Sir, you are a hero. I read a bunch of definitions, explanations and examples and only yours can make me really understand MCMC. Now I can continue my final assignment
Yeah I see you, League of Legends. hiding out there in the task bar-- thinking you'll just chill until Mr. Picton gets some free time. Well this great intellect has moved on. When given a choice between toxicity and flaming or creating helpful videos, I'll have you know, Jeff Picton chose the high road.
The town of Monte Carlo is in the tiny principality of Monaco (that is, a territory originally ruled by a prince) on the Mediterranean coast of France. Monte Carlo was -- and still is -- famous for its iconic, palatial gambling casino.
Nicely done. Would have been better if the Hastings correction to alpha was discussed. It was mentioned and even kept in the presentation, but then neglected. Seems either losing it, and justifying the loss would be good, or leaving it out would be better.
This is an awesome lecture that clears the mcmc concept. I am curious to know how can we apply it in partitioning of jobs on 2 parallel machines in order to minimize makespan?
Great video! Do you know how I would use the Metropolis algorithm to select random points from the tails of a Normal Distribution (or do we always have to sample from a Uniform distribution?) at a higher probability than selecting points close to the mean? i.e. I need the target distribution to be a Normal Distribution and the proposed Distribution to be the tails ((-4*sigma, -3*sigma) and (3*sigma 4*sigma)) of the Normal Distribution? Is this possible? Thanks a lot!
Hey Jeff, how does the software construct the normpdf of x(i) and x_c in the gaussian code example? Considering we start off with only a single x(i) value and then sample a single point x_c, how can one create an entire pdf to be used in the equation?
Good job, but you missed the punch line at 7:10 that a histogram of the number of times you land in an interval matches the shape of the curve; i.e., the number of times is a maximum in an interval centered at 0 and falls off in both directions. Maybe it was obvious to others, but maybe I'm a little slow.
Just in case it helps someone watching this very good video, here is some R code to demonstrate the Metropolis algorithm: # Metropolis algorithm -- Gaussian distribution library(ggplot2) mu
When you present Markov Chains, It seems to me that your Xi mean two things. Xi as a vector, is the GLOBAL state of the automata at time i. And you say Xi is also a single state of the automata. A better way should be to say Xi is the global state, and name the individual states Sj Xi = {S1,S2 ... Sn}
at 15:33 the first product between X0=[0.5 0.2 0.3] with T is not equals to [0.2 0.6 0.2]. actually it is [ 0.18 0.64 0.18], and converges to [0.2213 0.4098 0.3689]. am I missing missing some thing?
Monte Carlo named after a casino in Los Vegas? You need to get out of the US a bit more 😂 What about Monte Carlo the gambling city in Europe predating Los Vegas by a couple of hundred years! Otherwise a great video. Cheers
Your history of the naming is wrong. Monte Carlo methods get their name from the gambling den in Europe where Ludwig Boltzmann lost his savings trying to use math to win, using methods that now quality as Monte Carlo techniques
The video is great, but why would you think that the name comes from a casino in Las Vegas and not from the original one in Monaco, that the american one was named after?? 😂😂
Thank for the video, I have some questions. Let's say that we didn't know that the distribution was gaussian, how do we decide what proposal distribution to use? Even if we knew that the distribution is gaussian, how did you know to use normpdf (which already centers at 0 with sigma of 1) ? If the actual distribution was N(2,1) instead, would you still use normpdf ?
Thank you so much! this vid is really helpful Can you explain why the alrogithm(22:28) creates N(0,1) instead of N(0,10) or N(0,140), etc...? is it because that the normpdf is based on N(0,1)?
Thanks for the code. As a programmer, seeing how something would be coded makes a lot more sense than seeing a mathematical formula. :) The last example was also quite useful and a great way to tie it all together.
Interesting. About the climate example. Wouldn’t cloud formation be important since albedo was and perhaps that would be more important than the feedback, or just as?
Some "Professors" teach students just to show how much they know about the topic, by using alien language (edit: but some are good prof). I spent hours in those language, but instead i can understand mcmc within 36 minutes. You're a superhero!!
I spent dozens of hours reading papers about MCMC. all that is sh... RU-vid - the best source of any knowledge. Evidence of this - is the lecture above. Well done, author, well done... Thanks
Thank You for putting effort in making this presentation. However it is presented like theory, theory, theory, practice, practice. That's from my experience is not as effective as theory, practice, theory, practice... From every bit of information it should be clear how to apply it. Watching this I have lost it somewhere in the middle, because there were no possibility to instantly test the understanding of it. When looking at MatLab examples, it is not clear what is observed, what is predicted, why is it done like that and how did You plot that graph, when there is no code for it. Yes, You have presented part of this information in the theory, but it is like reading book about bicycle and hoping that it will teach you to ride a bicycle.
You say the method will visit the nodes an amount proportional to "their probability" many times. But we don't give any probability to the nodes a-priori, so really the output of the method *defines* this "per node probability" no?
everythig was brilliant!! great job.. m interested also in knowing your approach to the functions step_param and ebm_model while it could explain a more clearer picture.. Thanks in advance.
Hi, great tutorial, thanks. I have a couple of doubts 29'30" About the initial guess, what literature can I read to determine such a value of the initial guess? 30' About proposal distribution and the cost function, is there any other tutorial or literature to understand how to design such a proposed distribution or using exp(-cost) should suffice considering a wide range of phenomena and datasets? Thanks again
I don't see the difference between irreducible and aperiodic. IMO the graph is aperiodic (in the sense that there is no subgraph where we will get stuck) iff it is irreducible (for every pair of states (x,y), x and y are mutually reachable with nonzero probability).
Paul Frischknecht irreducible is probability of reaching any state while starting at another state is positive. The periodicity, d, is the largest integer such that returning to a certain state i is always a multiple of d. ie if you can reach i after {2,4,6,8,10} steps then d=2 since {2,2(2),2(3),2(4)..} .. An aperoidic MC would be {2,3,4,6,7} here then is no d such that n*d will generate the periods.
Typically all of the molecules would be altered at once, as the position of each molecule is a variable parameter and the collection of these constitutes a state of the system. I described moving them individually to simply convey the intuition of making small changes to the system. But, my intuition tells me that selecting single molecules with random reselection would be fine and preserve ergodicitiy.
@@picjeffton When I find the product of the starting state X0 and the Markov transition matrix I do not get that the probabilities of the next state X1 are as shown [0.2, 0.6, 0.2] but rather [0.18, 0.64, 0.18]. Am I doing the multiplication wrong or is that part of the arithmatic error? Thanks for your help and the video.
