Hi, my name is Leon Roe currency trader and trading coach at trading 180 comm and welcome to this week's supply and demand Forex and gold fundamental and technical analysis if you're new a very very warm welcome to you And if you're a returning watcher and subscriber Warm welcome to you also, please don't forget to like subscribe and share with your fellow colleagues Press that subscribe and like button button. Sorry and notification bell so that you're alerted to all of the Latest videos when they come out anyways Trading 180 just a quick recap is just really our trade processes applying fundamental analysis to establish directional bias and then Technical analysis supplying the mass strategies to time trade entries established profit targets and risk management But let's get into first things first. I guess the week ahead and looking at the week ahead on trading economics com Monday, we've got balance of trade for China Really, we've got balance of trade. I think for Canada if you're trading the Canadian dollar I guess the forecast and the consensus is for definitely more growth in Canada balance of trade is important because it gives us an indication of you know gross domestic product and Also was one Tuesday. We've got the balance of trade for the U.S. Wednesday, nothing really Thursday ECB interest rate decision and the expect they're expected to hold rates The ECB and for good reason, which we'll get into I guess a bit later on Core inflation is expected in the U.S. Is expected to rise which again puts a bit of pressure on the Fed Federal Reserve to look for to look to high crates Which they you know are on that path As well as Friday, you got the pound. We've got GDP month for month again expected The forecast is expected to grow from definitely the minus zero point two for month for month perspective Canada unemployment rate unemployment expected to go down which is going to be good and again Michigan consumer can send a report not really that important or not something that I really keep an eye on so Some market moving news, but I think in general, you know overall we're looking at risk sentiment But let's get into some of the charts and a bit more fundamental and resentment analysis and start off as we usually do on the Dollar index and the dollar index is just a measure of dollar strength against a basket of currencies like the Pound the yen and the euro major currencies, but before I guess we get straight into the Dollar we've got to really kind of look at the macros the fundamentals as well as the risk sentiment and the risk At the moment is definitely off. You know front plate page of Bloomberg, you know the Russia invasion of Ukraine Ukraine updates Russia's VTB Bank reportedly set to exit Europe Doesn't look like anything's really getting better. Although in the background there are, you know proposed talks happening Which is always, you know positive So let's see what happens with that bad the moment We are on a risk off in Environment and one of the things that you know, you have to be aware of I think a couple of traders were asking me In the group and both on on YouTube and private messages emails was that well why is You know certain currencies not getting stronger and weaker for example You're certain pairs in a way like the Aussie yen and I'm gonna get more into that but basically every single Risk event should be one of the things that you need to take into account is the fact that You know is is the geography of the risk event, right? So for example, what countries are more affected by the risk event than others and not every risk event is the same You can't just you know, think that okay Well in a risk-off environment, you know, you should always buy the Japanese yen against every single currency That's not how it works, right? We can't think in such a binary and an absolutes because every risk event has different effects on different economies, right? so as an example of that this is from the Royal Bank of Canada and Russia Ukraine impact on the charts so of the countries we monitor the euro area has by far the greatest direct trade exposure to Russia Right, and it makes sense. So if you look at the euro Geographically and the euro area to where you know, the conflict is of course, you know The euro area going to be more affected than the UK then you know on the other side of the world I guess I've decided to call it the other side but Canada US and Australia right when it comes to imports and exports and How GDP is directly affected by what is going on? So from that perspective, you know, the current a currency's strength or weakness and an appreciation of depreciation Can be determined and influenced by How how well the country is doing right so from that perspective if if the euro area Is is geographically going to be you know affected and the direct trade exposure to Russia Then obviously just the reason why you're seeing You know the euro currency fall right or depreciate and devalue It's simply because of the the fact that the the Russia Ukraine war has on The euro on Europe geographically and and their involvement so from that perspective, you know We'll get into that bit there only in the euro But that's the reason why you're seeing certain currencies go, you know higher or maybe not react as they typically would in In all risk-off environments anyways focusing more on the dollar and getting back to the dollar and Sorry about that. We've got I don't know. I've put the thing out. Here we go so Fed's urgency for steep rate hikes lessons after wage gains control so Labor force participation in rising and pay growth has slowed strong hiring gives power room to make a more steady Approach and so the Federal Reserve are looking to hide crates. They were looking to hide crates At probably 50 basis points or zero point five percent but now probably less so simply because of a the the the the risk-off situation and The fact that the central bank don't necessarily have to raise high crates aggressively so You have to definitely raise high crates because of inflation rising inflation But maybe not so aggressively and that's helped also buy some data. It's a Jerome Powell Pals pushed to limit the Federal Reserve's Interest rate lift off this month to a quarter percentage point was bolstered by unexpected stagnant wages to stagnant wage growth It helps or contributes towards inflation So because they're stagnant. It doesn't necessarily contribute towards higher It may not contribute towards higher inflation in at least a short term Which means that they don't necessarily have to hike rates as aggressively, you know Amid strong hiring seen in February's jobs reports while employers added 678,000 to payrolls and unemployment fell to 3.8 percent average hourly earnings were little changed from January As a setback for workers, but it suggests the US central bankers aren't facing an immediate wage price spiral similar to the 1970s Which reduces the urgency to take bolder steps towards curbing hot inflation? And if you're wondering what the hell is going on that don't understand, etc. I Do have some fundamental Analysis videos talking about interest rates inflation and the relationship between that on GDP And how they're interlinked and I'll try and remember to put the the link in the description box below or There's a link in the top right hand corner So you can watch the fundamental analysis course and the basics of fundamental analysis and really why How these things come into play anyways From that perspective, you know if you've been watching my channel for any length of time You'll understand that I am bullish on the dollar, right? And again, I've been putting on the dollar for for dollar for over a year now and pretty much what you're seeing is You know prices go, you know higher and higher and higher, right? This is it's not a mystery as to why the dollar is going higher if you understand, you know risk sentiment and fundamental analysis and You know, this is just proof in the pudding that if you get the fundamentals right you can predict, you know medium to long-term trends so Again, I don't know whether traders would have got short there at me I was looking for pullbacks again as you can see from, you know last week's Video and the previous weeks and previous months videos you go back and look at all the evidence I will suggest in saying continually to say, you know, buy dollars and again not financial advice But why I was buying dollars and you can see really why, you know, the dollar's been making higher highs and On this really yearly trend. So from that perspective, I was anticipating a pullback at some point You know to a demand zone which helps, you know when it comes to buying on the other dollar crosses But sir, we just didn't get any kind of pullbacks, right? The dollar also being a bit of a safe haven Currency and all we've seen this prices go higher But that just now means that as we make higher highs I can now start to add more demand zones and just Literally, you know trading becomes a whole lot easier than trying to guess, you know Which way prices may go in the medium to long-term if you understand that or you're really looking for is, you know Pullbacks right so pullbacks into that area is going to be really nice or pullback into this area No one knows which way which one is going to reverse from but the point being is that any pullback represents a bargain price potentially if the fundamentals are still in play So again not looking at necessarily buying the dollar index although you can also and brokers But for me this just adds confidence to buying for example, dolly dolly yen dollar Swiss Currency pairs if you get, you know prices come down into these demand zones and then it comes down into a nice demand zone on a on a dollar cross And then looking for any kind of upside potential if you are looking for, you know short trades and selling dollar at the moment nothing recent right so You do have a pretty a supply zone from 2020 Daily demands, sorry supply zone, but for me I'd want to see proof of value But I get my path is my direction biases is more to the upside anyways looking at the dollar yen And the dolly in from last week again from a risk-off perspective The Japanese yen typically tends to strengthen and you know, you've had a bit of a ramp up in risk sentiment With I think there was a nuclear power plant that got bombed Or taken over by the by the Russians and so again risk sentiment coming back off or more off I guess and So, you know, you had that pullback on the Thursday and the Friday for me again I'm probably still a buyer of the of the dollar At the moment or looking for upside potential not saying that it's gonna go to the heavens no idea But I think any fresh demand zones are gonna be decent. I think anything from that 1450 114 You know 114 50 half number down to probably anywhere