Markov Chain Monte Carlo and the Metropolis Alogorithm

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  • เผยแพร่เมื่อ 24 ธ.ค. 2024

ความคิดเห็น • 120

  • @Overdose21127
    @Overdose21127 12 ปีที่แล้ว

    I spent dozens of hours reading papers about MCMC. all that is sh...
    TH-cam - the best source of any knowledge. Evidence of this - is the lecture above.
    Well done, author, well done...
    Thanks

  • @hmsn22
    @hmsn22 8 ปีที่แล้ว +3

    One of the best explanations of MCMC I have seen on the web. Wonderful job . Wonderful

  • @jacobm7026
    @jacobm7026 5 ปีที่แล้ว +8

    Jeff, you're fantastic for doing this. I've been struggling all semester trying to grasp this concept intuitively. I've finally seen the light

  • @jeremyjacobsen4300
    @jeremyjacobsen4300 10 ปีที่แล้ว

    Great lecture. Thanks for showing code. This is the most straight forward MCMC tutorial that I've seen on youtube thus far.

  • @gumbo64
    @gumbo64 ปีที่แล้ว

    easily the best MCMC explanation I've seen, huge thanks

  • @badbad_
    @badbad_ 8 ปีที่แล้ว

    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

  • @Ash338
    @Ash338 12 ปีที่แล้ว +1

    Excellent presentation. Very clear, with nice examples and simple codes. Thank you.

  • @lukechen8606
    @lukechen8606 8 ปีที่แล้ว +7

    This video is cool! I really like the two examples you give, illustrating the idea of MCMC concretely and clearly. Thanks!

  • @DreamWorker-jm5xn
    @DreamWorker-jm5xn 5 ปีที่แล้ว

    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!!

  • @lauramanuel7619
    @lauramanuel7619 9 ปีที่แล้ว +4

    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.

  • @piotrbjastrzebski
    @piotrbjastrzebski 11 ปีที่แล้ว

    Something that presents MCMC in a concise and clear way. Like it a lot.

  • @NasusTCotS
    @NasusTCotS 5 ปีที่แล้ว +2

    This video might be the only thing saving my thesis. Thanks :D

  • @mayankpj
    @mayankpj 9 ปีที่แล้ว +1

    Nice work!
    You explained very clearly and the recording is also very nicely done...

  • @sethtrowbridge9122
    @sethtrowbridge9122 9 ปีที่แล้ว +55

    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.

  • @svetoslavbliznashki1710
    @svetoslavbliznashki1710 10 ปีที่แล้ว

    A great lecture indeed! Thanks very much :) The matlab code you shared really made it as clear as it gets. Keep them coming :)

  • @cdclaxton
    @cdclaxton 7 ปีที่แล้ว +2

    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

  • @gauthamchandra2081
    @gauthamchandra2081 4 ปีที่แล้ว

    very coherently explained, most videos go into unnecessary esoteric detail.

  • @ateoc9246
    @ateoc9246 5 ปีที่แล้ว +1

    in 31:41, have you any evidence for choose the accept/reject test function like this? If yes, where can i find it?

  • @ohrfeigenbaumhauweg
    @ohrfeigenbaumhauweg 8 ปีที่แล้ว

    Thank you. This really helped my understanding the model and the applications.

  • @premratan7511
    @premratan7511 9 ปีที่แล้ว

    Great video, Jeff Picton. It was really helpful. Thank you very much.

  • @yuanyuan3056
    @yuanyuan3056 7 ปีที่แล้ว +1

    Very clear explaination!

  • @paradox9086
    @paradox9086 10 ปีที่แล้ว +1

    Thank you so much for a very clear explanation

  • @paulfrischknecht3999
    @paulfrischknecht3999 9 ปีที่แล้ว +11

    @3:00 Wiki says it's from Monte Carlo in Monaco.

  • @metalismystyle
    @metalismystyle 10 ปีที่แล้ว +1

    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!

  • @aliabdollahzadeh1748
    @aliabdollahzadeh1748 9 ปีที่แล้ว

    Great work, almost answered all my questions. Thanks

  • @Paivren
    @Paivren 6 ปีที่แล้ว

    So at 19:30, the q distribution is equivalent to the transition matrix T from the markov chain formalism at 14:00, right?

  • @ablack0
    @ablack0 8 ปีที่แล้ว +1

    Thanks for this great explanation!

  • @ahme0307
    @ahme0307 11 ปีที่แล้ว +2

    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?

    • @RodrigoSilva-yn4on
      @RodrigoSilva-yn4on 5 ปีที่แล้ว +1

      I guess you're right! I also realized that, that's why I decided to read the comments!

  • @papiedra
    @papiedra 7 ปีที่แล้ว +1

    I didn't understood the difference between Metropolis algorith and MCMC?

  • @hannahshen2907
    @hannahshen2907 4 ปีที่แล้ว

    That is a really good explanation! Thank you!!!

  • @chx75
    @chx75 6 ปีที่แล้ว

    The Markov condition is not "x4 depends only on x3", but "if we know x3, x4 becomes independent of x2 and x1"

  • @cliffwang5481
    @cliffwang5481 7 ปีที่แล้ว

    Thanks so much for your inspiring explanation!

