide posterior, marginal posterior distribution for Lefty? Someone have an idea? What's that? Yeah, because all of them mean always. Yes. No, it's the most succinct version of it. It's a lever, right? And so the data can't tell you the value of that parameter, except that it's really big. And that's what happens. If you didn't have priors, infinity would be compatible with the data, right? But we know infinity is not a value we wish to consider, and that's what the prior says here. Yeah, does that make sense? You can't, four and five and six all make the same predictions. Because the data just, the likelihood is insufficient to identify the parameters. It's just how reality is.  So then the G parameters that come below are the block effects, six block effects. You'll notice these are very small. They huddle around zero. This means there's not much variation among blocks compared to the variation among actors. You can see this. Yeah, and what's going on. Down to the very bottom, is our alpha bar. Just slightly left-handed in this sample. Yeah. And then the two sigmas, and you'll see the two sigmas tell the same story that you can see with your eyes. Right, your ocular scientific instruments. You assess the variation among the intercepts for actor and the intercepts for block. You can see that the actors vary more than the blocks do, and the sigmas are picking that up, right? So the posterior for sigma among actors is around two. That's a lot of variation, right? This is not describing exactly your sample. It's trying to learn about a population that these chimpanzees came from. That's one way to think about it. So if you were going to take this experiment to a new colony, and you wanted to have a prediction of the variation among the individual actors. So you'd use that, for example, to know how many repeat measures are individual, then this sigma would be useful for designing the experiment. We'll do some more with that at the end of the lecture today. And then sigma g is practically zero. It's not exactly zero, but it's very, very close to zero because there's not much variation among blocks. And then I plotted those two densities for the two sigma variables in the right-hand part of this slide. A block, a sigma sub g for the blocks is shown in blue. The sigma sub a for the actors is shown in black. And you can see how different these are. Does this make sense? So the consequence of this, what's the consequence? There's a lot more shrinkage among blocks. If one of the blocks were extreme, it got shrunk towards zero really aggressively. The actors will be very little shrinkage because lefty, bless lefty, lefty proves that individuals, chimpanzees are individuals, right, they have personality. And, uh, okay. So, um, it's natural to ask then should we even have varying intercepts on block? And the answer is it doesn't matter. It really doesn't matter. You can put them in the model, it won't hurt anything. You can leave them out, you'll get the same inference. And the reason is because there's basically no variation among blocks. But it's a nice feature of varying intercepts and varying effects in general is that if there's not much variation among the members of that cluster type, it isn't harmful to add the varying effects because they get shrunk very aggressively in that case. So what I'm trying to show you here is, here's the model, same model, but we've taken out the block effects entirely in this model. You'll see that they're missing. There's nothing about block in this model. But we've got varying intercepts on the individuals still. And we can compare these two models using WAIC or, uh, or LU, you'll get the same numbers. And, uh, you'll see that they're very, very similar models. Their difference in WAIC is only two. And the standard error is very close to that as well. These are effectively the same models in terms of out of sample predictions. There's really nothing to get excited about the difference. And, uh, you'll notice that the parameter counts difference is quite small. Model 13.4 had, uh, seven additional parameters because there were six blocks and one sigma but you'll notice that it's not seven more effective. PWAIC is only about 11 whereas in the model that emits all those blocks it's about nine. So it's like a two effective parameter difference, uh, you know, rounding. I like to aggressively round, rounding even though it has seven more parameters. But those parameters were aggressively regularized because the model didn't discover much variation among those units in the data. This is like the fail-safe device with varying effects. Yeah? And lots of machine learning works the same way. It doesn't use exactly this structure to do the adaptive regularization, but deep learning systems also have this way to consider many, many features and aggressively regularize the ones that don't matter. That's a nice thing. Regression trees also another non-basin way. Well, there are basing regression trees, I shouldn't say that. Regression trees are another strategy. Lots of regularization strategies that will do this for features just make some sense? Yeah? Does it make enough sense that you can go home and draw the owl? That's really all I can hope at this point. Yeah, you got to go home and run the chain and draw the owl, right, and play around with it and look at the predictions. Okay. Let's add some more random effects. Why not? So this is also a chance for me to try and make that happen again, right? Lots of this. This term effects, which is a synonym for varying effects. The word random has this tendency to lead people to interpret the effects in a stronger way than I think is warranted. These are just statistical things that are used to regularize inference. The source of the clusters is irrelevant to whether we add varying effects or random effects or not. But you will read in textbooks this advice that, you know, so we're considering the issue here where we could add varying intercepts on treatment. There are four treatments. We have repeat measures of each, right? Every chimpanzee participated in every treatment. We've got tons of data per treatment. We could, we want to regularize those and we have in this model, but we have not adaptively regularize them. Why not? And some people will say, well, you can only put random effects or varying effects on things which weren't fixed by the experimenter. They're fixed by the experimenter. We call them fixed effects and then you don't use adaptive priors. That's nonsense. It's just nonsense. If you care about more accurate inferences, you use adaptive priors. That's all there is to it. So we can do this. It's fine. It doesn't matter. Don't succumb to the mind projection fallacy, that how you set up the data determines how you should learn from it. Right. And so to do that, all we have to do is add a sigma beta to the prior for the B treatments. Instead of, I thought there was like .5 before, I think. I won't go back to the previous slide, but I think I made it .5. And if we just make it give it a parameter, we can learn it. This is what the model looks like. Then I'm circling there the new adaptive priors for the treatments. There are four treatments. Four B parameters. We get one more sigma down at the bottom. We got lots of sigma's now, right? Stack them all up. And we run this model. It's no problem. And I'm just comparing this to the previous model. Model 13.6 is the one shown in the slide. 13.4 was the first one we did today where you've got varying intercepts for block and actor, but fixed regularized treatment estimates. And they're the same, basically. They're slightly different. The new model does regularize the more extreme one, beta 2 a little bit, but they're basically the same estimates. Why? Because there's tons of data per treatment. Right. So the varying but you're learning the sigma, it doesn't change the estimates very much. It trims the posterior uncertainty a little bit because there's not much effect. But it doesn't change your effective inference about the treatments at all. There's no harm done here. Okay. One of the things that will happen when you go home and draw the owl is you will get these warnings that you have probably already seen occasionally. Yeah? Have you seen these? There are these mysterious things called divergent transitions. Have you seen them? Yeah? They're great. They're kind of spooky. You get them and you have no idea what that means. Divergent transitions are your friend in the sense that they're telling you about something that is numerically inefficient about the Markov chain. If you have a very small number of them, it's hardly ever a serious issue. But it's easy to get rid of them. And there's a whole section in chapter 13 where I talk you through how to do this. And I want to spend some time today, probably next 15 minutes talking about these and how we fix them because it teaches you something really important about multi-level models. And that is that we can write the same model different ways in the code. And even though they're mathematically equivalent, the Markov chain will see them as quite different. And often this is just a required thing. If you want to run these models and sample from them effectively, you need to be able to switch between the different ways of writing the same model. I know this sounds like madness. But even though the algebra will be equivalent, the geometry is going to look really different to the Markov chain. And that's the intuition of that. So, here's what you'll see. This is my R environment, by the way. It's glamorous. I know all the cool people use our studio. I have nothing against our studio. But there are some, there is some value to using the terminal like it doesn't crash as much as our studio. Jeff's not here today. But if Jeff were here, he would not have had vigorously about this. So, you'll get these warnings, three divergent transitions after warm up and it gives you advice to increase Adapt Delta, or this case above 0.95, which is the default for Oolong. Sometimes that will work and Adapt Delta is this parameter I'll tell you about in a moment what it does.  