around here is gonna be where I'm looking for for buy trades And and that's really where I want to look for like I said the buy trades again Probably zooming down into lower timeframes and looking at you know support and resistance within that zone That 14 said that 1450 area. I think is really nice Many traders in the group recognize that as a bit of a CPR say a bit of but it is a CPR zone Intradiate demand zone. So so yeah, that is nice I think for a for a for a long trade again prices could cut through here And we could you know saying that prices are going to reverse of course, you know What we do in trading when it is look for the price reaction see what happens there the prices go straight through then It just goes straight through right becomes a bit more of a bargain. It could come down to the 14 20s, but I'm saying predicting anything just saying that as an area of interest and I want to see how prices react and what the Resentment is at the time and then decide whether I want to look for a buy or sell trade there But again, just looking more from a from a daily timeframe perspective Yeah, these zones I think are decent for a potential buy if you wanted if you do want to get Short on this currency pair at the moment. There's nothing Of interest, I think probably if you're looking for anything probably a pullback into a fresh area of supply around the 16 116 areas for for a bit of a short trade and less prices make lower lows lower highs like this Let me just get rid of these These drawings and then you've got let's say for example prices, you know Break that supply zone and then you're looking for a pullback into Sorry that demand and I should say if supply breaks at demand zone Then you're looking for that area as an area of supply and in a pullback into that zone But again depends on the risk sentiment and the actual currency pair Moving on to the Swiss dollar Swiss dollar Swiss Again potential for that pullback again more risk of sentiment coming into the market from last week Prices did sell off. We were in and I'm still in this trade matter of fact from from down here swing trading it Let's see what happens if risk comes back more on then I think this trade is going to be really nice If not, it's portrayed as already profitable.  I'll just look for you know more buying opportunities down at these lows potentially From a demand zone perspective, I want to get rid of that and Supply is probably around here. So yeah, I think at the moment I Think anything below This level here one second. Let me just get rid of all this. I think this area here We've got the 1950s, I think that's going to be a really nice zone to potentially look for any kind of long trades And if not then just below that area I think it's going to be nice at 91 round number or the 0.908 Area for a long trade again. I'm more bullish on the dollar than I am The Swiss Frank even in the risk off environment in the current risk of environment Moving on actually matter of fact For that if you do want to get short on the honest currency pair, you're looking really at that area there Probably maybe even a bit higher The 93s for a bit of a short trade Moving on to the dollar CAD and again in a risk-off environment You'd probably expect the the US dollar to strengthen over the The Canadian dollar you can see from last week last week's analysis of saying that price probably may come down to this area Here the one two six and then you know go higher. So it did move, you know, a couple of hundred pips from last week Again, these are the areas that you were looking for for shorts and longs, but um, I Would say yeah, this is probably now where I Think personally the dollar should strengthen more than the Bank of Canada in a risk-off scenario The Bank of Canada did high crates, which is generally positive for the For the Canadian dollar as well as commodity prices, but I think again Just from a risk-off sentiment kind of things escalating I do think that the The dollar I think in this environment probably should do slightly better not really a pair that I'm looking to trade There is a supply zone there So if you are looking at short trades looking to buy the Canadian dollar I think that area is really nice for a short trade again looking at any kind of long trades and buying the dollar I think any pullbacks below that 1.26 area is a decent long trade But nothing. I'm really looking at buying or trading at the moment moving on to the dollar New Zealand dollar US dollar And again, I think in a risk-off environment the US dollar should strengthen, but What's been happening recently is I think that the the New Zealand dollar Also looking to high crates and this could probably be more of a bit of a pullback but I do think because they are at least affected by the Potensions in the Ukraine. You're seeing prices, you know go a bit higher for me. This isn't a pair that I'm looking at trading anyway But if you are then I think this area Top as far as this one six nine round number where we are currently is actually quite decent for a potential long trade I really do you've got a wide zone of demand there and when you get those wide zones of demand what you want to do is break that down one of the ways to break that down is by Looking at areas of horizontal support and resistance Within that demand zone so we know that prices are making higher highs higher lows and any pullbacks I think into that 0.67 cent area or just above it I think would be a nice area to look for potential long trades You also have a bit of a mini area right here as well if you are looking to buy the New Zealand dollar That's been used as support and resistance in the past But again, not really a pair that I'm looking to trade short trades now long trades You're pretty looking at pullbacks into you know the earliest is going to be this 60.6775 area. So that's really the area to look for any kind of long trades if you're looking to take this currency pair Moving on to the pound dollar and the pound dollar Again in a risk-off environment and again the British pound probably being slightly more affected by the Russia and Ukraine invasion You're seeing again the pound sell off a little bit again referring back to the The impact of the Direct trade exposure to Russia. Yeah, the UK is there. So again, you can't expect really technicals to work out 110% simply because it's you know the prices are being driven And they're always really driven in the medium to long term by the fundamentals, right? So we've got a supply zone there And as far as a location is concerned, I do like this area As a as an area of technical, you know, it's it's a low But again, you'd have to really believe that the pound is going to increase in value somehow against the US dollar So for me not really something that I'm interested in I think if anything I think again if any pullbacks is pretty going to be more continued pullbacks And and the power for these resistances to the downside lower highs lower lows So a bit of a pullback to the underside of that area is decent for a potential short, but looking at the the pound We've got vacancies are increasing for every type of job in the UK So over 220,000 new jobs job adverts posted in final week of February figures show tight labor market That is surprisingly worrying Bank of England officials, but it's positive news. It is positive news for the UK economy And I think the situation it says that there's a quote here says we're new with renewable uncertainty and a huge rise in energy costs We are currently experiencing the business confidence We have seen over the past few months could well be dented in the coming weeks and months. So again, um, you know with the I guess the contagion of the Russia tensions and Ukraine tensions says John Gray vice president UK operations and analyst software Firm, uh, it will be crucial that we continue to monitor the data for signs of how Employers are reacting to this new situation. So, um, Let's see what happens again Again, but generally there is there is good news Um, uh, when it comes to the hiring and the UK economy, the problem is is again The tensions as well as the inflation problems, right? So let's see what happens there But for me, I think it's probably more downside if I'm looking to Trade this currency pair, then it would be continued the shorts that supply um, moving on to the euro Zola euro dollar again, um, it's a no brainer Um, I was looking for a pullback really into this supply zone to get short just didn't happen. Unfortunately So, uh, we've actually now That demand has been taken out and that now adds to another supply zone. So if we do get a pullback We do get pullbacks what I'm looking to do again, not financial advice I'm looking for, you know potential, you know shorts around here on a pullback um and again looking at uh from from europe The ECB to press pause and stimulus plans as war impact Wade so officials prepared to do what is needed to prevent to preserve stability and economies still think a hike in 2022 or still see a hike in 2022 with qv to end in september, um, but I don't know whether that's it depends on whether things, um, you know develop or how things develop So the european central bank is set to take a time out from plotting its exit from stimulus as it assesses the damage of Russia's war in ukraine could inflict on the continent's economy and you know, central banks don't want to hike rates Um, and their economy is really not growing, right? So from that perspective, they are behind the curve Um, and they're the most affected by the uh by the war So, um for me again, I think the path of these citizens is to the downside again I've been saying this for for ages, right? There was a period and I do believe there will be a time to buy the euro But at the moment it's just not uh now especially with the the war going on and as well as the impact of of um the the war on the european economy, right? Because that also, you know, you're gonna have to have an aftermath just because the war is over It doesn't mean that you should necessarily buy or that i'm going to be buying a buyer of the euro We have to see how the impact of that um of the situation um has affected the euro And if it's affected the more than for example the u.s Economy then again for me, it's still shorts all the way. Um Again looking to buy the euro and there's nothing there's no there's no area No level that i'm looking to buy the euro You'd have to really wait for proof of value meaning you'd have to wait for a situation like this to occur where prices start to, you know, move a lot higher then come back down Potentially, you know proof of demand for the euro that might be the floor But who knows but there's you know if prices do move up then that will be a proof of value And then you can assess if prices do you know come down anywhere around here Maybe pull backs on