Hello everybody and welcome to video number 35 of the online version of the fusion research lecture We are on chapter 6 turbulent transport and you might remember that in the last video we talked about Actually, we talked about the turbulent transport and in this video We will talk about turbulence measurements as this is a very important topic in fusion so turbulence Turbulence measurements Is the topic of this video turbulence measurement? Measurement and this is actually a field of active research this is a field of active or very active research and Just to give a bit of an historical introduction we come to the picture on the right in a minute the first proper turbulence measurements were conducted not before the 1980s really rather late. So the first proper turbulence Measurements Oops Measurements Sorry measurements We're performed in the 1980s in In small talker mugs and what was found was basically a broadband turbulence spectra So a broad band Turbulence spectra was found meaning that we have Components with different size over a large range of sizes being present in a plasma and It was also clear then that the turbulence was responsible for the observed transport so turbulence is responsible for the observed transport and The picture on the right-hand side actually is is a spectra of Turbulent density and potential fluctuation. This is a spectra measured in the TJK Stelerator and you can here nicely see in the spectra how the Turr how the dual how a dual cascade is found. So what was basically what I said Will is going to happen for a two-dimensional turbulent system that we have a dual cascade that we have here the Inverse energy cascade here and that here we have the direct endstrophy cascade with with different Slopes This is actually a measurement. So this was found. This was measured with lung reprobes in the in the TJK Stelerator and low-temperature Stelerator So this is a nice Example where the experiment a nice example for a low-temperature device being able to Reproduce what was predicted by by the theoretical expectations The density fluctuations coming back to the measurements the density fluctuations are up to a few 10% So the density variations They are up to It can be even up to a few 10% at the plasma boundary Up to a few percent more on the plasma center So it really depends where you are but the density the amplitude of the variations can be really large and You might have seen that already in the picture the Boltzmann relation is fulfilled. So the Boltzmann relation is fulfilled and the Boltzmann relation basically says that the Density the normalized density variations is approximately given approximately equal to the normalized potential variation And this is what is also called that there is an adiabatic response So this is I'm also called Adiabatic response Okay, another example or another important result is and We already had that in I think it was the last video that the amplitude of the density fluctuations scale basically with the gradient of the plasma, which is not surprising and the size of the Density structure the size of the vortices where ln here is The inverse gradient length over and not and This corresponds To the so-called mixing length model. So this is corresponding to the mixing length Model and the universality of that law so that the Fluctuation amplitude scales inversely with the gradient This is shown in the graph on the right-hand side where you can see here the amplitude of the density variations Fluctuations as a function of the inverse structure size of the product of the size of the structures times the inverse density gradient length, sorry And you can see how there is a number of variety of experiments being arrived and being Arranged around that line of a slope one here We have Stellarators and tokamaks there. So this really and and spending like three orders of magnitude. So this is really Universal law So in addition it was found that turbulent structures are strongly elongated along the magnetic field line So it was found that turbulent Structures are strongly elongated along the magnetic field This was found or can be made visible for example when you Make a gas a gas puff at the edge and then look at the Resighting H alpha emission that is a typical experiment for that So looking a gas puff at the edge and then looking at the H alpha emission What does that mean? This means that the perpendicular structure size is usually on the order of centimeters Whereas the parallel structure size is usually on the order of meters. That's so strongly elongated along the magnetic field line Now a very useful tool for turbulence measurements are Langmuir probes But Langmuir probes can only be used in low-temperature devices. So Langmuir probes can only be used in low temperature devices or When or when you take extremely care only in the very edge of hot fusion plasmas when you like have very fast reciprocating reciprocating probes that might also be possible in principle only in low-temperature devices And this is why these low-temperature devices are often which these these are also often referred to as wind tunnel experiments Wind tunnel experiments where you have a reduced set of plasma parameters Reduced set of plasma Parameters for example the density being reduced by a factor of hundred and by reduced I mean as compared to a fusion to an actual fusion plasma the temperature Being reduced by a factor of ten where the factor of ten here refers to the edge of the fusion plasma Come so yeah to the edge of the fusion plasma the magnetic field Being reduced by a factor of 30 or something like that Despite the reduced the set of plasma parameters. There are some similar dimensionless parameters. So there are some similar Dimension less parameters and These are for example the the plasma beta which can be approximated The dimensionless parameter by n times the temperatures of the plasma pressure over the square magnetic field and also the New which is here given by the density over the temperature to the power of three half Then the characteristic scales these are usually somewhat larger So the character characteristic or some characteristic scales Are often somewhat larger and An important characteristic here to describe the turbulence is row s row s Which is the sound speed Well the sound speed CS Over the iron cyclotron frequency Corresponding approximately to the electron temperature or the square root of the electron temperature over the magnetic field Defining roughly the size of the turbulent structures And The advantage of Langmuir probes is that they offer very good spatial and temporal resolution So this is the big advantage of Langmuir probes. So Langmuir probes offer very good spatial and Temporal resolution Which is good from an experimentalist point of view and is also good if you want to compare something with codes compare with codes Because then you can use Basically these kind of tabletop experiments to benchmark your numerical codes Which you can then use to make more solid predictions or descriptions for an actual fusion device An example for Langmuir probes here are Langmuir probe arrays in the cell radar TJK again the example Here are Langmuir probes and these are actually Langmuir probe arrays so Langmuir probe Arrays in the cell radar TJK located in Stuttgart And then the left hand side you can see these these here are the probe tips and The probe tips are arranged on one flux surface with a spatial resolution here of approximately 0.7 centimeters and Here you have them arranged in a matrix basically in a matrix order with a spatial resolution of one centimeter and As you might know Langmuir probes. These are just electrostatic tips So here as it's written here tungsten tips your tungsten tips then ceramic tubes and At TJK there is a data acquisition system for example used Which allows to acquire 128 channels so 128 probes simultaneously with a bit of a resolution of 16 bit and Sampling rate of 1 megahertz so microsecond time resolution So that is the sampling rate and that is a very nice system to describe turbulence both in good temporal and spatial resolutions In such probe arrays allow to measure the polo structure of transport for example so such Probe Rays allow For example to measure poloidal structure of transport Loyal structure of transport and you can see here a drawing so in The center. This is a poloidal cross section. This is a poloidal cross section of a plasma here. You can see the vessel wall and You might remember from the interchange instability as depicted in these two drawings on the right and on the left hand side that the interchange in stability Gets unstable on the low field side and is stabilized on the high field side Meaning if we put such a probe array To to this cross section Then we should be able to see this kind of asymmetry meaning that we would expect more Transport on the low-field side than on the high-field side. This is actually what we see here So here you can see the transport as a function of the poloidal angle Where we have here the low-field side where the maximum is located then here the high-field side where the minimum are located Meaning that this nicely shows that the transport is higher on the low-field side so this nicely shows that the transport is higher on the low Field side So this is a very nice experiment Okay, now how is The measurement of plasma density turbulence actually performed in fusion experiment, so the plasma density variation measurement in Fusion experiments we have for example beam emission spectroscopy Yeah, for example beam emission back trust Kopee in Beam emission spectroscopy We inject neutrals and then measure the light emitted from these and neutrals and The intensity variation then reflect the local density Fluctuation strengths. Okay, so you inject some kind of neutrals measure the light emitted by them and measure them very Precisely such that you can deduce from the intensity variation something to the local density fluctuation Then we have reflectometry reflectometry You might know standard reflectometry Which you can use to measure the profile of your plasma density, but when you have a Doppler reflectometry You actually measure the back scattered microwave the microwave which is back scattered on density variation And if this is Doppler shifted then from this Doppler shift you can reconstruct From measuring the K component the density fluctuation. So it's basically Doppler reflectometry Then there is also laser scattering laser scattering so measuring The light being scattered by small scale density variation and due to the short wavelengths of the laser This is more sensitive to very small density structures So these are just a few examples and a very important comment is also to be aware of that magnetic so far We talked about electrostatic turbulence and magnetic field Fluctuations has been measured so it is possible to measure that but No clear evidence has been found that this contributes significantly to the overall transport So the magnetic field magnetic field variation of fluctuation has been measured, but there is no clear Evidence that They Contribute significantly Significantly to the overall to the global transport Okay, that's it for this video which was a brief overview about turbulence measurement Remember, this is a field of active research. I showed you an example for a dual cascade Actually measured in a teacher case accelerator We talked about the strength of the density variation the density fluctuation Being up to a few 10 percent at the plasma boundary Then I briefly talked about the mixing length model where the density which says that the density fluctuation amplitude scales with a size of the Density structures over the size of the vortices and inversely with the size of the gradient which is quite of expected and That turbulent structures are strongly elongated along magnetic field line and that longer probes can be very useful But only be used to low-temperature devices and fusion you have to use as outlined here on this slide for example Be mission spectroscopy Doppler reflectometry or laser scattering and that magnetic field variations of fluctuations have been measured But there's no key evidence that they contribute significantly to the overall transport Okay, that's it for this video. Hope to see you the next video