So, let's start before we get to that what that means to reparameterize your model to saying what a divergent transition is. So, forget about statistics for a moment and imagine you're on a frictionless roller coaster. Right, terrifying thought. But a frictionless, real roller coasters have friction and where the wheels touch the track there's a lot of friction actually. Right, because sausage on a roller coaster track. Right, but imagine it's frictionless. So, as this roller coaster moves from point A to B to C to D, there are two forms of energy which are being adjusted, shifting, there's a total amount of energy comes from the momentum of this roller coaster in this system and it's frictionless so it'll never stop moving. Right, but the energy is in two buckets and even though the total amount of energy is constant in the system it has to be that's all energy is in physics, right it's this thing that balances the ability to do work and it's got a bunch of like pockets you can put it in but it has to be conserved it's just the thing that balances equations. It sounds mysterious, energy. It's just equation balancing. From point A and the roller coaster went down to point B it lost potential energy potential gravitational energy because it was high and that it's converted to kinetic energy to motion as it goes towards B and then as it moves up from B to C as it is pictured right now the conversion goes the other way that kinetic energy is converted back into potential energy because you get to the top of the hill and then the conversion will do it again and this is what roller coasters do, right they just keep converting kinetic energy into potential energy and back and forth but the sum of those two things is constant in a frictionless system and a system with friction energy is still constant but you're deep heat you get heat energy our Markov chains don't have heat energy which is why I want you to imagine this is frictionless it's like your frictionless roller coaster so what is a divergent transition then a divergent transition is when your roller coaster is on track right so and we can detect this inside the Markov chain by monitoring the energy of the system it's a physics simulation and it has energy and in fact in Hamiltonian dynamics the Hamiltonian is the total energy of the system and so it's actually conveniently calculated right inside the Markov chain if you look back at the chapter where I introduced this I think it's Hamiltonian Monte Carlo and you'll see it there I calculate the total energy inside that loop and we use that to monitor the chain if the energy is not conserved in your chain something's wrong and it means your numerical approximation is bad and you popped off the track why would that happen because we don't actually have a smooth continuous simulation we have those little steps these little linear jumps we get a gradient then we take a little finite step and then we do it again so we're getting a piecewise linear approximation of a smooth surface and so if the pieces are small enough and the roller coaster track doesn't bend too much that's fine but when the roller coaster track bends really violently or your step sizes are big then you can pop right off the track and you want to monitor that so it works and so these divergent transitions are when that happens from one position in the Markov chain to another that's a transition those smooth things that were drawn in the movies and divergent means it pops off the track pops off the true surface you don't actually pop off of anything inside the Hamiltonian simulation because it's a big manifold but you know you go off where you were supposed to be and you recognize this because you can monitor the energy so this is the summary slide to tell you all this and there's a whole section in chapter 13 because I want to show you some pictures to give you a little bit of intuition about it and so on the right here I'm showing you a posterior distribution which tends towards divergent transitions this happens a lot almost any time you have a parameter that's conditional on other parameters so let me, oh before I move to the next slide and explain this thing I want to say the bold statement at the bottom of this slide other sampling strategies other than Hamiltonian Monte Carlo have problems with exactly the same kinds of services but they have no way to monitor it because they've got no energy so gives sampling and all of those metropolis hastings based strategies they won't tell you when this is going on but they definitely experience the same problems but they don't have all these extra parameters like momentum that Hamiltonian Monte Carlo has which seem like a bother at first but turn out to provide diagnostics one of the reasons to use Hamiltonian Monte Carlo is because well it just works better than the other things especially in high dimension but another reason even if you're in low dimension to use it is because it freaks out when things are wrong and the other strategies don't you have to work much harder to get diagnostic information from them so if you're paranoid like me you like things that throw up warnings all the time yeah, you love warnings don't turn off warnings that's a bad idea very very bad idea if your smoke detector goes off when you cook in the kitchen well then open a window don't turn off the smoke detector same thing with Markov chains open a window, don't turn off the warnings so a little bit about divergent transitions let me show you a routine kind of situation and this arises all the time in varying effects models where you get divergent transitions it arises through this effect that's often called the literature the funnel so this funnel is turned on its side left hand parts at the bottom would look more like a funnel what is going on here I'm showing you a very simple posterior distribution two parameters, v and x v has a normal 0, 3 prior and x is conditional on v where the e to the v is a standard deviation this is like x is conditional on v when this is true you can get very interesting shapes with very very strong curvature so what you're seeing is v on the horizontal here that's that one and now x since the width of x depends upon v as v gets small x contracts and you get this very narrow valley so do you think that part there near where the 0 point on x that's this very narrow valley very high ridges the funnel and so your Markov chain has to get down in there and take some samples because it's part of the posterior distribution but the curvature is really tight there so your roller coaster has tendencies to pop off out in the big smooth plane where v is large you can take big steps and move around on the big expansive plane out there and everything's good and it's completely different and a big problem here is there's no single step size which can efficiently explore both of those regions of this posterior distribution the valley you want a really small step size in the valley otherwise you pop off the track and you want a bigger one out in the open area so you effectively explore it yeah so these kinds of posterior distributions are much more challenging for all kinds of samplers and Hamiltonian Monte Carlo is just nice as it throws warnings about these things so think about two kinds of behavior on the left I've set the step size large and I've colored in red divergent transitions I'm just monitoring the energy and when the energy at the start of the transition is different from the energy at the end that's a divergence now and the Markov chain will reject these samples but it can reject samples of Hamiltonian Monte Carlo and the rejection criterion is the difference between the starting energy and the ending energy because that means you've got divergences so this doesn't necessarily corrupt your chain but it does mean that it's way way less efficient than it could be and it could induce subtle biases in the posterior distribution because the places where you do the rejections are particular regions of the posterior and you won't be sampling there in the posterior distribution now in infinite time you'll be fine but you don't have infinite time again you've got to finish your PhD so I'm here for you to help you figure that out the other criterion is we can make the step size small but then you could just spend all your time missing the funnel completely as in this one I think I took 500 samples in each of these so now Stan will do better than this he's got no adaptivity thing going on and I've just made some examples for you Stan will sample from this quite well this particular example but as you increase the dimensionality like stack up the X's like in a varying effect model in a varying effect model you're not going to have just one X that's conditional on V you could have hundreds of X's that are conditional on V this gets pathological real fast in that circumstance so we want to do something