on higher highs higher lows, right? Um But yeah as it goes the divergence is still there and um until my path for this Resistance is still to the downside Moving on to the australian dollar and again australian dollar Going higher in a risk-off environment might seem a bit strange I'm not paired i'm trading, you know specifically but from the perspective of A commodity prices, right? So commodity prices making, you know, um higher highs Sorry, not that one. So commodity prices saw most in decades So as russia's invasion of the ukraine intensifies the volatility in commodity markets increased With the russian economy becoming increasingly more isolated by the sanctions. Let me just zoom in a little bit And its products boycotted Brent crude futures searched the 10-year high while EU natural gas new castle coal aluminium copper palladium And we hit all time and all time high, right? So that is helping actually commodity currencies like um the The australian dollar, right? So, um, I think wheat is um is making highs as well So you've got demand zones And uh, you know the australian economy is an is an export of wheat. So, um We've got Here so again, not all risk-off scenarios are the same You have to treat each one differently in the market. It's pricing in Higher commodity prices, which is boosting the australian dollar, right? So any pull backs if you want to get Long on the australian dollar versus the us dollar Then, you know, that's what you want to do If not, then then you're looking for short trades Then I think that supply zone is decent for a short on the australian dollar And buying the us dollar but again personally not looking to trade this currency pair at all The divergence it while it's there. It's a lot tougher Fundamentally, so it's not really on my list of of currencies to trade moving on to the Aussie yen and again traders are a bit baffled by the fact that the australian dollar is going higher and um Again, there are nuances to every single risk environment. And in fact if we do go to the um Or where is it now one seconds ing March 2022 monthly economic update You'll see the relatively Relative ranking when it comes to the most affected Economies in the asia region and the least affected Yeah When it comes to again the russia ukraine war and what you'll see is that japan Actually, um, it says Before I get to that says relative ranking table most affected at the top and least affected at the bottom So the most affected are japan. Yeah With a rank of 4.75 and the least affected at the moment is australia. Yeah So when you look at that divergence from a risk perspective, yes, you know, you're seeing um generally the the japanese yen should want to You know increase in value when it comes to it being a safe haven um Play currency play but from the from a from a from a I guess a nuanced perspective The australian dollar at least Affected out of the two plus you've got the you know the the fact that you have commodity prices rising Which you know adds value and demand to the australian dollar So that's the reason why you're seeing this occur So really if you think that you know, this is going to continue to occur Then any pullbacks will be decent buying opportunities, right? If you are looking at potential sales and buying the japanese yen then Then you're pretty much looking at this area The 85 round numbers round number where we are right now and zooming out a little bit I guess probably yeah the the market highs the recent market highs around that 86 um sent 86 25 Area and that's buying the the the japanese yen But I do think the power for these resistance is still going to continue to the upsides And especially in a risk if if risk starts to come more back on then off and Finally looking at gold and gold, you know making a tear as expected Again, many traders were were moaning and complaining and saying well, why is gold? You know come down and things like that Again, the market doesn't go up and move up in a straight line, right? It just allows the smart money to start to you know buy more at a cheaper price, right? So prices are pretty much moved in about a week 18 from the lows at 18 78 back up to you know, 1970s Right while retail traders are complaining the moaning and about fundamental analysis not working The fundamentals are working just fine. Just just just just fine So here we are and Again as risk starts to escalate still you can see Really where you want to be looking for a buy trade and again any pullbacks into those demand zones potentially You know are buying opportunities if you think that you know things are not going to get resolved anytime soon from this From a Short in perspective a supply zone perspective. You've got several zones. Let me just clear this up. I guess Probably from here to around where we are now. Yep there and then you've got another All-time high which is going to be here supply zone So again the continued conflicts should push the price of gold higher If there is again a bit of a A resolution then you're probably expecting a sell at some point But also as well be aware that the that gold does react to dollar strength or weakness And another contributing factor to potential gold strength will be you know rising inflation as well But I think gold at the moment is being driven by The increased risk of sentiment. Anyways guys, that's it for this week. I hope you enjoyed the analysis And like I said, don't forget to like subscribe and share This video with your with your trading colleagues if you have any and take care and I'll speak to you all soon


Amnesty International and others knock federal government as Minister of Information, Lai Mohamed, robbishes the Leci Massacre Report and the Inter-Party Advisory Council, IPAC, calls for President Bahari to assent to the amendment or the amended 2021 Electoral Act. This is Plus Politics, I am Mary Anna Corn. The Minister of Information and Culture Lai Mohamed has described the report of the Lagos State Judicial Panel of Inquiry on Restitution and Victims of SARS-related Abuses as one laced with discrepancies, inconsistencies and was unverified fake news. He insisted that nobody was killed at the Leci Toll Plaza on October 20, 2020. He also said the panel only wasted taxpayers' monies by coming up with such an unsensical report and he labelled it Tales by Moonlight. While joining us to discuss this are journalist Abdul Lahee Hassan, Karl Chinidu and Public Affairs Analyst Uche Chuta. Thank you very much Abdul Lahee for joining us. I am going to start with you Abdul Lahee.  What do you make of what's happening right now? Well, good evening. Let me say first that it was really a good attempt by Nigerians, thousands of young Nigerians including women and youth who in October 2020 went out en masse to protest against the police brutality and also called for the SARS, Particle Police Unit of Sprat. That was a good move but again people died and there was a destruction of properties, which of course led to the setting up of the panel of enquiries to investigate these killings like in Turkey and in Lagos state. Now a lot of us out there, I mean international community wanted to see what the outcome of this report would be and it's really not a good say out here, especially with Lai Muhammad because what we do know is that what he says oftentimes is not what the government intends to dish out to the public and even when he's being called that says don't go back later and say no I didn't say that so it's like us having no trauma in Nigeria. So this report really it is disappointing to have Lai Muhammad somebody that knowledgeable you know who had been in the limelight and the public sector for a decade in the response to such a report you know he it's enough to say that you don't agree with all the findings but to describe a report as it tells by moonlight a program which you know in the 90s was one of the favorite shows I watched because it's really like a tale for children is really unprofessional and if this is an attempt to go by I want to believe that Lai Muhammad wasn't speaking on his capacity as the minister of information for the Republic of Nigeria but really speaking for the entire government and including Muhammad Abu Ari himself and I would want to conclude by saying that this is an attempt by the government to throw a blanket on this report in a way to say we are not interested and even though there's a push for the recommendations to be implemented we will not go ahead with that because he said it did not he's going to change their mind on that too a minister should not speak to people like that because Nigeria is already tensed we have issues of insecurity from almost all the regions or zones of Nigeria unemployment is on the high inflation is today two digit that's enough problem for Nigeria to deal with already and you don't want to respond to them you know in such a manner which he did for me if we are in a civilized society and especially a person of Lai Muhammad who thinks he knows it all and he's highly educated I think this calls for his resignation well talking about resignations now one of the lawyers that was on that panel Adebu as that yesterday was calling for the resignation of not just you know the governor he's calling for a resignation of before before we get to the resignation part he he is being threatened by the way if you've been following this story a young lady who testified in front of this panel was almost butchered yesterday she was left for dead but thank goodness she's alive, Kemka I think that's her name she she made it and she was threatened you know and this is what Adebu is also saying that he's being threatened and he thinks that these are government goons for the want of a better word he thinks that these are supporters of the government but I'm wondering if the state government if Lagos state government put out all that money time and energy and put together a panel to investigate because when the first when people were making arguments as to whether or not people were killed or soldiers were even dispatched to that place the first question was well where's the evidence how are we sure that this is true but then the panel has come up with a report and now people are being targeted as a journalist and as someone who's watching from the outside I'm wondering um what do you think the government really is going for because is the government not ready for the truth or is it that they're not ready to deal with the consequences of what this report is supposedly to bring yeah I think I'll go with your second option yeah the government the government know when when we're talking about the government we need to look at it um in its um um how would I say 360 view of it all which includes the executive you know and the legislature and of course um the judiciary because if it goes down a lot of people will fall because