Funnest stone. Funnest C-Thor. Robito. Hey, hey, what is all this?  Yeah, we about to be. My boy thang. My boy thang. Don't go give him a boy thang. The best thing that I ever had. Next time I get the nastiest black-and-mild flavor they have. Ask them did I ask for it. Say it wasn't new, it wasn't nasty. Yeah, you want to stop. And get them too. They got one that tastes like elbow skin. Give them that one. Get them two of them. Give them two elbow skin black. We get the black licorice black-and-mild. The black jelly beans.  Y'all ain't got no pineapple wood chips? Oh, man. Y'all out of raisins?  Peel pressure. Nah, it ain't peel pressure. I don't want to reach you, man. Give me more. Hey, man, put some chips down.  Hey, man, y'all don't understand what just happened off in here, man. Shit, give them really, really nice feels. I'm glad that people feel they can kick it that way here. They can. Does that make sense? Yeah. Yeah. I mean, it's the trap. It is. Yeah, and it's actually the quite the opposite, man, because we ain't trapping nobody, really. No. No, we're entertainment trapping at this point. We're trapping this media. I see what you did, man. We're trapping out this content. Content trapping. Yeah. It's constructed like a Rube Goldberg machine. Yeah.  That was dope, man.  You saw that? You saw that? I saw your eyebrows jump from up under your shades. Yeah. Because eyebrows was up under your shades, and then they went, zoinks. Jumped up. Hey, Clayton, man, look.  I got motherfucking Rideau Brown in here. Come on, Rideau. Come on, Rideau. Come on, Rideau. This is my partner, man. No, see, what people don't understand is this really my partner, this is our partner.  And it's like, he ain't on this side of the world very often. Wouldn't he do? He do be working. He's from this coast, but he own it. You know, I would check in with him out there just for some grounds at some time. Yeah. You know what I'm saying? He put his hands in a lot of things, too, right? He's busy, man. But now I'm being out here in Atlanta, dawg.  I was talking to Rodney Perry today. He's like, yeah, you go to L.A. and people out there chasing their dream where there's niggas in Atlanta. That's like, nah, this is it. We living out as already. Yeah, we already living out dream.  We down here in Atlanta living out. I don't know what your dream was, but Magic City open at 7. I don't know what you mean.    Yeah, L.A. definitely is the place, you know, that's where the dreams are, dawg. At some point, you got to go out there and see what they talking about.   You don't see the dead dream. They're still acting for the last role she didn't get. You ever say the spirit of the dream? Yeah, this is even worse.   I was supposed to be Catwoman, you know what I mean? She just keep telling me. I was this close to being Jack Sparrow.  I swear the road was supposed to be mine. The Raven never sleeps. You just get the rolling out. The first part is, they were probably in a pop-up... Well, that's movie back in the day. I was in Portugai 7. I was there. There was no pumpkin here.  Do you know who I am? Do you know who I am?  Victim number 47 in a slush of him. You know me as Joe the policeman. You know what's going down, episode. That's my mama. Don't you recognize me? Rio, what's been up with the content, man? Man, just getting back into it, having fun. What you mean back into it? How is the pandemic? I think that's what it was. I think when the pandemic hit, a lot of people started putting out content. So it really, it made the playing field to the point where it's like, all right, you can really just tick tock. You can get a million followers on Instagram red. How'd it go?  You go viral?  If they go up with that thug, it's gone.  And they're going to loop it. And I'm gone on tick tock. It's weird, bro.  They be posting a lot of shit about me that they got, well, I don't know how to put it. What you mean? I love me that go viral on tick tock.  Nobody wanted it. So I think they like my content. Just when other people post it.  Yeah, I like it. Because I'll just be scrolling.  I don't have a tick tock page. I'll go and look at that. Just to see what's going on. I try to make sure there's a fake page out there of mine on tick tock. That's your burning page.  Yeah, I follow all the pages that post my clips.  No, it says Redo Brown. He took your whole name. So you didn't bother. No, I don't use it, though. No, I got a page. I just don't have no content on it. I got a real... I guess you got to have a page if you want that, right? No, I just made a... I don't have a page and then I follow all the bad bitches on that.  I'm tired of them dancers, though. They like praise dancers. I wish I could watch them bitches on sound or something. I don't know. Oh, you can't turn the sound off? I don't know, it's real. Because you keep hearing the same thing over and over again. But once you hear the beginning, it's just like...   I don't even know the song. I just know the part. Corvette, Corvette. That nigga really said... That's it. He really said that. He said that. TikTok taught me one thing.   It's way more than I ever thought it was. Yeah, they definitely up there now. There are some minorities... I don't want to just say white ladies.  Okay. I was gonna say this. Some fattest asses. Expand it and realize that... It's demographic, it's way more demographic than I thought it was. It's global. It's global. They're in a race now. They used to never be in a race.  South Pacific.  Inuit.   She said she was just sitting there on the vikings. Guess what?  I seen a black girl from Africa with a blonde hand, blue eyes.  So hold on now. Poling white women from Louisiana.   Yes. To me. But that's just for my own cultural bias. Because I've seen black asses be great in places they would never pose to prosper at.  At a funeral. They were prospering church. I've seen many managers come out the front and stick them keys in the cash register at KFCs across this country to delete them orders. With that belt, up in the back. Taco Bell. All that delta. You ever went through the Atlanta airport at 7 o'clock in the morning?   That belt with that motherfucker on the last hole? Yeah. Yeah. But the waist part don't fit.     I promise.  Ain't that crazy? Bitch had on some mud jeans. Right. It's all in the belt. It's all in the belt. That presentation. That's all how you present.     Bitch, you was a zoologist. You was wearing khaki shorts all the time.  Creeps out here. They creeping out the ladies, man. They go too far. Yeah. Being creeps.  Not a tool. And this is the reason why though.  Right.  It just don't work like that. You not built like that, man. The way they start, too.  It's about to be heavy.  I feel like women would be more freaky if it wasn't for the creeps. Women want to be naked, believe it or not. She don't want everybody looking at her though. No, it's not the part about everybody looking. That's fine. It's the creeps.  Never mind. There's too many creeps. What do the creeps do when she came out with her nipples out? Man.     That fucks it up for everybody.  Why would you do that?  Who worse though? Is the nigga that say that worse? Or when the girl stop putting her titties up and the nigga go, ain't he worse than the creep nigga? Nah, because he could always leave.  Mmm. That's better than being on the underdog. Oh my goodness.  Fucked it up with everybody. You just supposed to look at it and keep going, right? You're not supposed to be weird though, like, hey, look at them, look at them, look at them nips. Look like they hitchhiking. But what if a woman is staring right now with her titties out and just sat down and started watching us? Could we do the whole show without saying anything about the titties? What if a tits new to us? No, we've seen a plethora of tits. I'm going to continually check on those tits that are out. I'm going to give them a second look. Just because I want to make sure nobody's being a creep. But see, that's the thing about me. I'm the type of dude where it's like, I'm like a bird watching when they come to the titties. I'd be like, don't start on the titties. No, no, don't start on the titties. The longer you stay still and quiet, the longer titties will be out. But if you start on them titties, the party is over. Don't look them in the area over. Don't look them in the area over. Don't, don't, don't. That'd be the way it would be.  That's the thing about it.  Women. Even if them titties was put up, it ain't got to be about no cleavage. We've seen nice titties in a sweater. That's the true test of a tittie. What they hitting on in a Christmas sweater? They're gingerbread, man. Come on. What's he doing? If your joy ain't stretched out. My humbug. I thought you were just saying, oh yeah. I choose juice. Come on, man. But that's the thing about it, though, man.   Huh? What did you say?  What make it beautiful?  I can't even tell you what look good to you.  I like them look potato toes. I don't even know what... They don't bend. They must not bend. They know what I'm talking about. Explain. With the toes in the foot? Man, when she put them... With the toes in the foot? Where the foot is in the toe? No, no, the foot is over the toe and the toe is in the foot. Man, I have to show you a picture of them. It's too hard to describe. You should be.  You like webbing. A lot of girls...   You like Webbergale.   