about it what do we do? you've got two strategies you can do in this scenario on the right the emergencies go away but you could spend a long time before it finds the funnel and take samples from it yeah also makes the chain run slower however that's a fine trade off I think valid inference is worth waiting for the second option which is often way more effective is to reparameterize and I should say you only undertake both of these steps either of these steps after you've looked hard at your model it's correct because in my experience when the chain isn't efficient on the first go it's because I did something stupid like left out of prior completely like I haven't parametered has no prior at all that's like the most common my own personal most common mistake there's this folk theorem I think I showed you earlier in the class the folk theorem of applied statistics is that when you're having trouble estimating the model Tuesday because the model is wrong so the folk theorem holds and the first thing you should do is look at the model and make sure it's all there you didn't do something ridiculous after that you can attempt both of these steps so what's the reparameterized thing is weird when you first see it so I want to spend some time explaining it okay so it's a fact a wonderful fact that most any statistical model can be expressed several different ways in the formal mathematics if you'd write them on the page they're all perfectly transformable they're the same algebraically identical models let me show you some examples here's a really simple model alpha is some parameter that's conditional on mu and sigma you see these things in your dreams all the time alpha is conditional on mu and sigma we can re-express this little model multiple different ways we'll be focusing on the distribution of alpha alpha has some probability distribution here's another way to write it we can say that alpha we can say that alpha is deterministically the sum of mu same mu is in the first line plus some new parameter beta and we assign beta distribution normal zero sigma this now alpha in the middle of this slide bottom of this slide has the same distribution as alpha at the top you see this we've just re-centered it we've taken mu out of the prior for alpha and we added it back on later but you can always do this with a normal variable you just translate it wherever you want it to be make sense? now you're thinking you could do that why would you do that I'll show you why but right now this is just about what you could do we're just in modal verb land we're doing could and we'll do should later so we can go one step further we can get sigma out of the distribution as well now we say alpha is equal mu plus z times sigma and we assign z a normal zero one parameter z is a z score or a z score if you come from a barbaric place no sorry this is a fight between Canadians and Americans whether you say z or z some people have opinions about this I don't alpha is mu plus z sigma and z is normal zero one but when we multiply those individual z's sigma they're back on the scale that we want because sigma gives their width gives the width of the target distribution and then we add mu back in and it's translated to the position we want and alpha and all three of these expressions is the same distribution does that make sense yeah good times and I know why would you do this you could do this yes but it's like that Jeff Goldblum thing the scientists were so busy asking what they could do you remember that we should do this sometimes absolutely and the reason is because even though it's mathematically the same your roller coaster sees these distributions differently because the shape is different the geometry that it has to cruise around on is different this is a cool effect in a very handy way to make your Markov chains more efficient so on the left we have the form the kind of default form that I showed you often called the centered form this is not great terminology but as always I got to teach you the terminology that's in the papers so how do you understand that it's centered there are parameters inside the distribution so there are parameters that are conditional on other parameters since they've been located by sticking parameters inside them someone invented this term it didn't make sense then you just have to learn it that way centered means that there are parameters inside the distribution of the parameters non centered is the radical version where we try to take all of the conditioning out of the distributions and stick it inside some linear model and so the right hand version here is the non centered version where we have the z score normal zero one prior make sense? Just as a definitional issue right now let's look at the geometry of these two equivalent distributions we get the same information from each on the left we've got the one I showed you before the funnel, I'm showing you some good Hamiltonian trajectories down to the funnel where we get divergent transitions the roller coaster goes down in there and flips over and the same thing but in the non centered part now we've got a Gaussian bucket again and we can just cruise around this Gaussian bucket forever doing nice oscillating paths it's beautiful and that's what you get, they're the same distribution actually you can convert between them but the one on the right is way easier to cruise around in under roller coaster one of these is much more violent right than the other and so when we re-parameterize the version on the right do our varying effects that way you typically get many more effective samples from your Markov chain than you do on the left so again with my hand written Hamiltonian Monte Carlo code not effectively tuned or not I'm showing you the difference in the funnel those red points are divergent transitions that are rejected they're left out of the Markov chain and you start back over where you started again whenever that happens and they're scattered around but a lot of them are down in the funnel and the ones that are outside the funnel by the way are ones that start in the funnel you start in the area of high curvature and you get out of it and you still have a divergence so and then on the right same settings no divergences at all 100% acceptance rate nice Hamiltonian Monte Carlo so this is a big difference and it's really nice let me show you what this looks like in a real model how to do it so this is the chimpanzee model again with actor and block just as before this is a centered model because it has parameters inside the adaptive priors and it's sample 5 divergent iterations what I'm going to show you is if we non-center it make it into a non-centered parameterization it'll be more efficient so let's focus just on the linear model first this is the first thing to wrap your mind around is that linear model up top is not going to be written with these z-scores and sigmas inside of it because each centered version of a parameter like an actor z sub actor times the sigma among actors and that rescales it and then alpha bar is just out in front we've taken that out of the prior two we just put it inside the linear model so it's the same but it looks way worse doesn't it it looks like a much harder model now this is the trade off you can't have it all and then the same for block I made these things called x for block because I didn't want to have z twice so now it's x-scores for block times the sigma sigma gamma for the block standard deviation and the treatments are still fixed effects so we leave them as they were yeah, makes sense and then the rest of the junk so the new bit down here is where we used to have the alpha and gamma priors that were adaptive we now have z normal zero one and x normal zero one so there's still vectors of parameters these are varying effects but they're standardized varying effects and we have to de-standardize them to make the correct predictions so that de-standardization happens inside the linear model fun? yeah, I teach you this because there's really no avoiding it this is the most important thing to understand about making varying effects models run right and lots of things are basically varying effects models because in complicated models you often have distributions with conditional and other parameters that happens all the time factor models, all kinds of things have this phenomenon going on inside them good, can I move on to the next slide? I have no reason to rush here we can stay on this slide the rest of the time it's necessary okay, I know that you're like no please move on so in code here's what it looks like there's this really long linear model now yeah, that's okay it's all the same and now we've got z here, d norm zero one x block d norm zero one the rest is the same, it's that easy now what is this, get us you run this thing and again you should really go home and run this and see for yourself it'll also sample faster you can compare the timings this chain will run faster as well and the physics simulation runs better but what I'm doing here on this slide is I'm going to compare the effective number of parameters for the number of samples per parameter for both models, these are structurally equivalent models same data, same analytically the same posterior distribution and they are if you look at the precy output, they're basically the same they're the same posterior distribution for sure, both of these have worked but so nef sub c is the number effective parameter is a vector of the number effective