there is no way that the military it doesn't matter who was that the military or the police or the the more polar as they are called they cannot on their own authorize that this part or the plant to any area at all they call a rough spot for that has been exposed or of course um has some tendencies of violence you know uh you know taking place they cannot be there without an authorization so what I'm trying to do might take care is nobody wants to fall nobody wants to fall including the state governor nobody really wants to take nobody wants to show that that responsibility but you see until we have people who become accountable not only to their words about actions then we are not ready to change as um as a society as a state and as people we are not ready to do that so nobody wants to go down president mohari for all I know is going to end his tenure when um 2023 um so he's not thinking like he's not thinking much about what the outcome might be but among the ministers we are some of them do for now as we know have intentions of becoming governors but are not talking about it yet they were doing for the right time to to declare or make public the intentions you have honorable members you have senators all for I know have long-term political ambition say in the next 20 years nobody wants to go down because they feel that if this goes down um it's going to somehow create a dent in their political career or credentials so nobody wants to take responsibility that's what I say Carl you work with civil societies and um this is also a class for concern I'm curious governors of states seem to be very quiet on this particular issue law makers seem to be very quiet about this issue our process now out which one way or the other is indicting not just one person but many even the the Nigerian army the Nigerian police and governments at all levels because again the army takes its order from its boss and its bosses take orders from the commander in chief of the armed forces which is mr president so again um what's your take on all of this in Broglie or for one of a better word hula baloo hula baloo Carl yes I am here you go ahead the issues are very simple here because the president is the commander in the armed forces so like you rightly say the armed forces take direct command from him and we know that the technology of our secret mission here that most state governor can even order the military out of their parents without the go ahead from the president and commander in chief so I think that the pop stops to the trouble is present on this matter whatever the Nigerian army did on the field comes back to him because he is the commander in chief he's the number one military person in Nigeria whether he is a civilian president or not because he has that authority as commander in chief so whatever the military did are the likely to get conspired directly to president Muhammad Bawari because they were asking for that interestingly and I wonder why do you think that the lawmakers and our governors seem to be a bit more quiet on this issue and not pushing us we hurt them very vocally when they were talking about vat now again we're also not hearing anybody else other than those who have political ambitions talking about this issue and pushing I'm talking about the likes of the former vice president at Iqab Abu Bakar we've also heard from a former senate president who obviously has intentions to run and other politicians who have political ambitions those are the people we seem to be hearing but those who seem to be serving us those who we voted into office to represent us and represent those people who were killed seem to be very silent about this why do you think that is well like I said there's the sense of collective sense of guilt and shame over the leki massacre because the political class for the first time we are actually brought out in the true colors they they deserve to be so and besides too the fears of another round of riots is also keeping all the political actors together on one board so that like let us stay together and make sure this thing doesn't erupt once more I think that it is actually very sad that people are no longer talking about the land that we are lost at leki but instead they are I don't it is unnecessary debate so actually whether it took place or not but that is the normal leki on my ground so like once more I think they are all they are all in it together and they want to cover it up so that you wouldn't get out of hand okay this is interesting um how about young people the average young Nigerian this obviously um is something that is worrying remember just recently um there was an attempt to protest and march on the anniversary of the death of people at that toll gate and we saw the might of the police we saw the might of you know the government at that toll gate how does the the aftermath of this I mean the report has still is still being you know looked at by the government but this report has been given we've had some of the important parts of this report made public um and we hear that even after the army had left the leki toll the police came back to do some more damage and with all of the back and forth with line mohammed calling it uh you know a tales by moonlight and saying that there are many consistencies and it's fake news how does this affect the psyche of the average and Nigerian and the average young person who's fighting for good governance who's asking for a better life and asking you know that the police will stop um wrongly profiling them well the like the they wanted to come out again on October 20th and the police went to leki toll gate and stood there trying to stop them from having a memorial was living a protest was also a memorial of the lives that were lost now the issue is actually bigger than we are actually talking about it has international ramifications bohari and his government are basically right now on trial for international crimes and maybe because he feels he has some immunity um nothing's gonna happen but you have to deny this as much as they can because come 2023 a case is already being lodged in the hake international court for crimes against humanity shooting innocent civilians and this is what they are afraid of this is why everyone is quiet it's a big deal it means political people in political office may not be able to travel freely after 2023 and not be arrested it's a crime you just like it's a Tiananmen square or a you know combat in in Nigeria you can't do something like this without any ramifications the international community is watching and they're waiting for 2023 and immediately his term expires in 2023 elapses this is going to take a whole new dimension and this is the reason why lai has to deny this to the last even with overwhelming evidence he has to deny this government they can and you're going to notice only lie is going to talk about this issue no other government official is going to say they don't know who to be quoted lie has not moved past his mode campaign mode he still feels his new position would in the apc trying to wrestle government from the pdp so he hasn't changed so he can see anything that that's a method that has worked for him is still working for him he's not he doesn't have the capacity to move to become an official of the federal cabinet as a minister and speak as a minister he doesn't have the capacity it's asking for too much for him to speak as a minister so he's going to keep on saying things like this but he's going to be the only one speaking like this everyone is going to remain mute because they know that anything they say can be held against them in the court of law international court of law i'm still going to push you on the issue of the psyche of the average nigerian what what happens to us because we see a mass movement people are leaving it's now a thing you know i go on linkedin and i see people asking nigerians if they're interested in moving away from nigeria and so many people are raising their hands because they seem not to be comfortable in the country so um if we're seeing so many people move away from the country for fear of whatever um what does this now playing out and and the fact that government is making a caricature of it or a joke out of this what does it do to the psyche of the average nigerian who's still staying here and having hope that there will be a better nigeria i mean demoralizes us you know like on on october 20th you know once this report came out and the government began to deny it people were downcast young people were downcast we we we we leave the memories all again first of all the report came out we're thinking about it then the government denied it and there's sadness and but the the truth is that all nigerians can't leave the country even as much as i hope to and wish that i can happen it's still our country and um we we we we have to deal with this we have to keep on fighting we have to keep on hoping we have to still try and keep on make our leaders accountable yes there's despair amongst young people especially with the way government is denying it but it's some small glimmer of hope where another government lego state government released this report we are putting a federal system and lego's is a federating unit of nigeria so there's still hope um just because some people at the center are denying it doesn't necessarily mean they didn't happen it doesn't mean there won't be restitution it doesn't mean that justice will not be served we are hopeful um so we we're not going to lose hope this is a we're happy that this happened because it means that there's some small hope it actually gives us a sign of hope that things might change i'm going to come back to you um abdelahi um if there's uh if there's a collaborative um oath of silence per se um by all concerned including those who are in the political class like i said illa and who were supposed to represent us so those who used to speak up before but are now silent um i'm thinking um what happens come 2023 is this going to affect not just the ruling party uh but of course the opposition because most of these people who are in the national assembly and some of these governors uh are also part of these opposition parties again every state more states where these protests took place or where there's been reports of police brutality set up panels um to look into this issue but it's only lega states that has followed through so what happens to those panels should we not be asking those questions in the other states again nobody's talking about it and why now um first of i don't believe that margarita as a nation if at all there is we don't have an opposition party we don't because if you observe clearly the trend has been that people from pdp after a while we criss-cross they jump over to apc after a while when it's an election time they they come to