  • @MrFenh
    @MrFenh 8 ปีที่แล้ว

    Great video. Thank you, Jeff!

  • @SandroBoschetti
    @SandroBoschetti 11 ปีที่แล้ว

    Thank you very much for your great lecture. It is really being of great help for me.

  • @콘충이
    @콘충이 3 ปีที่แล้ว

    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)?

  • @ddaniel5857
    @ddaniel5857 11 ปีที่แล้ว

    It is really being of great help for me, thank you very much!

  • @TheGoodInquisitor
    @TheGoodInquisitor 10 ปีที่แล้ว

    Thank you for your clearness. Now I really have an idea.

  • @picjeffton
    @picjeffton  12 ปีที่แล้ว

    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.

  • @VisajDesai
    @VisajDesai 5 ปีที่แล้ว

    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?

  • @Mooorifo
    @Mooorifo 11 ปีที่แล้ว

    Have you got a written program for the disks?

  • @undertehlaw
    @undertehlaw 12 ปีที่แล้ว

    At 9:58, when "another" molecule is chosen, was that through a process that had a chance of reselecting the first molecule again?

  • @francisbaffour-awuahjunior3099
    @francisbaffour-awuahjunior3099 3 ปีที่แล้ว

    What is the explicit equation for the energy balance model?

  • @juliusctw
    @juliusctw 9 ปีที่แล้ว +6

    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 ?

  • @ankitranjan8292
    @ankitranjan8292 8 ปีที่แล้ว

    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?

  • @RAP4EVERMRC96
    @RAP4EVERMRC96 2 ปีที่แล้ว

    Nice lecture, whats your Elo? :p

  • @haseebshehzad2372
    @haseebshehzad2372 8 ปีที่แล้ว

    I need the document presented in the video. Any help? Thanks

  • @SergioHernandez-wd7mb
    @SergioHernandez-wd7mb 7 ปีที่แล้ว

    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

  • @ribaat2024
    @ribaat2024 12 ปีที่แล้ว

    i couldnt agree more with you! Well done author!!

  • @momnaahsan8079
    @momnaahsan8079 4 ปีที่แล้ว

    Great Lecture. Thankyou.

  • @harmonyliu8239
    @harmonyliu8239 7 ปีที่แล้ว

    one question: How do we choose the proposal q? Is there any requirements for this choice?

  • @grandeterra1698
    @grandeterra1698 8 ปีที่แล้ว

    Jeff thank you for these videos. I am self studying MCMC and is there any chance that you may share the simulation codes?

  • @ruili6415
    @ruili6415 5 ปีที่แล้ว

    Clear explaination. Thank you Jeff. A question existing in my brain is: How do we set the judgement criteria during the model iteration?

  • @paulfrischknecht3999
    @paulfrischknecht3999 9 ปีที่แล้ว

    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?

  • @PedroRibeiro-zs5go
    @PedroRibeiro-zs5go 7 ปีที่แล้ว

    Very very good explanation!! Thanks! :D

  • @yonatan1myers
    @yonatan1myers 10 ปีที่แล้ว

    At last a clear explanation of this

  • @bv9613
    @bv9613 5 ปีที่แล้ว

    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?

  • @chloeduan8301
    @chloeduan8301 8 ปีที่แล้ว +3

    ths is so great, thank you!

  • @tamerkhraisha6974
    @tamerkhraisha6974 7 ปีที่แล้ว

    Excellent explanation

  • @bobcrunch
    @bobcrunch 9 ปีที่แล้ว

    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.

  • @vidyashankar1389
    @vidyashankar1389 9 ปีที่แล้ว

    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.

  • @harmonyliu8239
    @harmonyliu8239 7 ปีที่แล้ว

    So nicely explained!!!!! Thank you !!!!

  • @SaulBerardo
    @SaulBerardo 11 ปีที่แล้ว

    I'm also confused. A clarification about it would be welcome.

  • @arnaldopereira8435
    @arnaldopereira8435 2 ปีที่แล้ว +1

    Make more videos, Jeff!

  • @picjeffton
    @picjeffton  11 ปีที่แล้ว +4

    Well there is a Monte Carlo in Vegas... but ya you're right.

  • @nautiyogi8386
    @nautiyogi8386 6 ปีที่แล้ว

    Brilliant tutorial !

  • @ozgurakpinar1710
    @ozgurakpinar1710 8 ปีที่แล้ว

    Dude, You are awesome.

  • @MaxKesin
    @MaxKesin 9 ปีที่แล้ว +2

    Great video - do you have any more from this class?

  • @jonathansmall4573
    @jonathansmall4573 7 ปีที่แล้ว

    I tried running that matrix program. Unfortunately it doesn' tconverge to (0.2, 0.4, 0.4) as you said. I don't know what I am doing wrong.

    • @picjeffton
      @picjeffton  7 ปีที่แล้ว +1

      Jonathan Small I messed up the arithmetic in that example.