parameters sorry, number effective samples per parameter this is the centered model, which is the first one we did and sub n c is the non-centered one and I'm just showing you in this table per parameter, all the b's, all the a's all the g's the a bar and the two sigmas those numbers and they're always bigger for the non-centered model sometimes double so what does this mean? it means you don't need to run the chain as well and with a really big data set this is a huge savings for two days to sample I definitely worry about these things before I let it run for two three days you don't need that in samples that run the chain for less time but I don't have to fight my scientists for cores as much does this make sense? this is often just like the best thing you can try and as we have examples going in the next week I'll often show you this trick we're going to repeat this trick next week as well and lots of things and I'll show you how to do this with the phylogeny you can non-center the whole analysis and lots of stuff to make it work last thing that we really need to talk about this week is how you do posterior predictions with multi-level models and the answer is you've got to make some choices now that there are different levels to interpret the model app because it's multi-level you get some agency back and you get to decide how you want to think about the generalization of this model there are different aspects of the posterior distribution which may be relevant to you depending upon your scientific purpose and the most direct way to consider these choices you can make is when you generalize your inferences from this sample are you interested in new units like new chimpanzees are you interested in the same chimpanzees if you're interested in new chimpanzees say at another colony I think the ones I showed you were in Texas those are Texas chimpanzees you're going to pick Leipzig chimpanzees to make predictions for you wouldn't get to use the alphas those alpha parameters are irrelevant to you they're in the posterior but you can't use them to make predictions for a Leipzig chimpanzee or rather you shouldn't lefty, remember lefty's alpha you're not going to use that and just assign it to some random chimpanzee here however the other parameters are definitely relevant because they tell you about some statistical population you've learned about the variation possible in a colony of chimpanzees substantial and that would give you a prior for what you do to design an experiment here so let me give you an example using the chimpanzee model of how you might project different kinds of predictions out from this thing if you're interested in the same chimpanzees it works very much like every chapter we've come to before you just use those parameters to generate predictions but in other cases you've got some choices so when we do the new clusters as I say at the bottom of this slide you've got a bunch of different ways you can generate the predictions and different visualization options so let's consider as I say here at the bottom of the slide if we have the same actors you can just use link and sim as before it works just the same as forever you push samples back through the model and you get those chimpanzees this is like posterior prediction check to make sure the model worked if you've got new actors this is a kind of counterfactual thing imagine sampling new actors from the population now we're going to literally do that inside the model we're going to sample from the adaptive prior in the posterior distribution and get new chimpanzees out and there are different ways to draw these and I'm going to show you three you can think about an average actor in a new sample I'll show you what that looks like then there's something else confusingly called marginal of actor what does that mean? an average actor is literally like the average actor so we take the statistically average chimpanzee which is definitely a construction maybe a dead space but statistically average chimpanzee and we ask what the model says they would do that would be a chimpanzee at the population mean at alpha bar marginal of actor is different let's sample a bunch of physical chimpanzees and average over their variation that's what marginal of means you marginalize over the distribution and that's different as you'll see because it includes the population variation and then my preference honestly is usually just to show a sample of actors from the posterior is a bunch of lines you know I love these line plots the posterior distribution is full of chimpanzees now and we can plot them it's just full of chimpanzees infinite number of chimpanzees so one at a time what's the average actor look like this means actor with the population mean intercept alpha alpha equals alpha bar for the average actor and how do we do this? well since you know the model you know the model because you're taking my class and I have cruelly made you manually write the log posterior for every model we've done in this class you're welcome to do generic predictions for it leaving out any bit you like or plugging in anything you want and so we can do this quite easy as a trick here all we have to do is replace the intercept samples all with zeros now all the actors have the average intercept and then we can use link so the way I've done this is we can extract the samples and then just put in this big matrix of zeros and run the link model as well all this code is in the book and you can draw the outlet home you can also just directly simulate it so what do we get from this we get a graph like this you can focus on the code later when you go home focus on this graph here's the average actor it looks like a charlie brown shirt is it zigzagging and there's uncertainty about it but that's the average actor what about marginal of actor now we've got a sample of a bunch of chimpanzees and we have to average over them so we're going to generate a prediction interval for the whole population of them and as they vary and some of those individuals are left handed and some are right handed and that makes it wider codes in the book and you want to go home and play with it now it's the same charlie brown shirt zigzag but it's much much wider yeah? why? because the chimpanzees vary a lot they're really different from one another does it make sense? and finally the last thing to look at is instead of drawing this as an interval you can just sample a bunch of chimpanzees and draw them now these individual trends are chimpanzees you have 50 simulated chimpanzees looks like more than 50 it could be 50 let's say it's 50 and you'll see that one of the things that happens here is that because there's a posterior distribution for all these parameters and there's this big wide distribution occasionally you get individuals that are on the other end at zero we didn't see any of those in our sample but the model hasn't excluded them as possibilities you can get extremely right handed chimpanzees just like lefty and those are crowded up on the bottom ones all the way at the top but you still see the treatment effect echoing through this that's the exact effect that's something that you get I often like plots like the one on the right hand in this slide because you see more at least I see more but you see more than you do if you draw the compatibility interval the big smooth space you get to see that there's a bunch of individuals you get to see for example that as an individual approaches either boundary the treatments have less effect and you finalize one of your models and you hit the seal in your floor and you get less effect so it makes sense? good? okay you go home and you draw the owl and you'll see how this works and when you have your own data and model you make some decision about how you want to explore it and draw it this way it always depends upon the scientific context of how this works okay homework I have prepared a homework assignment and I still have yet to do it all but it is written and I will post it this afternoon and what you're going to do I call it frogs and contraception it's not the frogs that have contraception there's multiple data sets you're going to work with read frog data some more and this is a basic varying intercepts model but you're going to add predictors to the model I'm going to go ahead and give away the plot and say that the point of this is I want you to look at really focus on what happens to the variation among tanks as you add predictors to the model so you're going to fit multiple models some will have more predictors than others and then you're going to look at the sigma the sigma among tanks across the different models and there will be a pattern hint and that's what I want you to focus on so that you learn what's going on with these things the second data set is a historical D contraception data set it's a really nice data set and I know there's posters from India but this is all I could find with some quick googling not the same place I know and in this there will also be a varying intercepts model and you're going to explore shrinkage in much the same way you explored it with the tadpoles but now this is real data of incredible consequence for planning and I want you to explain the shrinkage pattern that arises in the data set okay with that as always thank you for indulgence when you come back on Monday we're going to extend directly from here to add varying slopes we're going to let everything vary and I call this adventures in covariance because it opens up the possibility for a huge number of exciting things including phylogenetic models and network models and other kinds of stuff thank you have a good weekend it'll be very warm here in Leipzig and I'll see you on Monday