I really judge it... I really look at that pinky toe nail to see what kind of condition it's in. That tell you what type of life she done had. I've seen a girl... She had no pinky toe nail but it was painted still on the toe part. The toe was painted. Every toe nail was painted then the pinky toe had no nail but it was still painted too. I've seen that. The floating... Technology has come so far though. They can put a false one on there. False toe nail? Why would you just wear a shoe all the time? Why would you put a false toe nail on it? You don't know what people have been through to be who they are. I would, yeah.  What's that? You said that. Oh shit's a fun man. I think people fell in love with them man because they feel like a lot of people are lying dog.  Every time we try to come out and do something positive they don't want to help.  Go to the website. 85apurl.com 85apurl.com Man put it on the screen. You know what I mean? There's a lot of you in it. A pearl.    Let me get a hat. What's up man take that off. When the 4X is going to be in. Where you from man? Y'all ain't got nothing for babies.  We all going to get some ones. Save it for your baby.  He going to want this. Me too man.  I wear it everyday. I like it. Shit soft man made out of hooded material. Even the pants. We got sweatpants made out of hooded material. Come on man.  You can watch this. It's the same.  We make it short. I had this hooded for the whole 5 years. Yeah I know. Look still bright. All the way. And niggas don't know how to wear clothes. Cause we have a good washing routine. We got black. We got red. We got blue.  White socks. Rolling trays. We got to keep doing these motherfuckers. I'm about to call LL Cool J. Right.  I don't know what they want me to do.  It's nice and thick. Why does that cost that much? We don't own no factory. We have to cut a deal.  Exactly.  It's imprinted on it.  You ain't got to worry about that. It's real. That's what I'm saying.    I had somebody say me a DM say hey man it's a 85 south show I'm talking up for y'all what you think.    Taking boot out my kids mouth. Right.  Okay it's Christmas time. We ain't gonna see the money tell April anyway.  I don't know what else to tell them. Yeah. I love getting those kind of stories man. Those are definitely the ones that I had the most fun with. What's some more of your favorites? My favorite one of all time got to be the one I just did with Money Bag and Katie just to sit with them and take a sketch like that that I would say is complicated you know what I mean.  But to go into that room and do a sketch that was four minutes long and to skate around that and to get everybody to be like nah this is actually funny like that's probably my favorite sketch of all time.  How long have I been sleeping? Oh man that was the old I was sitting down on the couch. Yeah.   Oh you don't gotta tell me. Me and Dave had sessions where you fall asleep in LA and wake up in this one o'clock and you gotta try to figure out if in and out still open. Come on man.  Different ethnicities have food that's open way later than I should be open. They don't even pull up the one o'clock. Where did you come from nigga? I thought this was a part of it.  I doubt this is a Mexican hamburger on the flame bread. Tortuga? I don't know bruh. I wanted two tortugas. They gave me a tortuga. They didn't give me a green guy. I didn't want a green guy.   But it do burn a little bit. It still burn a little bit. It had all the sauces out.  That should be good to the motherfucker though dawg. What about the hot shit?  Nah I don't trust that. The hot shit? Yeah. And you know what? This is the one thing I love about I don't want to say Mexican specifically but the Hispanic food trick.  Stay for you. While you waiting.  Alright man.  You know what? I got mangoes but they gave me some. People watched this show and then they sent me this thing. People watched this show and they sent me pictures of food and they be like let me cook for you and I be like what if you sent me pictures of food that I don't eat?   You don't even know my eating habits. Bull. Bro I'm the most picky eater What did the niggas send you? They don't matter.  If you want to impress me send me a grilled ham and cheese plain. This niggas childish when it comes to the menu. Oh yeah I'm the type of nigga I'll get high and I'll start.  Nah niggas this niggas will break down whatever dish. Nope. That's a hamburger take off the tomato the lettuce and the bud. Put the bud on the side equally for the same amount of motherfucker time.  Do you have a potato bud? I don't want it. I just want to see if you can eat it. No I don't eat onion bread. I want to pop it over there. Pop it over there. Let me get the shrimp and grits Okay pop it over there. What's your pop it over there? I got the shrimp and grits and I got the alligator bites. You know what my pop it over there. I take the alligator bites and I throw it in the shrimp and grits and mix it all together. You know what my pop it over there. That's amazing. It's swamp salad.  That's swamp salad. Hold on I'm about to tell you my pop it over there. Tell you my pop it over there. I don't have one. Give me your pop it over there. I don't have one.  No look. Home. It don't be... That's where it got. That's where I eat it. No the good thing about being a picky eater is I can literally get some food from anywhere. I just got to be a certain way.    Man I can tell you everything that happened to me. I don't want to hear this now. I've had something. I almost said I've eaten.  You ate it. I've ate it. And it made me regret it. This ain't for me. Like you did it the bowl? What the... What happened bro? What did you eat it?  Scrabble.  Look grandfather, I love you. But it's 8 or 9 degrees in the afternoon.  I'm just... I'm just not a bean. I'm not a bean person.  We'll eat it. Just try it and then it'll make me sick. It's 90 degrees. Eat these goddamn peas.  What you mean you don't like broccoli? Look this is the hottest summer. What are we doing? It's burning. I can't live here for a pot of simple. I was talking about I grew up around a lot of... I can't live here for an outer pot.   Nick, you ever ate boiled fish? What? Was it boiled when you bought it or did you have to boil it? How you boil fish? Exactly.  You never heard of boiled fish. No, I didn't know that was fish.  Baked is baked can be alright if it's done right.   Yeah.  Oh these don't taste the same as the mother onions. Bitch they onions.   I don't apologize for nothing because don't none of these motherfuckers have to feed me. I know what I like.    That's with the little skewer, with the shrimp, wrap, bacon. I'll just nigga turn to tell you when he in.  So I'm getting some type of the fettuccine Alfredo. I'm getting that too and then we going in like that.  I worked at Papa's restaurant. Papa got a lot of restaurants.  It was a sharp pain right here. And when you said that it triggered your phantom pain. You can't eat it no more. No, because one bad experience. One bad noodle. One bad noodle. Because I felt the exact pain the way it kicked in. Oh shit, that's what it was, it hurt me that time. Hold on. Comedy club? I think it was at the comedy club. That shouldn't count.  I'm real cautious about it.  The comedy club when you is small.  That's not fair.  Comedy club made you different people. Outside of the chicken wings you can always tell what the club is standing at. Based off how good the chicken quesadilla is. That's what you go off of? If it's a good chicken quesadilla it's a real classy joint. Shit, real talk you go to the kitchen and see who's all in there. Nah. I feel like you can't go wrong with the chicken tenders. No matter what club you at. Some of them shits don't be fried right. But I mean chicken tenders every night at some point. Bro, it's some comedy clubs out here that could be like four star steak houses. They got good steak and good burgers. I can't think of it right now. When your comedy club got good steak burgers, I feel like it's a classy joint. Yeah. As long as y'all got something that y'all do good, like amen, amen. If the motherfuckers at work they be like amen, get that goddamn prime. This is the one flaw that comedy clubs don't understand they doing. They don't have enough dessert options. And the ones that they do, they so underwhelming.   Like, I don't know what I'm lack to. But they give me that brownie with that ice cream on it with them sprinkles on it.  You don't home? Like research? Like my nigga every time we add dessert.  These niggas break a toilet. Ensuring purposes. Yo, take ice cream off the menu. Yo, why do we take ice cream off the menu?   All the stalls is taped up. You think it's a warm cookie? Give him a cookie and a skillet.   No ice cream?  Most of it. You picked it up and moved to LA. What was the first thing you saw that made me be like, what the fuck?  When I was in LA?  Man, when I first seen how early Tony Oskitz got up to work.   And that nigga was up at 6 o'clock in the morning.   I'm posting all these videos out for the week and then I'm gonna have my Instagram going. And I get that going at 9 o'clock because that's what's going on in the East Coast. And by the time it's 9 o'clock here, it'll be 12 o'clock there and the niggas is on lunch. And I can take a break here. And I just got the world jumping here in LA because it's 9 o'clock in the evening. And I'm like, y'all going back to bed, nigga. But being around that shit, I wasn't waking up at 12 o'clock no more. After being at his crib for a week, so I'm waking up at 11. Being at his crib, I'm not waking up to things like that. You got the whole extra hour. Extra hour. I'm just waking up a little early. It's steps, nigga. It's a little bit. Boy, you let me down that time. I ain't getting up at 12. Nah, I'm up. I'm dressed at 11. I see this nigga doing it. Waking up at 11 or dressed at 11.  You know he been up to the 6.    Hell, yeah. I learnt a lot from that. I learnt a lot just by you and you tell that story. Nah, bro, if I was still in Boston, I would be doing it different.  I learnt that from that nigga, you know what I'm saying? Tony Oskis is a real nigga. He always shares a platform with the people that surround him.   