you know like that has been the trend people just keep jumping from one party to the other so there was never really a healthy opposition anywhere in Nigeria that's one um two you would understand clearly like the states where people were killed including police officers you have equity you have or shun uh maybe and parts of uh the north for instance there are all apc states so for me people are still not practicing democracy as it should be practiced so it's more about the party the interest of the party and who we owe our allegiance to as opposed to what benefits the society and of course put in national interest first so if this happens come 2023 well this is where i see you two have the qualification who have the necessary requirement and um the knowledge you know in terms of leadership now leadership i mean every sense of it not leadership because you are a boss at home your family a wife and two kids doesn't make you a leader i mean the leader understands when to take actions that even if it means hurting people next to you but you have to now what happens is uh what will happen is that um definitely there will need to be a change of government and we need to have people new people out of the system as we know now people who are yet to enter the system you know say um occupy um sensitive positions and this is the time for us to start now so beyond answers let's have people like uh my my poor panelist one of them is quite young you know to lead a campaign where people with the requirement people the qualification can come together already and see how leadership you know can can come back to the youth and because you cannot have somebody's people from the 70s and 80s use that old mentality to govern a state where like everything today is changed we are now at the modern age you know 24th century you know this needs to change you know that's what i see okay um back to you car um again ask civil society he's he's made a he's made a great point we need to fight but how do we fight why i'm asking this every single time a group of people and it has nothing to do with answers a group of people stand up against the government it's either we see a group of people that are being paid to stand against those people and speak for the government or we see the full might and the power of the government whether it's federal or state again how do people fight twitter is it's still it's now become a back burner it's nobody's talking about it anymore and so if you have money you can use a vpn and go and go ahead and vent to the space because nobody's going to listen to you um so some of these rights have been taken away from the average Nigerian you really can't protest the government is going to come out and say you've not been stopped to protest but that again the Lagos State Police Commissioner will come out and say you're not allowed to protest don't come out tell your children to stay at home so how do you fight what do you do how do you go about letting your voice get heard without losing your eye your arm or even losing your life well it is the supreme irony that the government that came into power to protest has done everything possible to ensure that protests are outlawed and truly a sad world and uh of course how does it affect the psyche of Nigeria you can place it place it just oppose this side by side with what will happen in any other country which soldier will open fire on somebody waving the national flag i think it's national item nobody does that and that was the mindset that these young stars went to with to look like a because everybody was so that as long as you have your national flag national item nobody will touch you and you saw the horrendous massacre that took place in Lake so what if you ask how does it affect your psyche it generally does because for once Nigerians are confronted with the spectrum of the government a country that does not care for and of course it's it's it's also not perfect that people should be making every effort to jump the boat jump boat and live so as uh with regards to 2023 i really don't know what's going to happen because the answer is the question is who is going to vote and for who like you said they have shut down the social media space they have shut down the protest space they have shut down virtually everything and of course with the security across the country so i Nigerians are really scared right now and i don't think that even if you call a protest i do this it will be sure that a lot of people won't come out because the government has demonstrated that it is capable of doing anything no one's sufficient of murder of course we've seen situations where those who protested at the n-stop panel they go have been targeted and have been attacked for one after the other so the the atmosphere in the country right now is for the young people who are put into society and everywhere there is this poor people here everywhere this goes mental uh well uche you you have the last word and the blickness that i i sense in in in um in carl's statement makes me really not know what to ask you but i will ask um so going forward what's the shred of hope that we can hold on to because there's nothing we can do like you said we all can't run away from nigeria it's our country and we cannot be run out of our own country so what do we do going forward what's the shred of hope that we need to hold on to um what's that thing that the average nigerian who's watching tonight can hold on to and that they can give them hope well let's let's continue participating in the civic processes um civic processes in the sense of voting and also putting yourselves in position to be elected uh yes i understand that the the electoral system has been hijacked by the states even security forces which can show their candidates of choice always emerge as winners but it does but they still can do so much they can they can still if we participate in the numbers that we came out on october 20th um 2020 they can't rig the elections the same way they've done it before in the past so we we need to come up with force we need to show ourselves on that election day and say you know well let's build up let's build up momentum to the voting day in the same way we built up momentum in 2015 when the present government was in the position and they riled up nigerians and told them all sorts of scary stories of corruption and days and they're turning nigeria into uh some utopian states let's let's build ourselves up in that momentum i like the way you keep on the stress in 2020 the stress is about change of government keep it on let's hope and let's let's let's be our final push let's be our final push and say you know what 2023 that's what we're pushing or pushing for candidates in in the national assembly and governorship position as president people who will do the right thing and we're going to come out on that day regardless of rain sunshine whatever and we're going to put in and vote in candidates who represent our ideals and the nature of the world okay well uh abdelahi hassan khal chenidu and of course uchi chuta thank you very much gentlemen for being part of this conversation thank you all right well thank you all for staying with us we'll take a short break now and when we return the electoral act amendment bill is at the forefront of this conversation


Hey, Psych2goers, welcome back to our channel. Have you ever had a feeling in the pit of your stomach as if something was off? Something just didn't feel right. This is known as a gut feeling. Our gut feelings often relate back to our survival instincts and primal wisdom. But how can you tell if you're overthinking or if that strong feeling of yours is correct? Well, here are six signs that your gut feelings are correct. Number one, dreams. Do you often feel your dreams are trying to tell you something? Many psychologists analyze dreams. Sigmund Freud, the founder of Psychoanalysis, believed that unconscious thoughts and forces constructed a wish, which was then expressed or represented in a dream. Many believe there are symbols and hidden meanings from our subconscious minds in our dreams. So if you notice that strong intuitive feeling of yours is showing itself in your dreams, it's best not to ignore it. It may be that your subconscious mind is trying to tell you something important. Number two, you feel you need time to think. If you feel you need a moment to sit in silence and think through a strong feeling of yours, do so. When we feel overwhelmed with an intuitive feeling we can't shake, odds are our body is trying to tell us, this is real, trust me. Number three, you feel you're in danger. Our primal instincts are more often right than wrong. When you can't help but feel you're in danger, you should never ignore it. It's best to leave a situation that makes you feel this way and listen to your gut feeling. Number four, trust muscle memory. Are you quite skillful at a certain sport, hobby or art? When it comes time to perform your skill, it's often best to trust your muscle memory as opposed to overthinking. Trust your instinct. A study by the University of Chicago found that while novice golfers did better when they thought carefully about their putts, the performance of more experienced golfers got much worse when they reflected on what they were doing. So sometimes it's simply better to trust yourself. Number five, your body is trying to tell you something. Do you feel panicky? Are you short of breath? Has that feeling in the pit of your stomach moved on to a literal concerning feeling in your stomach? Like seriously, you may need to see a doctor for this pain. Well, when your body is physically telling you something isn't right, it is best to trust it. Our heart rate often increases when we sense danger. Our breathing can click in. There are ways in which our body responds to danger. So it's best to trust your mind and body. And number six, you have a clear desire and feel this is right. Do you have a passion you can't stop thinking about? A strong desire to follow a certain career or apply for a certain job? It's a good thing to follow what makes us happy and fulfilled. So if your body is clearly telling you this is what you want in life, despite what others say, listen to your passions. Listen to that gut feeling.  So you're not just hearing from your gut, you're really just hearing from yourself. It's time to listen. Speaking of which, my tummy is rumbling for some cornbread cakes. Definitely, time to listen to this gut feeling. So what type of gut feelings do you often get? Do you trust them? Let us know in the comments section down below. If you found this video helpful, don't forget to click the like button and share this video with someone who could use it. Subscribe to Psych2Go and hit the notification bell icon for more content like this. And as always, thanks for watching.