Hello everyone and welcome to an unexpected episode of Jurassic World The Game! This is the second time I'm recording the intro because while recording I got a code 19 this thing and then the game just like crashed I don't know what happened like the screen froze and that completely busted the capture and then it was like okay you can keep on going so hopefully it's not going to happen this time but yes it's an unexpected video do you know why? well that creature is being well it hasn't been released because it's a tournament I didn't realize it was going to be a tournament creature just because I don't really pay too much attention to the updates that are coming to this game unlike Jurassic World Alive which I do but this one I just let you know things happen there I can't be like oh I need to save my creatures to do this battle or whatever so do I get mine? I know I've already collected that okay but collect food because we're pretty much there we maxed up on food completely we'll get some books because now we're on over 10,000 which isn't too bad I also have the Trophy if we go here it should be here where are you the golden behemoth oh it's Vulcan that's right so the Vulcan is the Triceratops the regular one is it and then you've got Juggernaut I don't know why we've got that and there's gold Juggernaut so Juggernaut I think was the original boss and I don't think we faced him for ages because then Vulcan took over so we now have that one we have that statue we do yes where can we place it? oh I want to place it there I want to place it in the middle I want to place it there in fact you know what that's what we're gonna do that's what we're gonna do we're gonna put these fountains in a storage oh yes now we're gonna close out that we're gonna go back into market we're gonna scroll all the way to the gold and place you right in the middle boom there you go so gold it has a decent radius but when you compare that to a fountain which has 3 radius for 10% double double it does whatever I could get 20% well 40% extra for having 4 fountains there or I could have 1 Juggernaut to get 5% really we want to go with the fountains but hey also I need to check out that how do I get more of these so it says do I not have these no I don't ok so I don't have an endoraptor endoraptor level 40 and how many I got 45 out of 52 1, 2, 3, 4, 5, 6, 7 so yeah Spinosaurus at the moment is the highest reward it's not the t-rex for the thingy what you call the hologram so when you get smiled on to level 40 the thing is right a lot of these creatures is what you need for the hybrid and if you've already got them and you didn't collect the uh the mission then they're stuck there so I need to get Zephactanus up to level 40 and prognathodon up to level 40 Smiledon which I've already got that up to level 40 and fused it but didn't get it uh an endoraptor level 40 oh I don't want to do that there's no point oh I don't want to get it no no game I will not fall for your tricks so we have the shake of the earth also hold on did I do anything in here oh that's right now I there's never I've never seen this before in the game but I got a random update as soon as I logged in it said do you want to buy one of these for bucks and there was three options Leedsic these was one of them um so that's the first time ever that I mean this thing's not released yet and it was 3,000 bucks for one Leedsic these you know what I thought yeah let's do it let's do it let's do that cause that creature is not released and if I can get you know at least one I'll do it so I bought it for 3,000 it was a right rip off um what oh also I've got discord if you didn't know link in the description below um and it'd be quite interesting to see what's the worst trades that you guys have ever gotten and there should be a channel in the discord for Jurassic World the game I think um and post your worst trade in the discord in that channel a picture I'll allow it I'll tell the admins you're allowed to post a picture there um cause I've seen some bad ones I've had some bad ones but I'd like to see what the worst ones are and you will get shouted out in the next video at least I'll definitely show the picture like look at that that's awful the phoenix 44 statue and just trade it for coin yeah you know how about that even worse 1000 cash for 3 million coin oh I'm so tempted to do it just be like ah whatever but here it is this is the please pleasesuchus so that's the new creature like I said yep it's going to be the Dacosaurus and Geosaurus animation set it is however a tournament creature which means that why how do you should oh what look at the picture it's completely list oh my god call the assurance we have a day off that day do you not feel like like logging into your team speak and working from home bit there it's just ah stretching yeah okay well um let us put in I don't know something that well it doesn't matter what I put in here I can put in this Spinosaurus the two to join the sources it's still only going to give me 20 cups so and I get to win it pretty much straight off about so might as well do that but let's see if we can get this video trending oh my god supreme Carlos look at that guy wow he he wasted money on supreme hold on let me just turn it down a little bit there we go go yeah let's even get this trending like the alkalon video good god I still don't know how that video like youtube just pushes it consistently it doesn't matter for the past how many years that video has been up or at least recently anyway I if I go my monthly statistics for top 10 videos of the month it's always up there always I don't know why it just is he he he maybe if I you know I should just replicate this thumbnail exactly except for instead of have alkalon have like please just please just suck us there instead hmm maybe maybe the thing is nobody's unlocked pleasure suckers so I can't really do that because I didn't have it and it's not an aquatic tournament because tournaments used to be if it's a aquatic creature you'd have to use your aquatic dinosaurs and and you take a lot less battles to level up look at that we've already skipped pre league we're in survivor and I'm expecting probably about maybe 20 battles to get high but you never know maybe we'll win it on the spin wheel I have never won the prize of the like the main prize on the spin wheel since the Mosesaurus yeah that's that's how long it's taking me I think and I played that for like 48 hours straight almost I think it was that was ridiculous but I did it because there was a chance there was a chance like a 0.1% chance of unlocking the Mosesaurus pack on that spin wheel Jesus there were different times man weren't they wow just thinking back to that I for a start I wouldn't do that now just because I can't be bothered good god I think I would rather just hack the game these days not that I have never hacked this game everything I've got to be legit I think if it was to hack now it would just mean that all the money I have actually spent in this game is wasted because then I should have just hacked back then and saved myself a bunch of money thousands hundreds of thousands no I haven't spent that much I don't think actually there's a task for you you're all watching up to this point watch all my videos and calculate how much money I've spent on the game how many months I had VIP for oh god don't do that don't do it the guy who was counting how many victories each dinosaur got I think he did it for a certain point and I think he might have hit like the Arkelon video and as soon as you hit that Arkelon video I think he just died he was like yep not doing this anymore can't be bothered he could have just thrown me a random number and I would have just believed him but bless him he tried he tried his best okay so he's just gonna scroll all the way down to you and then that's the mission done because I think you need to speed up three times in a day and I think it's 50 bucks you get for that or maybe it's DNA it's something half it's something decent oh god ooh that's T-Rex's oh I don't like it we've got to be careful here because these T-Rex's might be able to kill my hybrid banana beak because they have an attack of 176 that's dangerous numbers when they get to like 6 or 7 attacks so we've got to be careful here 2 2 2 2 2 2 what you gonna do what you gonna do oh he goes for it oh good still 421 not bad not bad we go for 2 hits kill him take him out if we're a cool zoomekid we can go yeet hahaha dude Tyrannosaurus Rex what you gonna do buddy well I'm gonna hit you with my tail and oh no I'm gonna kick you out don't mind there you go you're dead king of the dinosaurs is a tyrant dinosaur take it oh look at that ooh we got 4 extra cups there that takes us to silver woah 717 I mean I'm doing this not too long afterwards uh after it's clocked over so who knows oh if I get a pack if I get a pack dammit I don't know I think it's it just teases you it teases you with the fact that you the prize wheel because as soon as you click that your prize is generated and remember when I made a video I was streaming it exactly and then noticing that the prize was switched out that's that's the level of detail we went here on the gaming beaver channel hahaha oh dear uh also I just want to say a big thank you to everyone who