That's what it is, man. We just up in the studio vibing, man. This is one of them ones, man, when your dog pull up in the city and I was like, shit, let's get one in. Hey, man, man, Carl, what you think your future baby mama doing right now? My future baby mama is probably laying in the bed right now, trying to decide if she about to get up and pee right. She got to pee, but she can wait a little bit longer. She's waiting to pee? Right. And she's tired, but she want to get up and take a shower. Every time I see this nigga, we just do that. Ask that real-the-best question. What's your future baby mama doing right now? Right now? Yeah. She climbing off the balcony of her neighbor's porch that she left her keys at work. Right. Damn. What's your future baby mama doing? Called me. Oh. Damn. That one was too real. Is that close? Mm-hmm. See how y'all did that? I know. Damn. It's about that time, then. Congratulations to you. How y'all did that? Yeah. We spoke it up. Evil. Lurking. I know evil. Evil? All right. Evil. Evil. My future baby mama probably, probably somewhere right now saying she can't sleep with the fan on, but she just took the other blanket at her little board room on the other bed because she cold, but she gotta have that fan on. Box bag. Yeah. Future baby mama in the bed right now trying to figure out how she gonna finish this work for tomorrow while this nigga in the living room playing on the playstation. Sucking her waffa. My future baby mama is laying in her house by herself without no nigga. Telling herself she don't need a man for shit, but in the back of her mind she telling herself she want one. She thinks she's so independent, but little does she know. She plugged her phone charger in, but it came unplugged, so when she wake up her phone ain't gonna be charged.  It be loosened up.    Oh yeah. And she looking at baby pictures.  She masturbate to her own nudes. Damn. Yeah.  But if you ask about them she swear she ain't got none. She selfish. Whatever bro. I ain't got a whole lot of future baby mothers. I might got one or two left. That third one she really gonna be blessed cause I'm gonna be really done with life. You know what I'm saying? No I'm just saying. I feel like I feel like I'm old at least one more. I want an athlete though. Why? I don't know. I just want a child that's just an athlete. Your kids don't. I read that wrong. Oh no no no. I thought you wanted an athlete. I was like what you wanted. I want a kid that's an athlete. I mean I want a kid that just goes through sports. He's like no I just want to play football. You know how to do that right. Everybody you should just do it. Just do what? Just work them out while they sleep. Some kids just ain't built for it. No no when they sleep you just work them out. Kids have their own desires man. Really when they kick babies? Yeah. Kids they got their own desires man. You can't push them to do nothing. You don't want to do it. You just have to display the options to let them pick. Your son might be the next best lacrosse player they ever was.  Then it might not be your baby. Now this niggas just. It might not be your best. It don't matter if he's good or something. This is the whole wide range of sports. Hell yeah. I mean it don't mean he's going to get to be the best sports. Oh wait wait wait. This was about him. That was a little too personal. I'm sorry. You was real specific. What if he's only four or nine? I heard that. That came from a dark place. Nah man. I'm not that small. I didn't say you were. But he had a height. At some point. At some point. He's working out for the kid and he just ain't that tall. Nah. But still it doesn't matter. There's a lot of people that's all types of heights that do all type of shit. Yeah. Right. You gotta be like. Nothing can stop you from being great in this life.  Maybe that's that short. It's a sport now man. He could be a professional. Professional what? You guys keep saying professional. What? Games are there. Hey man. Michael Jordan said it best. The ceiling is the roof. There you go. That is 6'6 bro. Tell me something somebody under five feet said. Highlight. I don't know. Tell you something somebody under five feet said. Great job. Get in where you fit in. Who said that? A lot of people.  Get in where you fit in. Hey man. Yeah man. Nothing. No limits. There's limits. Bruce Lee said that. Come on man listen. If you want athlete. The kid got to choose to do it. You can show it to them. There's ways you can go. You know they say the way. You're supposed to do yoga. If you're an athlete. Whatever. They say soccer first? No. Soccer building endurance. There's a little toddler. There's soccer to get their endurance together. So these motherfuckers can run up and down.  And then from there. Once they get to like being like a little kid. Where you can actually then whatever they want. They got a good foundation. That's what they try to say. Right. That makes sense. Yeah. I mean if you're an athlete then it's easier though. You could just have enough kids to where you figure out which one is good at sports someday you have it. That's the short. Short cut. That's the short cut. Yeah. Make them challenge each other. No. Well I mean Michael Jordan was an athlete. And his sons didn't do the same thing. That's because they didn't live up to your height. Don't do them like that.   No bro. They was training with sports. They have more important things. The people was training with their daddy shoes on. How you gonna get good with your daddy shoes on though?  That's not even that good. They're not even the right kind of shoes for you to be hooping. That's how you get good. You get good and adversity nigga. You don't know what basketball did to that family at the house. It might be a back story that you're not ready to hear. Basketball destroyed my family okay? Talk about it. You want me to dunk?   We're in your laps Martin. We're in your laps Martin. Get dinner with us. Every box in my house. All in here in the other room. He was just coming to see me run. I'm so good. Wow. There's no individuality in this family. I make the baseball team. He makes the baseball team. It ain't for myself. Now you're playing baseball. She's gonna steal all the glory huh? Just want to know yourself.  I'll just fall back from the sports. And I'll just do my own like t-shirt and apparel line.  He's got a few months. Wow. Wow really. You made it funny. It's not that funny. It's funny. You made it funny. Wow. That's your buddy.  Every time they tried to branch out. He ain't coming. Look man. Mom look. I know you look. I've been doing the art. You know we came out with this really dope cartoon. You brought it up.    This is my dad. I'm going back to class. This is so good. I didn't make the team. How many points? I didn't make the team dad. My god. Yeah 40. I'm hooping the driveway.   I wanted you to fly son. I knew everything and I couldn't dunk this whole time.  I'm hooping the driveway.  You can't keep up with that. That's too much pressure. Hey pops. You know when we do like if I try to come. How you. I'm no son figure it out. You see there's a driveway right there. There's a pool court right there son. It's the inside one and outside one. Ain't no excuse for you. Really ain't no reason for you to be asking me nothing. Why you asking me? I said you do it before. You hear that from your dad. Michael Jordan he tell you that. Hey. Hey. You were out here and you were chasing me. No, not them tapes. Not the playoff tapes.  You were out here with your lips poked out.  What do I do for y'all? You do me like that. Oh. You think I didn't see them goddamn shell to Adidas in your closet too her.    What about mama though? OK. All right. OK. No, man. I'm not going to do that, man. Stop, man. Ryan didn't look at the stats. Leave that boy alone, man. What are you doing, Ryan? Nah, man. Stop, man. You're insidious. His stats is probably good, but they ain't going to be good because of who his father is. Nobody's stats are bad. If he averaged a 22 in high school, that's really good. Bro, that's because that's what you don't understand.  Everything he did was superior. Michael Jordan won a score of 45 points with one sock on.  I just made that up, but it's probably a trade in one sock on. One sock on. Because somebody stepped on his foot, and he couldn't get a sock on that foot. But he could get that Jordan number six on. You know, he had to wear them pennies. Probably he cut the one off the back. He had to wear them ones. He didn't have to. He didn't have one penny shoe yet, but they were one. And they had lost his luggage. And it was the only shoes they had in this size. Lost it.   Think of the motherfucker who helped them lose it.  They was trying to get that motherfucker food poison. They was trying to assassinate him. Like the Del Castro, man. If you worked at the airport and you seen Michael Jordan's luggage, you planted guys on that.  Y'all don't work. You know the niggas who's still in luggage at the airport. It's about three motherfuckers, man.  Who, man?  Michael Jordan, nigga. Niggas! Yeah. Niggas, he got the space jams in there. Come on. That's the jersey for the game tonight? That's for the night. Think about it. The space jams in there. You know how they knew it was Michael Jordan luggage, too?  Like the jeans, all the jeans, the formal leg jeans. Niggas, some jink hoes. What are these? Niggas, some extra wide leg jeans. Man, come on.     I don't know why y'all even did that.       Is it opening or is it just, you know, it's open. It's open. Y'all been open, though. Ain't closed.  No, it ain't dead Atlanta ain't afraid. It's just dead. Niggas.   No, from LA, we're in LA. It's shut down.  It's shut.  Yeah. But there ain't everybody out there. The people that were gonna go out. Right. Yeah.  Yeah, people, you can tell that there's still a lot of people wearing that mask out here. Hell, yeah. So in LA everybody got their mask on still. Oh, yeah. I mean, the mask, I got so many of them. I like when? So many of them. I like it. Do you match your outfit with them? Hell, yeah.     I like being like a Mortal Kombat character. I like being like that.  They didn't want to have a hood on. Come on now. Give me a mask.  Man, I'm gonna wear the mask well after this time to stop wearing a mask. Yeah. I'm gonna have a white man. I got masks lined up for the next three months. Fool these niggas. Yeah.    Man, I don't know what Clayton going through.  Shit. At least if I were to hurry up and go, you know, you go look at the mouth with this. Damn, y'all getting money like that.  Yep. That's a surgery. That's crazy. Whole mask. You can have a mask mask on. You can have like a mask mask. Oh, yeah, I've seen the people with the... I had them over in the chamber. Really? Yeah, I got a few chamber. We'll chamber them. Yeah, a few chamber them. We'll chamber them. I hope it don't get that bad. Nah, man. Shit about to get a little bit better. What do you mean?      All types of playlists. That is too much. Man, what brings you down this way, man? Did the comedy show yesterday with Ryan Davis. Yeah. Came out here and did that. But I said, man, every time I come out here, I end up bumping into y'all, man. So Atlanta's just becoming a spot where I come out at least once every two, three months, man. Yeah. Just to come out and get some work done.  