    • @jonathansmall4573
      @jonathansmall4573 7 ปีที่แล้ว

      He he. Actually I tried again. This time using in-built matrix multiplication function in Python. It worked. Thanks :)

    • @FA-tq9ip
      @FA-tq9ip 4 ปีที่แล้ว

      @@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.

  • @picjeffton
    @picjeffton  12 ปีที่แล้ว

    I agree. I just didn't feel like opening latex to write out the equation and just took a screen cap of it from a paper I had.

  • @QuantCoder
    @QuantCoder 12 ปีที่แล้ว

    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.

  • @leonardomaffeidasilva9774
    @leonardomaffeidasilva9774 4 ปีที่แล้ว

    thank you. Really helped me

  • @antonmarkov3715
    @antonmarkov3715 6 ปีที่แล้ว

    Thank you very much, that helped my a lot!

  • @eraptor1955
    @eraptor1955 12 ปีที่แล้ว

    Very well done!

  • @Mark-IamNum1
    @Mark-IamNum1 4 หลายเดือนก่อน

    It is named after the casino in Monte Carlo - not in Las Vegas.

  • @GabiRav
    @GabiRav 11 ปีที่แล้ว +31

    Great explanation , but....MONTE CARLO IS IN MONTE CARLO , not in LAS VEGAS :-)

    • @TanguyI
      @TanguyI 10 ปีที่แล้ว +3

      You Americans, so egocentric :-P
      Very clear video BTY. Thanks!

    • @JP-re3bc
      @JP-re3bc 7 ปีที่แล้ว +3

      Ah the legendary quality of American public education.
      Yes! Monte Carlo is in Africa, and Africa is some place in the south of Europe. No?

    • @RalphDratman
      @RalphDratman 4 ปีที่แล้ว

      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.

  • @MrGeorgerififi
    @MrGeorgerififi 7 ปีที่แล้ว

    nice simple examples. thank u

  • @Cfx45321
    @Cfx45321 11 ปีที่แล้ว

    Great presentation. Thnx

  • @renzocoppola4664
    @renzocoppola4664 7 ปีที่แล้ว

    You made it sound easy.

  • @yongliangqin8673
    @yongliangqin8673 8 ปีที่แล้ว

    excellent tutorial

  • @scottmacnevin3555
    @scottmacnevin3555 7 ปีที่แล้ว

    Well done! Thank you

  • @abdullahalsulieman2096
    @abdullahalsulieman2096 ปีที่แล้ว

    Jeff, I have an algorithm that I need help interpret.

  • @rafaellima8146
    @rafaellima8146 7 ปีที่แล้ว

    Thank you so much!

  • @picjeffton
    @picjeffton  12 ปีที่แล้ว

    May I ask why?

  • @dsm5d723
    @dsm5d723 4 ปีที่แล้ว

    Taleb brought me here; the Kali Yuga keeps me grinding.

  • @great2816
    @great2816 8 หลายเดือนก่อน

    monte carlo name came from famous casino in monaco not vegas i believe.

  • @JuliaLondonChannel
    @JuliaLondonChannel 5 ปีที่แล้ว

    Gréât vidéo 👍🏻

  • @GabiRav
    @GabiRav 11 ปีที่แล้ว

    Can someone explain this?

  • @paulfrischknecht3999
    @paulfrischknecht3999 9 ปีที่แล้ว

    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).

    • @ahealey5961
      @ahealey5961 9 ปีที่แล้ว +1

      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.

  • @waguebocar9680
    @waguebocar9680 7 ปีที่แล้ว +2

    very programm monte carlo

  • @SoumakBhattacharjee08
    @SoumakBhattacharjee08 6 ปีที่แล้ว

    nice video.

  • @225kirt
    @225kirt 11 ปีที่แล้ว

    I liked the song

  • @picjeffton
    @picjeffton  11 ปีที่แล้ว

    You're quite right. For the purposes of this video though, let's just pretend that is how arithmetic works.

  • @marcosmetalmind
    @marcosmetalmind 4 ปีที่แล้ว

    very good

  • @czarekkawecki6548
    @czarekkawecki6548 ปีที่แล้ว

    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?? 😂😂

  • @xenonmob
    @xenonmob 3 ปีที่แล้ว

    snazzy intro music

  • @SotirisSar
    @SotirisSar 10 ปีที่แล้ว

    a good one! thank you!

  • @stipepavic843
    @stipepavic843 7 ปีที่แล้ว

    thx alot ! also good old league of legends days XD

  • @zilezile4942
    @zilezile4942 4 ปีที่แล้ว

    Learn more about logistic regression with R
    drive.google.com/file/d/1qcq_186AMe2XK9aNiSLxLbvXlAmryWXX/view?usp=sharing

  • @dannyndnyad4182
    @dannyndnyad4182 6 ปีที่แล้ว

    18:24 u are welcome

  • @GoodTechConf
    @GoodTechConf 8 ปีที่แล้ว +1

    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}

    • @gerarudnik9534
      @gerarudnik9534 4 ปีที่แล้ว

      was looking for this comment. thank you!