is watching these videos um I mean it could be the quarantine that's helping these videos perform better um but they're doing really well and hey if that's what you guys want to see I'm happy to do it for you I'll play this game right up until I die hahaha actually I won't be able to because in 5 years time or something along those lines Lydia's going to discontinue it just like they did Jurassic Park probably I mean uh maybe the thing is right Jurassic Park builder was so old and so outdated that I don't I was going to say can I get it again again we could get 1500 dna but uh oh hold on let's get the prize oh oh no no it wasn't or did I get it no we need to open up three packs well well well well use three different classes creatures and three classes do three trades huh no spend food and collect three mods well tell you what let's do that let's just go on the food and 40000 there you go that's the mission to spend the food and or maybe if we've got a pack we've already done that ooh close is it this one I don't mind I don't mind spinning this wheel in fact actually I shouldn't have spent any more food but nothing's spoken really when you think about it increase HP by 20% and that's another mission because we owe it three mods or four mods I think it's only three mods and there we go that's that done right there we go two missions complete look at that BUM BUM BUM so we've got God it must be weird listening to me isn't it well you've got used to it this long um we got two more packs to open we could do three trades um senizoic and the aquatic was really is just 10 bucks to do that and we get what 120 so we got 110 bucks we're doing that but we'll keep on going we've also got to fight the fusion to get that micro sdna pack so we should probably do that as well claiming territory is nooo because it's quite hard shape the earth we'll do this one I mean the tactic is to just go for like three tijongas replace the middle one and then put in a good creature like that and therefore you can go for a reserve right off the bat they will waste two hits killing it because two hits can kill me because it's a tijongasaurus oh god that is the worst even the world to face up against we've lost you know what we've lost I'm just closing it I'm close that now lost would you I guess I went to the ranks so quick I didn't realize what opponents who were facing that was done that was what he could have done actually is save myself some books I think and closed out before it loaded into the battle because otherwise they got used so there you go do that and then wha maybe we don't switch all the way down to those crazy levels and we use a conoraptor let's see I think that was unlucky that was a really tough team but let's see let's see what we face up against yeah it was a really tough team so we definitely want this one one it kills pro ceratosaurus you would dress it well the live not too long ago you darted a lot of you even though I don't need you but you're only available in what incubators and uh limited events so might as well dart it there we go lost little old dodgy there but in comes conoraptor conoraptus so yeah if you do want to I mean we need to win this tournament because there's a chance very high chance that this creature that pleases us is going to have a hybrid um so if you just do this right away do the battles as soon as you can get as high as you can and just maintain it because you don't want to leave it to the last minute because I think I've done a video on how long it takes leaving it to the last minute and it cost so much bucks and so much time I think it's a good couple of hours it takes to do it uh to go from zero to hero to the top uh domination lead dominated lead you're going to die untuck the pelter although you might oh yeah cheeky bug 200 damage well then I'm going to go for six is that a jump or a bite oh it's a bite um no there you go so that should take us actually I don't even know where we are where are we oh 26 cubs there oh getting close to the top of hunter you see so this is the tactic because this way you guarantee damn it getting the I mean I need a pack um you guarantee getting uh as many cups as you can whilst at the same time um you need something good how about that that'll do I mean if we win this this is a possibility of 40 cups it depends what we're up against if it's all flyers were doomed uh not bad ooh what do you think I'm going to say 28 cups this time 28 cups because really you want to do as few battles as possible because you don't want to waste bucks because each time you enter it's five bucks and books don't grow in trees now do they especially seeing in this climate ludea changing it and taking all the books out of packs and out of events and yeah and everything else eops it's pretty good we can definitely kill that in two hits that leaves one to reserve and then they'll probably switch out because uh second on the source will have a weakness to me and we might I don't know if you're the killer one it will we ooh it's close but he has terrible look at that attack awful you're going to switch just do it get it over with yep dino swap and then it'll attack right away look at that that's how you know that bots because if I switch I have to wait a little bit and then choose what to do but as soon as they switch they're done like they either block or attack they go is done and over with but uh for a normal person like you'll never see them swap in a creature and then take time to think about what they're going to do they swap in the creature and then instantly done and that's how you know they're not real people so I don't even know if they call it PVP do they still call it PVP I'll check because that's a lie I wonder if they could be sued for that like false advertising because that I mean there was a time back in 2015 I remember there was loads of app games coming out saying that they could do PVP and all this stuff and oh wow 34 comes we got for that whoa take this straight into that was good um let's have a look does it say PVP in the tournament I wonder oh no so close is it predator league I mean look at that JW 11421 I mean does it ever change does it ever actually show people's pictures and stuff I mean it does because we've seen their pictures and their names but all they randomly generate what's this legendary twins oh cool okay let's see the prizes ah aquatic twins legendary so for the aquatic you get your own oh that's awesome I like that I like the helicopter that looks great oh that's nice that's nice I like it oh there you go so there's pictures and names I wonder if they run them because technically as well I remember doing a video for an app game and they wanted me to blur out everybody's names and pictures for privacy because I mean maybe they didn't have the permission to use it so I wonder but yeah PVP this is supposed to be player versus play it says PVP it ain't PVP Lydia um so I mean I don't know is that legal I don't know I don't know I mean why would I sue them I've got nothing to gain so it ain't gonna be me it ain't gonna be me uh should we use ah because we're in like the top 5% now we've got to use like lefonax or something we've got to I would also like some tournaments that aren't just you know land dinosaurs we used to have a mixture we used to have aquatic we used to have 10% of zoic tournaments and they were so much nicer because to get if you did what I'm doing and did it straight away you'd get to the top of the league in like 10 battles or not even that within one battle you were in the gold or something I don't know what that was you could probably go through the playlist and find that tournament but it was super short this video would be done by now so you went for two hits one and two reserves and the others are herbivores which means they're definitely dead 160 attack 178 attack and that's nerfed look at you a common hybrid better than sucomymus level 20 shows how pathetic sucomymus is isn't it oh how good this dinosaur is we'll go for 3 in case you block for 2 and then you have 152 where you are a legendary hybrid I suppose so common hybrids are as good as a legendary well common hybrids level 40 good as a legendary hybrid level 10 makes sense uh well you're dead you only had 4 so we'll go for 5 and 1 reserve for the yolo points I like the way this guy looks he looks awesome it's a shame he's not a senator's oak I'd love to mix it up like that have this guy taking on a mammoth they look so good dammit why can't you do that okay should I do it should I just like photoshop the thumbnails should I just have like a gorgasuchus like as if we're fighting it in the water and then just have like photoshop a t-rex in there or something there could be so many cool things you could do in this game but you can't because this game doesn't let you remember when it was a glitch we could fight land creatures underwater that was cool I like that that was awesome can't do that anymore don't know why but just can't let's get ready the other video to upload now I don't know if this will go up today because reasons yeah it's not gonna go up today so sorry it should have been to but it ain't let's go oh it's an indominus rex gen 2 ooh if that is a real dude that's which it isn't that is really hard to get unless you board it in a pack if you fuse it damn if you fuse it can you just buy it outright you probably can't you're not you're not supposed to be here right well there you go that's an easy win like to see a level 40 though level 40 though oh he switches