Yeah. What they saying? Oh, man, just to, you know what I mean? I had a lot of people that, you know, talked to me about doing podcasts. And my whole thing about doing podcasts is like, man, I don't wanna do it unless it's right. I don't wanna do anything anybody else is doing. I want it to look different. I want it to feel different. And everybody I've talked to when it comes to podcasts, when they get to that whiteboard, they gotta write something down. It's like 85 South Shore, the blueprint. These are the niggas that are doing it, right? It's not even, I mean, all of us are talking about it. But to be in those rooms and those buildings and all everybody in there is like, nah, this is the formula right now. This is a podcast done, right? They get the right guess. It's the right amount of time. If you wanna do something, it's gotta be like this. That's the crazy part about this. It's just, it's not that complicated. We're comedians, but this is not even a comedy podcast.  And it's the coldest podcast in all of the land. You get what I'm saying? Say, yeah. We talked shit, we been, this was being done before it was even what it was. Right. You know what I'm saying? We're into it, man.  Just to watch it.  I remember the first time I really watched it. I went to one of my homeboys' house and we was about to play Madden. And they was like, nah, we gotta watch the 85 South Show. Bro, you mean, that's how you know we coming up? Yeah. When you get to go before Madden? Until we watched the 85 South Show.  And I'm, I already know y'all. So I already seen this shit, but I was like, man, let me see what these niggas is doing. Right.  Right. And I'm like, oh yeah, this is different. This is different. These niggas got food, they watching it and they tuned in for an hour. Right. I'm like, oh yeah, this is different, man. I can't just jump in the podcast world and think I'ma get in front of a camera and I'ma be able to do that. That's not that. Right.    Man, yeah, they show love everywhere. Like, it's international. Man, it's dope, bro. Well, look, man, don't let this be the last time you pull up on us, bro. That don't even make sense, man. Every time Clayton out in LA, man, he come through the crib.   Oh, yeah, you did come by the other crib. We did the, when we was banging on the door, we did at my crib. I felt like, God, we did that. Crazy ex-boyfriend. You seen that sketch? I'm in the bed with Shorty and a nigga banging on the door, the lowest banging on the door, and he's like, hey, come on, open the door. We just broke up yesterday.    Oh, come on, that's like, man.  Right. You know what I mean?   It's real. Real situation.  Niggas wake up in these situations all the time, I guess. Yeah.   No, not at all.  It's just insane. For the pandemic to hit and y'all was just hitting, the way y'all was hitting theaters and all that. And for it to hit and y'all to still be giving out content weekly is, that shit different, man. It's different to be able to do that shit, man. So I applaud that, especially, I watch everything. So to be able to get up and be like, oh, these niggas definitely got some content for me. I was on Instagram today and I seen the picture with Red Graham on the couch and I could tell by Red's smile, I'm like, oh, this interview's gonna be crazy. Oh yeah. Shout out to Red.  Yeah, so that's what it is though, man.  This is the 85 South Show with another exclusive, my partner, Brito Brown, listen to me.   We ain't had to do markers like this.  On my own, current music produced by J-O-N. Look, look, D-Niggas be hangin'. D-Niggas be talkin' like they really bad at D-Niggas be fake. Whoa, I got some work to do. How been a murder to stay in my life? I pray to the Lord, because I need to help, yeah, I need to change. Look, I even robbed me a nigga in jail, only spend 30 days in the cell that let you know that I'm thrown off the shelf. Don't make me come off of these shelves, one movin' no kilos, I'm serving no bail, just a couple ounces up on the scale. Break it down, I'm the servant of the year, and now you can tell me by being a player, nigga. Look, on my own, I was standin' on the block. On my own, yeah, ran from the cops. On my own, it was beef, loaded glass, bustin' shots to the top. On my own, on my own, huh. I was standin' on the block. On my own, ran from the cops. On my own, it was beef, loaded glass, bustin' shots to the top. On my own. Hey man, I wanna appreciate y'all for rockin' with your boy D.C. Young Flizzi, you did, huh. The 80 vibes, hold up, hey. These are 80 vibes, you dig what I'm sayin'. Bring it back, uh, check it out. D-Nigga be hanged, whoa. D-Nigga be talkin' like they really bad at D-Nigga be fake, look, I got some work to do, hoppin' a murder do, stay in my lane, look, I pray to the Lord, cause I needed help, yeah, I needed change, whoa. I even robbed me a nigga in jail. Holy Spirit, 30 days in the cell, they let you know that I'm thrown off the shelf. Don't make me come off of these shelves, one movin' no kilos, I'm serving no bail, just a couple ounces up on the scale.  On my own, I was standing on the block, on my own. Ran from the cops, on my own. It was beef, loaded glass, but some shots to the top, on my own. On my own, on the block, on my own. Whoa, ran from the cops, on my own. It was beef, loaded glass, but some shots to the top. J-O-N produced that, you dig? Yeah. Appreciate y'all for havin' me, even though that's another song right now. Yeah, we think that I ain't really bout it. Uh, I'm a gon' head and chalk up about it. They think that I don't really do it. I ain't new to this, more I'm true to this. You poppin' the pills up on the corner, though.  These niggas from the west side, on the west side.  Niggas, uh, niggas be talkin' they from Atlanta. Where you from? Where your birth certificate? Show me some. Where your birth certificate? What's 85? You did.


Proste, Mikel, za njih, da se zelo zelo površal. Tristno, da so me prišli vzivati čas, da so vzivati. Zelo, da bovamo kako tudi tudi dve, in kako mi vzivamo, da se nekaj parametrično metod izgleda. Zato, še tudi zelo, da se objevamo na kapičnega, da so prišli vzivati, da se postočimo z Michaelem. Ok. And before getting into this specific paper, maybe let me just tell you a little bit, a couple of things. So basically this paper is indeed part of a kind of larger research project on the use of classical invasion non-parametric methods. A little bit as Matteo was saying, with the idea of seeing whether adopting an even more general approach to handle parameter time variation and non-linearity pays off, in particular during problematic times. And at the same time trying to import these methods from the statistical literature, adapting that to the kind of data that we have to analyze, so persistent and heteroskedastic. And again, as Matteo was saying, trying to design estimation algorithms that also permit to apply these non-parametric methods when you have very large dimensional data sets. So I remember my first contact with non-parametics was at the PhD as a student, now decades ago as implied by Michele, right? And so I was reading a paper by Wolfgang Arbel, which actually then became a book that you may remember on non-parametric regressions, and I was very fascinated by that kind of techniques, except that then it was virtually impossible to put it in practice. So this was the early 90s, so the most you could hope to do was a single regression with one or two regressors and all more than that. And instead nowadays we are lucky to have so much more computer power that made these methods again feasible also for very, very large data sets, multivariah systems, and so on. And so this is why I try to get into it a little bit more. So I mostly worked with a couple of quarters and group of people, so on the classical non-parametics, mostly with George Capetanius, and this is mostly to non-parametric model time variation. And the idea is to work with kernel estimators that again have a long tradition, for example the work by Peter Robinson and his co-authors. And in the standard non-parametric setting with time varying parameters and kernel estimators, the assumption is that you have deterministic evolution in the parameters, which can be a little bit restrictive for the kind of economic or financial applications that you have in mind. But then maybe now, eight or nine years ago, Ljudius Giraitis, Capetanius and Yates showed that actually under a little bit more stringent conditions you can apply these non-parametric kernel based estimators also when you have stochastic time variation. So you need still some assumptions like relatively smooth parameter evolution, the fact that the parameter evolution kind of dies out asymptotically and so on, but it can be done. And so at that point, the first paper in this line of research, which is actually joined to work with George and Fabrizio Venditti, who at the time was at the ECB, was trying to use these non-parametric techniques to introduce time variation non-parametrically into VARs. And at that time, the kind of benchmark that you could use was for the large dimensional case, for example, the forgetting factor approach of Gary Coop and Dimitris Korobilis in a Bayesian contest, but we wanted to stick to classical. And so we uncovered a very old literature dating back from the 60s and to Tile on what are called stochastic constraints. And basically these stochastic constraints are a pretty neat way of introducing regularization into classical estimators. So basically you can get things like lasso or ridge or elastic net by working with these stochastic constraints. And so in this paper basically we were using these stochastic constraints to handle the large VAR part and the kernel estimator to handle time variation. And so we were showing that you could indeed estimate even a VAR with 100 variables allowing for time variation and the method was working reasonably well in both simulation and in practical applications. And again link to what Matteo was saying, we also showed that you could also do kind of structural VAR analysis or transmission, short transmission with time variation non parametrically. And then again with the idea that maybe time variation is also important for more structural analysis, we tried to implement similar machinery to the case of instrumental variable estimation. And there you know you have a first stage that is typically your structural relationship where there is an endogenous variable and then you have the second equation that links your endogenous variable with the instruments. And so the idea is that maybe the relationship between the instrument and the endogenous variable can be time varying. But possibly the structural relationship itself could be also time varying. And again we kind of extended these non parametric methods also to handle this type of situation and for example then you can use it to estimate New Keynesian Phillips curves or equations where you have unobservable variables that can be estimated with errors and so treated as endogenous and so on. And then again we went further and we thought that maybe you can also put