Matteo, thank you everyone for sticking with it and so let me start sharing the screen and oh I see already quite a few chat messages. It's just hello and okay it's just hello but yeah that's that was a little bit gosh there's many questions before I even start. So I'll have a look at the chat and tell you when there are questions. Oh that's very kind thank you Matteo. But before we start are there any questions regarding the last two lectures before we move on? Okay so if not then the what we're going to go for now is the today is the multivariate normal distribution so we're moving from one-dimensional distributions to two distributions so multivariate and this is particularly relevant because as you know the course is called probabilistic modeling and in fact a fairly large class of models so all linear models essentially can be understood in terms of multivariate Gaussian distributions and the computations that you need to do on these models to do base and inference are simply conditioning and marginalizing multivariate Gaussians which is a particularly important task. So the one thing that I will use heavily today from last week's lecture is the is the change of variable formula. Okay so I'll recall that if you have a random variable x distributed according to px of x and you have a deterministic function then the distribution of y is the distribution of x the density of x evaluated at f minus one of y times the derivative to the minus one evaluated at f minus one of y. Okay and as someone observed last time all that I'm saying here is basically say that p y dy has to be equal to px dx if we want to use you know a simple although not entirely accurate mathematical notation. Okay so one useful exercise for you guys to do so let x be distributed according to a Gaussian distribution with mean zero and variance one then show that p of y for y equals x squared is a gamma distribution and in fact it is a special gamma it's a gamma that is called a chi-squared so it's got a particular shape parameter which indicates that it's the square of a Gaussian. Another immediate application of the change of variables rule is that if I have x that is distributed according to a Gaussian then y equals a times x where a is any number real number y is also going to be distributed according to a Gaussian still with mean zero and with variance a squared. Okay so I saw that there was a message in the chat and I'm not sure how to get to the messages so if you have a question just unmute yourself and ask it please it's by far the easiest thing because when I'm sharing the screen it's um oh it's still a good afternoon one good uh so this is a very simple consequence if you wish to use the change of variable formula the fact that the you have to replace instead of x y divided by a and so the density would become e to the minus y square divided by a squared but you also have to have a square root of a squared in front of it which is the derivative part. Second fact that I'll let you prove as an exercise or you can take it on faith but it's it's it's straightforward so let x1 be distributed according to a Gaussian distribution this time with a mean and one and variance s1 squared and x2 being distributed as another Gaussian distribution with mean m2 and there is s2 squared then y equals x1 plus x2 is also a Gaussian distributed variable with mean m1 plus m2 and variance the sum of the variances so this is a they're all well known facts of course you can rescale a Gaussian and it will remain a Gaussian you can sum two independent Gaussians and they will remain will give rise to a third Gaussian distributed random variable so now the question is let's assume now that we have uh d Gaussian variables so all of them are distributed according to a standard Gaussian with mean zero and variance one and they're all independent so I can gather these random variables in obviously a vector in rd and because they're all independent it's trivial that the density now in d dimensions of this vector random random vector is going to be the product of let's say p1 of x1 times pd of xd and by a trivial calculation I can rewrite it as you know each of these is an exponential of minus xi squared so I can rewrite it as one of a z exponential of the square norm of x with a minus sign and then two okay so this is my simplest type of multivariate normal distribution is the one which has got zero mean and spherical unitary variance so I can rewrite it as and I use the same symbol and for the one-dimensional Gaussian and the multivariate Gaussian but I'll put a squiggle underneath for the vector so the mean is a vector of zeros here and instead of a variance I have a matrix which is the variance covariance matrix which is the identity in the dimensions now all multivariate normal Gaussians can be obtained from this basic multivariate normal Gaussian via linear linear operations linear and affine operations so if I define now y equals to ax where a is a d by d matrix plus m this each entry of the y vector so m is a parameter vector of course so it's it's not a random variable is a number on our inner d each entry of the y vector is a linear combination of axes so Gaussian variables plus a constant so I certainly have that y is going to be Gaussian distributed as well now the question is what is going to be its mean and its variance covariance matrix and so if I move to higher dimensions instead of a single number for the mean and a single variant number for the variance I need a vector for the mean and the matrix for the variance so I can calculate these very easily because the mean vector by definition of mean is the expectation of the random variable y the random variable y is obtained from this formula so it is a times the random vector x plus the constant vector m and the expectation is a linear operator so this will be a times the expectation of x and the expectation of a constant is just the constant itself the expectation of x is zero because I've started with the centered spherical Gaussian so this is just m so the constant shift is the mean oh I missed the question okay what about the variance sigma how do I calculate the variance sigma well sigma by definition of variance is the expectation of the square minus the square of the expectation so the expectation of the square here since it is a matrix I have to take x times x transpose this is the covariance matrix minus e of x times e of x transpose now e of x sorry I meant y yeah so we got so I see things flashing but then they I know here is professor can you show the formula for variance covariance matrix id of the x vector m so the variance so id is just is the identity in the dimensions yeah so it's one one one big zero here and then of course sigma is not the variance of x is the variance of is the covariance of y and now the expectation of y is m as we have already computed so we have expectation of using the formula for y I put ax plus m times ax plus m transpose minus m m transpose okay now I have to work on this now using the linearity of the expectation I get a expectation of x x transpose times a transpose so I've taken the product of the two terms the quadratic term in x then I get plus twice a expectation of x times m transpose minus the expectation of m is a plus sorry the expectation of m is m itself and transpose minus m transpose okay so these two terms go away this term the expectation of x is zero yeah because x is a centered spherical Gaussian now the expectation of x is zero the expectation of x x transpose it's its second moment which corresponds to its variance covariance matrix because the mean is zero so the expectation of x x transpose is the identity in the dimension and so we have that y is distributed according to a Gaussian with mean m and variance covariance matrix a transpose okay notice that it makes sense because of course the variance covariance matrix of a Gaussian distribution needs to be a positive semi-definite matrix and this is a positive semi-definite matrix because it's a square or a matrix essentially okay so these straight away tells you how you can for example sample general Gaussian vectors so if someone asks you to sample values y from a Gaussian with mean mu and covariance sigma then what you need to do is sample x from n01 so sample independently each entry of a vector with d dimensions then compute such that a a transpose equal sigma d there are many algorithms for computing the square root of a matrix but the best numerically stable one is the so-called Cholesky decomposition and then compute y as a x plus okay so in many cases I mean it happens quite frequently actually you might have to sample random variables from a specific distribution if your specific distribution is a multivariate Gaussian with a particular correlative structure all you need to do is to compute the square root of the covariance matrix and then transform spherical Gaussians to obtain general multilinear matrices multilinear multivariate Gaussian matrices okay so just to recall very briefly the steps so to introduce the the multivariate Gaussian distribution we started from spherical Gaussian and we showed that you can obtain the general multivariate because I can obtain any sigma and any mu by taking a linear transformation of a spherical Gaussian and in particular of course the you know the sigma that we compute as a transpose contains all the various correlations of the variables because all the correlations are induced by this linear transformation and this as a bonus shows us how we can compute how we can sample random vectors that have got a particular correlative structure so let's take a one-minute stop for questions if there are any either unmute yourself which is the best solution I think or by the way because of the change of variables formula we also know what will be the density function of a multivariate Gaussian what you will have is that y will be distributed according to you know I have to have my exponential bit first minus a half so where I had x I'm going