ooh that's why because it has 500 attack oh it goes for that's a lot of damage well you're dead in two hits so one two and then I mean I don't think Sparantank could kill me three I could be wrong ooh 200 two four six we're good we're good if you had four might have been able to kill us with three's three's not a kill right there we go whoa come on we right we are owed like 40 cups from this that was super hard like if you compare the stats of each dinosaur two tishongasauruses just averaging down we should get loads for that what do we get 40 oh 37 close very close we're almost there almost there almost there gonna be term number one percent right come on come on oh 10 bucks I suppose that reimburses me for two entries ooh 10% off the market on Cenozoics ooh tempting tempting um let's go for our acocatosaurus you're kind of safe going for a carnival chances are they're not gonna have a full team of amphibians I say that just you wait no there's one in there though and that is a soup that's a that's a super hot team thank god that there are two herbivores in there though and that the amphibians last meaning that he will have to waste a turn switching it out and then hopefully we can just I mean we're gonna take two we're gonna have to take two to kill and talk to leaving us with one reserve then he'll switch out having one attack and hopefully he does go for that Cenozoics won it oh that is lucky 15 extra wow okay that that's very lucky and that amphibian I know for a fact doesn't have high attack now he'll switch and hopefully he goes from an attack we're hoping because that'll take us to like 500 so from 1,700 damage to 500 watch you switch it switch it and watch you won't you'll just go for it straight away look there you go didn't have any time to think about what he was gonna do just did it again another reason that their boss but at this point if you've been watching my videos for this long I think you know that they're not real people oh this one's a tough team man this has to be 40 this has to be the 40 cups I had to go for one block I had to I would die otherwise I can't take three hits I'm in dire straits here guys oh I'm in dire straits luckily I have Tijongasaurus to fodder itself off three he's gonna have six and he's gonna go for four oh he's got five he's gonna go for four because um his bob attack oh kills me 808 four oh wait what okay I could have blocked for three alright so he's got two block and we kill him in two and we have seven whacked him on the chin man so one two you're dead factor in the two that you've got you're dead and then you know might as well and there it is acrocanthosaurus takes us to dominator leak and gives us a lot of super DNA and in fact we can make another I root oh what the 40 cups you kidding me oh so close like um there you go top 96 what's the highest 300 400 492 dominator league reached will we get it because when you're in dominate league you have a higher chance of landing on that pack you're getting better prizes but we're not gonna do it I could I could stay here for 24 hours straight and not get it I've done that in the past so what are we oh look at all 10 20 40 55 extra DNA there so are we good we're almost got another mono stegotops and we have enough for another Indoraptor I think yeah 2000 so we could if we wanted to but let's see if we can get some more micro sdna here um you know what I'm just gonna go for those like Indoraptors all you need man all you need right I don't even kill me here I don't think so we goes for it okay okay that's fine in fact actually you know what's on it I'll just go for three reserves because I've got three Indoraptors and if I had only one level 40 wouldn't be able to do this make sense right listen to be very nose papa be with those bears yeah she knows right I think he's got one block he has all a lot of health as well like I think he had one block oh he didn't oh good whoop or if he did he went for a reserve instead please don't have a reserve oh thank god he's gonna kill me whoo okay uh reserves four reserves go for four please oh go for five go for five that'd be great oh we oh okay uh tell you what let's do that then let's do that right he should go for seven he should go for seven five six I knew it ah the right amount okay so he's got one block he's got one block but we have eight okay so one two three factor in that one and then we gotta go for four block because even if he if he goes for a reserve he's got five and I'm pretty sure we can die into it so we gotta go for four block right okay uh how much health does that guy have oh eleven thousand whoa you have to go for four you just have please do it oh that's lucky that's lucky that's really lucky what I didn't even know if we killed it in three it was very close very close four was a definite kill though okay there we go that is for one of the three battles the next one is actually oh that's a lot harder because that's an amphibian meaning I can't just go all carnival right what do we do here guys what do we do we I tell you what we do we'll go for a logemus and then he'll switch into gorgosuchus so we need a good flyer a metrophodon actually no because then metrophodon will be killed by argytinosaurus nope nope it's fine it's fine that'll be fine and then you don't because that has loads of attack yeah there we go top tier team alright let's go for one reserve right off the bat shall we look at that what does it have a 500 attack for an argytinosaurus what do they cook up in that lab is it gonna go for one yeah there we go okay we'll have one I'm pretty sure we'll have one this so I'm just gonna go for three reserve because sod it why not metrophodon is gonna kill us thing really quick oh you buggy he's got one block okay but you die in two hits and we've got six so that's three and you know what I'll just go for three reserves there you go beautiful so I don't even kill me outright no we can't we might not I could have went for three block I could have but I didn't oh that is lucky either zero hits or one hit I would have been happy with so right so he had three three and he hit me with one so he's got two block one two three four he's dead factor in two and then one reserve there you go boom done it bam right so he's gonna go for what he's gonna go for two he's definitely gonna go for two out of his five leaving them with three block now I can't kill him in two I can't kill him in two he's gonna have three he could have three reserves one two I'm gonna have to do that that's a safe play yep I thought he would but I just to be safe we did go for three reserves whoo and there it is now I feel like there's an algorithm to this I feel like if there's if I've made it to that last creature they go all out attack so as long as you played safe you're kind of okay so you don't there you go takes the cake you made it my top ten even before you were released and finally it's an all out carnival team Indoraptor early for source Indoraptor let's go right one reserve right of the bat this is a crazy team we're facing up against and look at that Metrophodon level 28 just to put it in perspective for you okay um I'm gonna go for three reserves because you still can't kill me level 20 Indoraptor is better than level 10 but really still not worth it uh one two oh I could have killed it factoring one just in case I could have packed it in two but yep I'm gonna risk it and it paid off whoo he has a lot of attack uh one two two will not kill me I don't think but he might go Michael no he doesn't oh my god we didn't even need that other Indoraptor I'm gonna go for three just in case and he went for two bucks so hey playing it safe and finally what you gonna do one two two he's gonna go for four out of his six to kill me and that's it I didn't even need Indoraptor Gen 2 again sorry Indoraptor level 20 again would really love it if dinosaurs that weren't used could be used again would be great I get it for mods but for regular battles there that's probably what we get ooh ooh a lot of Capricutius DNA I mean fair enough I suppose I'll take it that's another pack added to the list of the things that still need to open close how about we do the battle stage infinite ooh oh and it's a good one oh it's a good one let's do it all carnivores Raja Stega yes and in this place oh it looks great I love this battle arena it's awesome we're doing all of this stuff we're doing all the things guys we got to the top of the tournament we've completed the other thing the super DNA and we're now doing these events he went for one attack didn't he okay might as well go for one block what you gonna do what you gonna do nothing that's right nothing uh one two and then factor in one just in case cause you did go for one attack and BAM takes it out and Soprano Titan is worrying that 5000 attack is crazy numbers oh it goes for three I think that's all he had he might have one extra may have he may have one extra 14,000 attack I mean hell okay so one two oh lord you know what that'll do that'll do oh he's dead thank god did he have one reserve or was that just me I've got 18,000 health though look how big this guy is he's huge whoa 7,000 he's got 20,000 health I didn't I've just seen that 20,000 for the telecommies I can't take it on a legendary hybrids okay oh god oh I'm gonna get my butt handed to us okay what might as well just go all out 8 this has got a killer surely six BAM 18,000 extra whew dough mess do not mess that's a hundred and a common pack which gives us another 50 bucks a guan long and as well