at work these non parametric estimators into panel models with stochastic time varying coefficients that are a little bit an extension of the random effects that you would use only for the intercept and so this is work with you by who is a former student is now at Monash. And then paper number four in this trend of literature with the idea that you want to handle these large data sets you could do time varying factor models non parametrically. Actually there is some work in that or maybe even better you can work with targeted factors so this three pass regression filter I guess most of you are familiar with it was introduced by Kellian Pruth in a journal economist paper 2015 and it is the idea that you want to summarize the information into a large set of X variables keeping in mind that you want them to use these factors to predict the variable of interest. And so this is basically a generalization of partial least squares and so it is called three pass regression filter because it's very nice you can get the whole thing done by a set of OLS regressions and so the idea is that you could have time variation in all of these three steps and again it's a little bit more messy than the standard factor analysis but hopefully now we cracked it and so Janice is presenting this paper at the EIA meetings in Oslo in a couple of weeks. And then finally something on which we have worked a little bit also recently so with Robin Brown and again George and so this is even more structural so here the idea is to put these non parametric estimators at work in the context of proxies var. And again proxies var have become a very common and convenient tool for structural analysis and again there are ways to introduce parametric time variation so Paul has a nice paper in restart on a Bayesian method for doing that. Here we wanted to do it again using these kernel type estimators and again you need to twist a little bit in the theory but then it works pretty nicely and in that paper we have applied it specifically to understanding the effects of nonstandard monetary policy and quantitative easing on financial variables and so it focuses on the UK but we also got some results for the Euro area. And so this is again all classical and it focuses on again more general ways to handle time variation both for forecasting and for structural analysis. Then instead there is some work that I have been doing again over the past 3-4 years on Bayesian non parametrics and again this is a kind of funny story because as an undergraduate I was trained by Bayesian statisticians because basically at Bokoni they hired as professors in the 70s and 80s those that were the best pupils of the Finetti and so there is a very strong Bayesian tradition except that it took 4 courses to discuss Bayesian linear regression model because I learned everything about exchangeability all beautiful theory and so in the end again I kind of abandoned it and then instead a kind of old memories reemerge and so first we did a series of papers mostly with Todd Karak and Andrea Carriero on parametric Bayesian and then by chance at the conference I was lucky enough to met Florian Huber and I was introduced to his research group and so we started working on this kind of Bayesian parametrics and again this is mostly importing techniques developing the statistical literature and adapting them for use with the economic and financial data and so the first paper in this trend of research again is work with Florian and Michael and also Todd and Gale Koop and this has to do with tail forecasting with multi variate Bayesian additive regression trees that are a tool that we will also use in today's paper which is basically a Bayesian version of boosted trees or random forest as you will see and it tends to work particularly well and particularly well in the tails so for doing GDP at risk inflation at risk so it would fit very nicely the title of the conference and so one problem with this real analysis that maybe will come back also in other papers today is that this kind of methods like quantal regressions were indeed designed for statistical data sets or micro data sets in economics and so often in the tails you have very few observations and when you apply them with quarterly but even monthly data often it's not so clear that you can use them and there is a nice paper that you may have seen by Victor Chenuzokov and co-authors in Ristad where they propose a kind of rule of thumb to decide whether you can still use quantal methods or you should use extreme value theory and for most of the political macro applications the rule of thumb tells you that indeed you should move to extreme value theory and a possible way out of that is indeed to be done and so to try to use shrinkage to reduce the dimensionality of the parameters or maybe like in the second paper to take a panel approach and so to hope that say the tail behavior in many countries is comparable and so you can get additional information on the tails by pooling different different data sets and so in that second paper there is a model that has the feature of combining a linear and a nonlinear quantal regression where the nonlinear part is again modeled with the BART specification and it's nice because it shows that when you are near the center of the distribution the weight on the nonlinear part is very close to zero while when you move close to the tails instead the nonlinear quantal regression becomes and then paper number 3 again since of course there is also a lot of interest in inflation in general and given that we are in a central bank applies this kind of technique specifically to forecasting inflation so in this case US inflation and instead paper number 4 it's also something that we will look at a little bit closer today it works with a different kind of Bayesian parametric technique and again we will come back to this today but as you will see it's just another way of approximating unknown nonlinear functions so with BART basically you use a basis of step functions and with the Gaussian process you use a basis of Gaussian functions with different means and different variances ok so then there are a few other papers that are maybe more applied using these techniques one has to do for example with how do you construct linear projections with this kind of more flexible techniques the second one applies it to climate again in particular looking at the effects of tail climate events on tail economic events and the third one oil in the tails is something that we are working with about Maestro and again given all the problematic events that we have seen in the recent past in the oil market but in the gas market and so on we thought that it could be and then instead the third method Bayesian parametric if you wish that I've been doing some work on as to do with Bayesian neural networks but on these Karin knows much more than me and she will tell you a little bit later today and so let me now move instead more properly to the paper of today so the paper of today is basically a kind of overview and the idea was to look at specification and estimation of some of these Bayesian parametric models specifically thinking of using them for forecasting possibly large sets of macroeconomic financial variables and focusing on VART and Gaussian processes and comparing them with various types of Bayesian VARs and again with big thanks to Marta Bambura the application is on the Euro area and on these very nice real time data set that Marta and Kotor have put together and were very nice to share with us so let me tell you a bit about the econometric framework so the idea you have a general model that is like equation 1 and so here you have a set of explanatory variables that can be legs of Ys but they could also be exogenous regressors that are grouped into X your target variable is Y and the relationship between Y and X is unknown so it is this F function that are unknowns and then there is an additive error structure and so we need to say something about how to approximate capital F and the little F that compose it and something about the error structure so the simplest possibility is to assume that F is linear so this would give you a VAR and so indeed our benchmark forecast exercise will be a Bayesian linear VAR with as you will see global local shrinkage priors that already is a pretty tough benchmark but also to make it maybe a little bit fair as comparison with these more flexible models we also consider a version of this VAR with time variation in the coefficients a little bit like in the original work by Giorgio Premicieri where all the coefficients in the dynamics can evolve according to random walks so this makes it pretty flexible but at the same time the parameterization remains relatively small then the first non parametric Bayesian techniques we consider is BART so basically as I was telling you the idea of BART is to approximate this unknown F function with an average of trees so for us we will use about 250 trees you can also of course change the number of it and I mean if you look at some of the previous paper or if you look at the chipman at all paper there is of course a much deeper discussion on how you would do this but basically the starting point is the tree so the tree you need to decide if it is a shallow tree so if it is relatively small or if it is a tall tree and you have to decide how many branching you have and you need to decide what is the number of the final values and things like this so this is all handle as you may see in the paper again hopefully very soon all the details on this but just to give you a simple example imagine that you have a single dependent variable y and a single predator x so basically in this case your tree would be basically just branching maybe if we look at the picture it will be even clearer ok so you have to decide first whether your x variable is below or above a certain threshold value this gives you the first branching then in the second branching again if you are to the left or to the right ok and so basically you need to decide you need to treat as stochastic both the number of branches that you have and the threshold values in there so there are proper priors to do these and on the right hand side you see how this tree would work with simulated data so in this case simulated data are generated with trigonometric functions and so the true expected value is the one that you see there that looks like a sine or a cosine so like a wave and the tree is approximated with this step function and so you see that basically one possibility to improve to get a better approximation is to work with taller trees or the other possibility instead is to average a lot of shallow trees and so here again in the left you see the same picture that we saw before and instead to the right you see what happens if you average 250 of these relatively