to have I have to replace x with y minus mu times the inverse of the square root of sigma d so I'll have y minus mu I can either take it as an invertible major as and then because of the inverse of the derivative I'm going to have a determinant coming out here the square root of the determinant which is this in here so in short so this is the pdf of the multivariate Gaussian now one advantage of a variation that we've made is that it's immediately clear that the entries of the sigma various covariance matrix are the correlations in the second moments of the Gaussian so now if I want to marginalize t exponent sorry t is not an exponent is a transpose okay and so you can either take it to be symmetric yes please so sigma is indeed I mean it is symmetric it doesn't have does it have to be symmetric sigma has to be symmetric you see and sigma will be symmetric because it's a transpose so if you transpose these you know when you transpose the product of matrices you transpose the the the individual matrix but you also swap the order so if you transpose the a transpose you will get a transpose yeah sorry yeah thanks so it has to to be symmetric then why do we need that algorithm to find a square root I mean you said we need to find the square root of sigma I mean why would we need that then and why do we need that because to sample I mean this is what you know to get it won't be a right it will be square root of a transpose which won't be a the square root yeah but normally you're not told them normally you're given sigma you said give me samples from this general Gaussian with these various various matrix sigma then you have to compute the square root of sigma yeah so what I'm asking is it is to find a we use square root of sigma right yeah but square root of a transpose is not going to be a square root in the square yes square root of a transpose is going to be a because the definition of of I mean of square root of matrix is a matrix such that a a transpose is going to be okay so it's this definition of square root thanks so there's many many things that we may want to do with gaussians motivated gaussians and a simple one is marginalizing them okay so suppose we have now a 3d Gaussian so our vector y is made up of three numbers one by two y three and is distributed according to Gaussian with a certain mean and a certain various various matrix okay now if I'm interested in let's say a projection let's call it projection one two of y which is a vector y hat which consists only of the first two components so I'm marginalizing out the third component so what is the distribution of this vector now obviously it's going to be a Gaussian but how do we compute its mean and its variance variance matrix well it's actually really very simple so what is the expectation of y hat well I have to take the expectation of y1 and the expectation of y2 and that's obviously going to be mu one mu two without the squiggle underneath which is the projection one two applied to the mu vector yeah what about the variance covariance so we know that this is pi one two what about the variance covariance matrix okay so what is going to be well variance of y hat well what we need to do as we did before is compute the expectation of y hat transport yeah but I'm going to say that's just going to be you know the first two by two rectangle square in the sigma matrix yeah so this is going to be equal to the sigma matrix where I take just a chunk okay because this is going to be you know the little matrix expectation of y1 y1 transpose by this number so y hat which is the projection on the first two axes of y is going to be normally distributed with the mean which is the projection of the mean vector and a variance covariance matrix which is obtained by applying let's say the projection to the two sides of the variance yeah and that is equivalent to selecting the first two rows and the first two columns the indices up to two okay so marginalizing means removing in multivariate gaussians the other thing that we might be interested in doing is conditioning now conditioning is a bit so let's say we have a vector y again is three-dimensional and it's distributed according to a Gaussian with mean mu and variance covariance matrix sigma and now suppose that you fix let's say y3 what is the distribution of the remaining two entries y1 y2 excuse me professor yes please oh you said I I I didn't catch the last thing you said marginalizing is removing what entries it's just basically you know you take away so if you're marginalizing the third entry you take away the third entry from the mean vector when you take a third column and a third row from okay okay I okay I understand I see it was just a bit illegible oh yeah yeah you're right it's totally legible let's let's write it a little bit better so what about conditioning yes so can you again repeat what is projection projection y1 I mean what you wrote as pi I didn't yeah projection just means that uh you know mathematically you can see it as projecting on the hyperplane defined as y3 equals zero yeah so parametrized by y1 and y2 okay I mean like I mean why did you I mean I understand this marginal marginalization but I don't understand why you used this notation I mean yeah okay so the the question is is a is a good one so why is marginalizing just ignoring one well that is what marginalizing is you know so marginalizing mean regardless of all of the third vector for example the third dimension of the vector here we're marginalizing y3 so it means what is the distribution of y1 and y2 regardless of what y3 is doing yeah and what I need to do is essentially averaging out y3 so the way I've introduced marginalization on Monday is by doing an average yeah I mean thank you but what I'm showing you here that's that's that's why it's kind of interesting and not entirely trivial is that doing that average in the Gaussian world is equivalent to just removing entries yeah so y1 and y2 are random variables on their own accord they're going to be Gaussian random variables because they're obtained from the big y y1, y2, y3 by a linear operation which is this projection what is going to be the distribution of these Gaussian random variables well we have to compute it's since they are Gaussian it's first and second moment and to compute that we can either do an integral which is a pain or we can use the linear transformation on the moments which is what I've done here so that's why so that the kind of the message that I wanted to convey really in this lecture but particularly in this part is that in the Gaussian world because you know that the distribution is entirely determined by the first and the second moment then you can obtain the same results by computing moments which can be much easier as it is in this case as you can do by doing integrals so I saw there was another question popping up here why is y1 yes of course it's yeah well I mean the transpose of a scalar is itself so let's just remove it for the sake of clarity yeah one more question okay thanks yeah so that's not an entirely trivial thing but because you're in Gaussian world you can do computations on the moments and that is the same thing as marginalizing uh now conditioning instead is a little bit more complicated uh so what is the distribution of y1 y2 well we we have to to look at it so it's going to be a Gaussian again and why is it going to be a Gaussian well how would we compute so what is going to be p of y1 y2 given y3 okay well let's just write out the the full the full gory details so we have a normalization constant then we have exponential of minus a half y minus mu transposed sigma minus one y minus mu so this is the the full but here you know we fix y3 so y3 is a number now it's no longer a random variable that's how you do condition you stick the number in the formula okay and we kind of have to write it out so we define sigma as then here we would have uh sigma one two three sigma three three in the end so what is clear it is it's still going to be a Gaussian here because if you stick a number here this will remain a quadratic form in y1 y2 so the exponential of minus a quadratic form is still a Gaussian the problem is that you have to invert this partition matrix so this is one of the most painful calculations particularly when you have more than three dimensional matrices you have to look up something called the partition inverse formula excuse me could you perhaps specify what is for instance sigma one two comma three all right yeah yeah so okay that's fair enough so what i'm trying to do sigma is a three by three matrix so i want to retain the so i'm selecting the first two variables as special and the third one as special because the third one i'm fixing as a number so i'm dividing the three by three matrix in a two by two matrix which is the covariance matrix before between the first two entries and then a vector here which is the covariance between y1 and y3 and y2 and y3 so this is a two by one vector this is its transpose and this is the variance of y3 okay awesome yeah sir to get this form did you directly use the base theorem uh no uh i mean i'm not there is a good reason why base is involved but you don't have to use base theorem you're just conditioning so directly y3 you just substitute the value of y3 in the absolutely that's how you do conditioning you substitute a value in okay and so as i said this is quite a a rather painful calculation and you need to look up something called the partitioning inverse formula is a rather lengthy formula in terms of the inverses of these various matrices now that tells you basically the blocks the inverses of the blocks so it's also called the blocking inverse lock i don't want to go into this but look it up if you wish there is another thing so there are two ways in which you can define gaussians so what we've started here you see when we started talking about marginalizing we start with a multivariate gaussian and give its mean and its variance covariance matrix and then we've