as some loyalty points what's the next one another common damn but we got another 35 books for doing that one now we need to just do some quick um aquatic battles I'd rather do one without mods we will use one two three a really low level creatures and put in something that is pretty decent and hopefully that'll average out to something that are three things that are quite terrible hopefully uh no actually um something that's good against me oh that is horrendous oh this is a horrible team we definitely lost what we do oh also I need to have three things of different types I've just wasted this I'm gonna get nothing out of this I'm literally okay I'm just gonna close the game I'm gonna get nothing out of that like literally nothing I'm not gonna complete the mission and I ain't gonna win might as well not waste my time and yours because it's a little bit more valuable and just not even like follow that through because that was awful so we'll go into this again go all the way into the bottom and then one two and a three and there you go three different types so I've wasted five bucks but hey we're still gonna get a hundred and five I think profit out of this of course of course they're like one level higher proto stager hmm okay okay go on then hit me hit me you know you want to you know you want to oh oh okay that's fine that's fine maybe able to kill me yes can't kill me in two hits but I'm gonna go for two resets Dacrosaurus is actually my MVP here but he's last unfortunately hopefully I can take out the other oncopristies on his team I just realized this oncopristies does like the that drastic park when he puts his mouth closed yep not gonna waste any attacks because I only do 12 just kill me kill me already nose like having a nose like this yay sweet embrace of death dolly on chops okay so one two and then factor one extra and then three there you go kill him dolly yes and we got the advantage so he might even switch we're gonna win maybe the bases the other team on what your best dinosaur is maybe oh two attacks okay interesting why even bother doing that the thing is with these live battles or quote-unquote pvp battles you can't just speed the battles up you have to slowly watch the animation oh yeah and it's dead as well brings in our his own left to client is okay left is serious sounds more about it sounds better I like it look at his Goku picture going ultra instinct still have a watch that actually Dragon Ball Super I should I should do I'm just gonna go for all out six oh is that enough I don't think so oh oh it's like 15 what's it gonna do one two three it might have to go for four either way we still kill them one hit why is he thinking about it I you're gonna go for three or four you're and you're a bot don't pretend to think that in one minute be was playing but the heck complain they don't think next moment doesn't care there you go just go for four oh god what do we win from this that's the question what do we win and he flies away right go on novice prize why is it novice is it because I didn't put in really good creatures well you know that'll do close that one and finally a random battle so we need to go into Glacius and a Zoic go for the lowest and that one that one oh yes that one and deodoris and there we go that is 110 or 105 books and all we now need to do to get that extra pack is do three trades okay right type matchups don't exist in this battle all right then the son is oh it versus the mess is oh it who would win kind of evenly matched here three hits to kill each of us oh he might be he might go for it he might go for it don't okay that's fine well if we're just going to play like that I'll go for all these reserves six are attacking numbers he might go for it oh five that's good though I'm happy with that yes that's right and then kyla sword would definitely go for just gnomes and not walk with it still so one two three kills it factor in one extra and then three reserves and hey do you know therium or a rafter it's some Jurassic world dominion stuff this pretend it's a normal elephant it's going to have to go for three to kill me oh is you're going to do it oh he doesn't well I'm going to go for one two three factor in two and then two reserves oh we got him wow rocks bang crushed it's hollow framed and stand a chance against the mighty force of a rock slide so one two three four five he's going to go for five out of his eight leaving them with three block and then it depends can we kill him in three because if we kill him in three he's dead he's only got three block yep there it is oh no yeah uh four eight one hundred and twenty yeah we got it we got it it would be one hundred and thirty two but one hundred and eighty five there you go and he's got three block perfect yeah and that is how it is done that's how you complete literally everything in one video uh well actually we need to do the trades which is probably going to cost us oh yay food okay so we'll collect those so that is a hundred and twenty bucks there and now to do three trades oh god no uh I guess one um uh not that one god no oh no not that one oh no not that one oh no not that one oh no what are you getting rid of that I literally just got to trade VIP points for an ankle of darkness uh actually I could refresh for fifty bucks do you think it's worth it fifty bucks no I don't want to lose bucks though I mean I never used that so I might as well trade that it's a wasted food but hey there you go and then oh god oh no uh should we just trade one thousand VIP points uh why not and there you go that is it three trades done boom some extra food which we don't need and corn we don't need but we get this and I'm not going to fall for that I'm going to open this one is it worth it one thousand VIP points probably not because that's like two legendary packs um and we got fifty five bucks so technically if I had spent fifty bucks and got some easy trades I would have made a profit of five bucks instead of losing a thousand VIP points oh well never mind we got some back well guys there you have it hope you enjoyed this video and until next time I'll see you later oh bye bye


Namaste, my name is Craig, I'm from the University of India, Canada, but I'm still an Indian. That's why I'm still an Englishman. I started living here in India in 1978. I'm going to talk for about five minutes on a little bit of introductory stuff, my scaling background, and a little bit about large-scale scrums framework one and two, and the majority of what I'm going to share will be about the competitive contract game and component teams, two aspects of scaling I'd like you to understand more about. Let's start with a little bit about scaling background. Years ago I wrote this book and it helped introduce Agile to the world, along with a lot of other people who helped introduce it. And one of the statements, incorrect statements at the time when books like this were published years ago was that Agile and Scrum are for small groups, but they can't work in the large. And I knew that was not true, and I wanted to focus in the area of large, multi-site, and offshore application of large-scale Scrum. And so I started on this journey of focusing on really large-scale product development with large-scale Scrum. For example, in 2004 I was invited to act as the lead coach of lean development at Xerox where I worked for several years, although what I know about lean thinking is just a very small fraction compared to the insight of people like Mary and Tom Poppendijk. But nevertheless, they're involving the creation of these digital presses, which might involve 500 to 1500 people, software, mechanical, optical, engineering. And these will involve tens of millions of lines of code, thousands of moving parts. And we apply lean thinking principles and aspects of Scrum to creating these. I serve as Chief Scientist of a company called Valtek, and we have an offshore delivery division here in Bengaluru. And starting in 2006 I started to live here in Khoramangala, and with my colleagues at Valtek, India helped to evolve agile offshore development in the application of large-scale Scrum along with other companies here, such as ThoughtWorks and so forth. This is a picture of Valtek, India. And starting in 2005 I started to be invited to work with large telecommunications infrastructure network equipment providers such as Siemens Networks, NSN, Ericsson, and so forth, and then also large-scale investment banking groups. So basically large hardware software systems and large financial systems.


Hi everyone, Joe for jaspyscasebreaks.com. We've got Cardinals, Broncos, Jags, Chiefs, number block randomized for flawless, and then that break itself will be in a separate video. That's how it works if you're new to this. Big thanks to these folks for getting into the Cardinals, Broncos, blah, blah, blah, number block. Let's roll it. Let's randomize it six into two eight times. One, two, three, four, six, seven, eight. It's a great moment too. Eight times Ray Phillips, Joel. Eight times four numbers, and eight. After eight times, we've got seven down to four. Seven down to four, Ray down to Joel. There we go, making sure I got all that. All right, so Ray with seven, Michael with two, Aaron with one, Danny with zero, Ray with five and three, Aaron with eight, Brian with nine, Danny with six, Joel with four. Let's order these numerically. And there you go, ladies and gentlemen, the break itself will be in a separate video, so look out for that. Jasper's Case Breaks.com, bye.