shallow trees and so you see that basically already 250 does a pretty good job at approximating the nonlinear expected value there and of course the larger it says or the taller the trees the better the approximation becomes so there is always a trade-off of course because you know the more trees and the more complicated the tree structure the more computational expensive the method becomes but this gives you an idea so again this is the idea that you approximate this unknown function with an average of step functions how about Gaussian process so Gaussian process there is this very nice book by Williams and Rasmussen that describes it both nicely technically but it also gives you an intuition of how the thing is working so there are various ways to think about it as I was telling you the first possibility is to think about approximating this f function with an infinite average of Gaussian distribution with different means and variances so this mimics the idea of having another orthonormal basis to approximate but the way that instead is typically introduced in statistical text is by thinking that this f function is unknown there is an infinite number of them and you want to put a prior on this infinite dimensional object and so the Gaussian process prior is a way to do this and then once you condition on the axis on the data that you have basically this gives you a finite in this case distribution on f1, f2, fd and so you basically do it like this and so this multivariate Gaussian distribution will be typically centered on zero but you can also center it on something else like deterministic components and it will be characterized by what we would call a covariance matrix and in this literature it's called a kernel a kernel function and so again depending on the type of kernel function that you use you will approximate arbitrarily well any types of a function so this is a very general tool for example there are choices of this kernel function kappa that makes the Gaussian process very similar to Bayesian neural networks so the standard choice is to work instead with a Gaussian kernel like the one that you see in the last line and this has the advantage that it only depends on these two parameters so you see the psi there and the L and so you see basically this D measures the distance so it is xt minus x tau and so you see that if the distance is equal to zero basically kappa becomes the variance and so that psi parameter is a parameter that controls the variability and instead the L parameter is what controls the smoothness of the function so you see that the larger is L the more differences between xt and xt tau change the shape of the function and so the next slide gives you the same picture we saw before so this is the same generated data from the cosine function so h is what I was calling Li before so you see that if you put Li that here I am calling h very close to zero basically you go back to the linear world and so you see that the posterior distribution that you see down there in the left side of this slide is very close to a linear regression function where if you choose a large value for h then you get much more variability in the shape of the function and so in this case you see that the posterior tracks extremely well the non-linear expected value that you get in there and so these two parameters L and xi are basically treated as random so you will put priors only on them also on them and you have to design a proper MCMC algorithm how about the conditional variances so because you know here there is a tradeoff because the more flexibility you put in the conditional mean the less relevant typically becomes to allow for heteroskedasticity and this is an empirical result that we will also reproduce while if you work with a linear var, Bayesian var it is particularly important to allow for stochastic volatility and so in this case we work with what is called a factor stochastic volatility structure so this is introduced in the statistical literature by Agui Aran West and also Silvia Fushisnatter worked on it and so on and from an economic point of view there is an older paper by Lucrezia Reichlin and co-author noticing that indeed the volatility of macro variables is pretty common and then we did some work on that also with Andrea Carriero and Todd Clarke like we have a JBS paper showing that indeed there is quite a lot of commonality and so in that case basically you assume that the errors have a factor structure so these F are common factors that themselves have stochastic volatility L is a matrix of loadings and then each error also has an idiosyncratic component eta that also is characterized by stochastic volatility and you see that the ethas are idiosyncratic so this H matrix is diagonal so basically here all the commonality in the epsilon is captured by L times F and so this is beautiful because once you condition then on this L times F you can do equation by equation estimation and so this is also something that Josh and Gary and other co-authors use to simplify structural inference structural analysis with VARs because it would give you independence to rotation of the variables so we work with this so we work with this type of stochastic volatility in the paper well in earlier results that I didn't put in there we also tried stochastic volatility with t-distributy shocks but in the end the results were pretty similar to those that I will show you and so I have not included them in here but so the idea is to look at tomoskedastic stochastic volatility this factor structure and possibly the t-distributy shock but again in the end they didn't help so much and so you see the models we have were basically linear possibly with time variation in the parameters barred Gaussian process and then homoskedastic or heteroskedastic so this is another example with simulated data to show you how it works so on the top left panel you see data generated by a linear regression model and so in this case of course the linear regression the linear model is the best one but you see that barred and Gaussian process are also doing a decent job of course they are a little bit more volatile and again the volatility would decrease if you increase s in the case of barred or if you work with a smaller value for h in the case of the Gaussian process but then you see that as long as you introduce nonlinearity so in the top right panel you get a kind of parabolic behavior the bottom left is the wave thing that we have seen so far and the bottom right is a kink regression function like you know at a certain point quantita with using kik scene and you get this kind of behavior and so you see how of course the linear model would give you a very poor fit and very poor forecast as well while this both barred and the Gaussian process can do a pretty good job in approximating generic types of nonlinearities so here both barred and gp have no idea what is the true f function it's exactly the same model applied to any data generating process and you see that they do a pretty good job whatever the type of f function in terms of the estimation algorithm I have very little time left so maybe we can go pretty fast but just to tell you that it is not difficult there is also a lot of code that we have put on github in case you want to play around with this and then we will also distribute the code for this very specific paper here the only thing that maybe I can mention so I can skip then the later slides the only complication is in the case of the Gaussian process because those two parameters so the xi and l or h basically you need metropolis asking steps for them and so that slows down a little bit the computations but only a little bit as you will see in a little bit so let me skip these that were just giving you a few more details so we can skip so we can use the final 7 or 8 minute for the empirical application ok so empirical application as I was telling you is done for the euro area with this nice data that Marta Bambura and cooters put together and kindly gave to us and so here basically the beauty of it is that it's a pretty long dataset quarterly starting in 1980 about 20 years for doing a forecast evaluation which is pretty uncommon for the euro area and again in addition you can do this in real time because they collected all the vintages for this data so there are about 15-20 variables in the dataset so the results that I will show you today are for a small model that includes only GDP growth inflation and the change in unemployment and hopefully in the next version there will be some variable models similar to the one that typically are used for the US ok then again in the paper we will describe there are also some things that of course you have to do to handle the ragged edges so how to handle missing observations with these nonlinear models but nothing particularly interesting from a theoretical point of view so these are the data the vintages so you see that there are some little changes in it maybe the latest example is you may have seen this latest revision of the real GDP growth data that Eurostat did for the last two quarters where now technically we have entered a recession in the euro area while in the first release the data where it is zero slightly positive so the idea is ok let's see whether this thing matters ok so how about the evaluation so again here we construct point forecast interval and densities and we are particularly interested in the at risk part just to be in line with the conference so we will look at the standard continuously rank probability score but also weighted version to give more weight to the left tail or to the right tail and then we will also consider more specifically the quantile scores and in particular the quantile score at the 50th percentile is very close to the mean absolute error and so it can provide a way to also get an idea of the quality of the point forecast in this case ok so this gives you an idea of the estimation times as I told you before specifically the linear VAR takes about 30 seconds for 10,000 posterior and predictive draws and this is on basically Microsoft top so it's nothing fancy then of course we run it on the cluster so of course much much faster but just to give you an idea of the time here and so you see that adding stochasti volatility changes very little things but volatility is pretty comparable with the standard linear VAR and the Gaussian processes as I was telling you are just maybe twice as expensive in terms of time and again this is due to these metropolis steps that you need to include in the Gibbs sampler but still it's something that you can do very fast even on a normal laptop ok so how about the results we discussed a lot with Michael because I said it's too crammed but he said no you have to show it so I'm showing it ok so let me tell you very briefly what's in here so these are