seen that in this case marginalizing is trivial but conditioning is rather painful because you have to do these matrices matrix inverse the other way in which you can specify gaussians is by giving equations so multivariate gaussians this is more interesting because i could say for example that you know x might be a two-dimensional gaussian and then i could say that y for example is equal to a x plus epsilon so it's another random variable y condition on x where epsilon is gaussian so what does it mean to have this equation it just means i have a random variable x and i'm observing a linear transformation of x plus noise now what happens here is that the pair x and y which are a four-dimensional vector and there are also a four dimensional random variable which because it is linear is going to be gaussian distributed but what are going to be their distribution what is going to be the distribution of this well the mean is very easy so let's call this vector z so the first two and two variables so this is going to be a concatenation of the expectation of x the expectation of y i can write it out straight away the expectation of x is mu x the expectation of y is a times the expectation of x plus the expectation of epsilon this one is zero and this one is mu x so in the end i have that the expectation of z is the concatenation of the so the mean is mu x and then the mean of y which is a linear transformation is a times mu x what about sigma of this linear transformation of this four-dimensional gaussian which is defined started from a two-dimensional gaussian and a linear equation now to compute this i need to do exactly the same computation as i did before for my definition of the multivariate gaussian and what i will get is a matrix that has got sigma x and then it's got a sigma x and transpose okay now the reason why i'm showing you this is that defining multivariate gaussians as equations has a huge advantage in terms of conditionals because i could just say so i've defined z as the concatenation of y at x and y but i could also just write that p of z is going to be equal to p of y given x times p of x because z is you know it's a four-dimensional thing which is made up of two two-dimensional things p of x i know it is mu x sigma x p of x of y given x is trivial when it is given in terms of condition of equations yeah because an important conditional so if i know x well what do i need to do to get y i just multiply it by the matrix a and then i add some gaussian noise p of y given x in this equation-centric world is just going to be a gaussian with mean ax because x when i'm conditioning on it that means i'm sticking the value in i'm fixing it and then sigma squared the identity okay why do i insist on this conditioning because someone asked before are we already doing base theorem well we pretty much are so one simplest calculation that we can do with Bayesian inference is to think of observing gaussian random variables linearly okay so suppose i have now my y which is well let's make it a scalar for a change a transpose x plus epsilon so i'm observing with spherical gaussian noise a random variable x which gets multiplied by by a vector a so the let's keep it in the two-dimensional case in the multi-dimensional case so i'm observing via an observation process which is multiplying by this matrix a i'm observing a random variable x with noise epsilon now the question could be what is p so we have a very easy way of computing the conditional y over x and we have a prior over x so the question now becomes what is p of x given y so what is the posterior to do this we need to apply base theorem so we have that this is proportional to the joint distribution so it's joint distribution where i then stick y equal to a constant and this joint distribution i write it as the product of the other conditional of the other conditional that is my equation times my trial okay excuse me yes please at first you wrote a transpose at the first line first line at at first no no the last the last page yeah because i was yeah so yeah i didn't get it what why it changed i get i changed it because i was well because i made a mistake oh sorry happens to me as well okay so don't worry this is the correct thing that i meant to say let me see there is another question oh yeah what about multiplicative noise you know multiplicative noise makes things a lot harder so if you have multiplicative noise then you are not in a conditionally you're not in a Gaussian posterior world so your posterior will no longer be Gaussian and you can't do these kind of computations analytically in general so the world of Gaussians is limited to the linear world where you can add and rescale by constant but not multiply random variables the the simple thing is that if you have the multiplication of two random variables then you know when you go into the Gaussian you have to take the square and you get some quadratic terms essentially so let me one more question so let me finish this calculation this the first basic calculation we really are doing in lives at least in this course so let's not worry about the normalization constants so here we're going to have exponential of minus one half let's make it a brace so it's the product of the two densities so they just sum and we've got one minus y minus x transpose times y sorry y y minus a x transpose times y minus a x times one over sigma squared yeah that's that's my conditional you see this is the conditional that I put in and then I have a term which comes from the prior which is x minus mu transpose sigma x minus one x minus okay so this is it this is the p of x and this is the p of y given x that is implied by my equation okay and now I want to know what is the probability of x given y as I said when you want the probability of x given y when you're conditioning on something you're fixing it so what it means I look at this quadratic form and I want to identify the quadratic terms and the linear terms so I know that this must be equal let's say let's say z prime x of minus a half x minus m transpose c to the minus one x minus m so I'm writing the most genetic quadratic form in x and this corresponds to a Gaussian with mean and variance covariance matrix c and this will be the posterior mean and the posterior variance covariance matrix how do I identify them well I have to compare the terms here okay so by looking up here I see so on the left I will have a term the quadratic term would be x transpose c to the minus one x yeah that comes here has to be equal to the quadratic term here the quadratic term here I got a term coming from the prior the sigma x minus one and then I've got terms coming from the likelihood so from the observation so this has got to be equal to x transpose a transpose a divided by sigma squared x plus x transpose sigma x minus one x okay so these are the you see if I develop the square here I get x transpose a x transpose a transpose a x divided by sigma squared I get a sigma minus one so the posterior covariance is going to be equals will be a transpose a divided by sigma squared plus the inverse of the prior or to the minus one and then I do the same thing with the linear terms and then I will stop because I'm out of time I would have x transpose c to the minus one m from here x transpose c to the minus one m and then this is going to be equal what are the linear terms here well I got some linear terms from the mean and I got some linear terms here so I'll have an x transpose a transpose divided by sigma squared y and then I'll have some x transpose sigma x to the minus one mu x okay and so m the posterior mean is going to be equal to c the posterior covariance times a transpose y divided by sigma squared plus okay so one small observation notice that the smaller the observation noise dominant the term coming from y so the smaller the observation noise the sigma squared or the observation the variance of the observation then the closer our posterior mean will be to what the observation is telling us which is very reassuring so this is our first basic calculation so we computed the we have a basic random variable a Gaussian random variable observed with Gaussian noise and we condition to obtain the posterior over x or over y over x given our observation so I think my lecture is now out of time I kind of said most of the things that I wanted to say but if you have any questions please ask now or write them down and like you can email them to the secretary and they can be passed on to me or something like that because I realize that we've compressed quite a bit today I have a question yes please why is the projection of a Gaussian variable another Gaussian variable I didn't get it very well because a projection is a linear operator yeah and every linear operation on a Gaussian remains a Gaussian okay thank you okay there's another thing in the chat is that the question okay has the reference for today's lecture a lecture now I've been uploading a website or matrix or will it be uploaded I think if you look at the Makai book all of these things are there in the chapter around 23 I think on probability distributions excuse me professor are there maybe exercises perhaps from that same book that we could do to help us better understand I think you know if you read that book that will help you a lot in all your life can you repeat the reference name again please it's it's on the website is information theory inference and learning algorithms by David Makai thank you yes and there are a lot of exercises in that book also yeah very very useful to get a grasp of Asian inference and information theory and I mean I think you'd be if you know that book very well then you know you can come and teach us okay so there are no other questions then we take a short break of 10 minutes and then go with the second lecture of Domenica Buetti okay ciao everyone thank you video ciao Matteo ciao cuon stai bene tu let me stop recording you can gossip


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