results for h equal 1 and the next results the next table will be for 4 quarter ahead and 8 quarters ahead so here you get 4 vertical blocks where it says none is the standard CRPS so it's the density then you get the CRPS over weighted on the left tail over weighted on the right tail and the QS50 that is similar to the mean absolute terror ok then in each vertical panel you have 4 columns and this is the full period so the evaluation done over the 20 years from 20 so from 2000 until 2021 and then you have pre-covid so until the end of 2019 post-covid with the warning that it is only 7 or 8 quarters and then you have recession and expansion as dated by the Euro area business cycle committee ok and then you have the 3 horizontal big panels that are GDP growth, inflation and the change in the unemployment rate and then you have the various models so the linear bivar is a benchmark so values smaller than 1 means that you do better than the linear bivar and so you see you have the time varying bivar you have the bar, you have the Gaussian process and so on so again it's pretty crammed but there are a couple of things that you can look at first the colors so when it looks bluish it's smaller than 1 and you see that there is quite a lot of bluish in here and the bold numbers are the best performing models ok so if you look at GDP growth the kind of result that emerges is that over the full sample you do better than the standard bivar and you do particularly better during covid and in part during recessions but the interesting thing is that one model that does pretty well it's already the standard bivar with stochastic volatility and so this relates to a paper that we did with Andrea and Todd and also to the work that Dario will present later on showing that basically if you are interested in growth at risk like the Adrian Boyer, Czenko and Giannone paper basically a bivar with stochastic volatility it's already doing the job for you because it allows for changes in the mean and changes in the variance and during recessions the variance increases and so this gives you the kind of asymmetric behavior in the 5th and 95th percentile that you would also get with the quantal regression. So for inflation instead the Gaussian process is particularly good both in general and during recession times or expansion times while for the change in unemployment rate you also see that there are some gains and also for this the Gaussian process is doing a relatively good job. So then again there are results for h equal 4 for h equal 8 let me skip them and then we also did an analysis that is similar to the Giacomini Rossi fluctuation test so here we have computed the same loss functions but taking averages only over 8 quarters enrolling the evaluation period over time. So just to give you an idea of when they work particularly well and so the different colors of the lines are models and here the only thing I would like you to notice is that you see the final part of each graph to the right is the COVID period, so it's after 2019 Q4 and you see that there basically when you focus specifically on the COVID period all of these Bart and Gaussian processes are doing much better than the standard linear VAR also once you add stokasi volatility in there. So let me just wrap up again this paper is basically a review on specification of estimation of Bayesian parametric modeling for forecasting in particular for tail forecasting and again since the method can be estimated equation by equation you can also handle like 20, 25 but also 100 variables and the computation costs are relatively small for doing these and then again as you have seen the forecasting performance is pretty good and overall in particular basically the kind of you see Gaussian process VAR seems to do particularly well during problematic periods and so if you want to have a relatively robust method for doing the at risk forecast this could be a decent choice so thank you so much and I will stop here. So thank you Massimiliano let's then open the question. Paolo Giron from Boston College I have a very interesting presentation so one question that I am wondering about the method is about stability so you didn't discuss anything about stationarity and you know once we move from linear models this becomes a dice aspect and if you look at the unemployment regressions as you go to HR equals 8 I believe you see a lot in the quality so I want to collect your thoughts about this and the other one what language do you use to program oh thank you so much so this is indeed quite important so the languages are and indeed we have lots of packages put together for this and stability indeed it's an important thing so for example what I didn't discuss is that in here we use the proper iterated approach for constructing the forecast from the nonlinear model so everything is simulated forward and so we do f of f of f of f and so that is indeed pretty tricky without stability so stability in this nonlinear world it's pretty difficult to analyze one possibility is say you can work this we have it done in this paper coming out in the IR so you can you can work with the best linear approximation in the pullback library sense to this model and then study whether say this linear approximation is stable or not, the other possibility you can just iterate forward the model like we do when we construct the forecast for say maybe 50-60 periods and see that the thing does not explode but at the moment we do not impose anything that would impose stability and again part of the thing is that this thing is kind of so flexible that in a sense it's less of an issue than in the standard linear VAR but indeed it's something that would deserve a deeper investigation thanks so it's a partly question partly a suggestion so my experience when using linear VAR especially including covid data is that it's important to have the stochastic volatility and on top of that it's important to have the sort of like scaling the extreme observations as you do in the restart paper you mentioned so in that respect it would be interesting for me to see how these methods that you propose like fair in compare to such a linear VAR where you really deal with the extreme observations in the errors like you know the best as you can but keeping linearity in the coefficients compared to when you release when you go to a nonparametric nonlinear method thanks Marta this is a very good suggestion so the idea of doing the t-distributy shock was to go a bit in that direction without all the complications of the restart paper so what we tried is that like a t-student with three degrees of freedom and again for Bart and Goshen process that didn't change much but for the linear VAR it changed a bit so maybe we can add the data at least for the linear VAR and do the comparison with that so that's a very good point thank you fascinating staff I'm always intrigued by this tradeoff between fit and forecast so you skipped you were very quick on the h greater than one can you say something because I see many red things there I assume that the longer is the forecast horizon maybe the worse is also because maybe the precision is not what's your view there that's another very good point so the thing that here deteriorates much is unemployment while instead for inflation you keep getting big gains like 10 to 20 percent also for h equal 8 and for GDP growth basically the ratios become close to one so it seems to be more variable specific than anything and it relates a little bit to what Pablo was saying so I guess as long as it doesn't explode and that kind of helps you also along the road in the other paper that you got with Florian you were using subspace shrinkage and you were also using Dirichlet process mixture on the variance are you planning to put it inside this and secondly when you were doing the real data in the bar how many trees are you drawing again 250 because I guess you're adding a lot of noise maybe because also when you were doing the simulation that when you have constant behavior you have a lot of noise I guess maybe the huge amount of trees can increase a lot the number of noise I don't know that that's the point because we saw with Florian in other works that's the point no thanks a lot Luca so basically Luca with Florian is another of the fathers of Bart in Microsoft this is very welcome no the thing on the first question so basically what Luca was mentioning I didn't discuss it you can also work with these non-linear processes for modeling the variances and so rather than having say stochastic volatility for the variance you could have Gaussian processes or the Dirichlet mixture processes that Luca was saying so in this paper that is another paper with Andrea, Gary and Florian we do not find big gains at least for the macro data from the Dirichlet mixture process at the point that the referee said take it out so we took it out and so here we didn't try that and instead the subspace shrinkage prior is something that can be used to further improve the computational efficiency when you are working with a very large model and so since here we are working only with three variables it wasn't so but for larger models indeed it can help and the idea on the fewer trees indeed that is a very good point so maybe we can try and see what happens if we go down to 50 whatever, so in one of the papers we also made a hyperparameter and tried to get it by the margin unlikely but here we can just see what happens, thanks Thank you, this was very interesting and I was intrigued by the BART some of the BART work and I wanted to know if you thought about kind of storytelling or structural interpretation of results and when you were presenting what came to mind is that when you presented a tree with many branches it seemed kind of easier to think about some structure and some macro dynamics playing out I didn't see that immediately when you have a big forest maybe of little bushes or not so what I was wondering is whether that's also a way of thinking about trade-offs of applied work for instance in central banks Thanks Dario so this is another very interesting point that would open up on how to do a structural interpretation of this model so there are two ways that we have explored in some of those other papers one is again to look at the closest linear approximation and then in there you can do the standard analysis the other one is to keep this structure focused on specific parts of the distribution like in one of the papers for example we show that the tail behavior in the bar is mostly driven by financial variables so in this sense it's true what you would get from the quantile regression can be mimicked also also in here and the third way of doing it is with these sharply values that would tell you what are the most relevant variables driving the nonlinearities but that's another very good point