In general, MC is used by rappers and the evolution of MC have made into pop culture to MC Hammer. Hence when MC Hammer says 'Can't touch this' this means that there is no way to approximate the parameter of the distribution that we want to aim. Hence MCMC can't touch this.
"A Markov chain is a sequential model that transitions from one state to another in a probabilistic fashion, where the next state that the chain takes is conditioned on the previous state." -theclevermachine.wordpress,com Let's apply that to his drawing of the various interconnected green lines. The OP started at a point on the line and progressed along the line. The progression is based on the previous point. The red points as depicted in the drawing are probabilities. Examples in real life are tracking of an aircraft, missile or spacecraft.There is variation and noise in radar. (Actually there is variation and noise in every measuring instrument). Another example can be a missile tracking an aircraft as in a heat seeking missile.
Agreed, the video introduces the MCMC concept in a rather high-level way so you get the intuition, somewhat, but you can't program the MCMC method by yourself with the help of this video. More details and math would be needed.
A little dissapointed that Arianna Rosenbluth wasn't included in the list of creators. She was also the first to use the method. Great explanation of MCMC!
I like your explanation. My physics background helps me a lot :). Many people learn algorithms just by learning their mathematics without knowing why we need that. Many tricks in MCMC, such as Gib sampling, Metropolis-Hastings algorithm come from solving statistical mechanics problems. And that's physics, not computer science :)
Curious to know how? Can you elaborate a bit on this - algorithm come from solving statistical mechanics problems. Or maybe refer a source to know more?
@@raghavendrakaushik4871 statistical mechanics is study of a large no of particles by applying probabilistic methods. It's all about applying MCMC simulations to spin hamiltonians. Spin is an intrinsic property of an electron(u can call it a direction of an electron) and these hamiltonian equations are not solvable analytically bcz they are non-linear. That's why we employ the MCMC technique (metropolis, heat bath) to sample configurations from a large ensemble of states and calculate our observables on only these sampled states. If we don't use MCMC simulations, we would have to average over all the possible states which is very impractical since for real systems bcz there might be infinitely large no. of states. My phd was also about applying MCMC to quantum many-body physics.
This reminds me of simulated annealing in a sense - the fact that the vector of variables was a state of the problem and the algorithm does a sort of hill-climbing to find better states, as well as the fact that annealing has to do with particles...
This was mostly pretty clear. The pace and tone of it are quite easy to listen to. I was a little unclear about how the circles corresponded to the solid/liquid/gas diagram at the end, or what sort of data was (or would need to be) collected to develop the correspondence. Was the idea that those circles would end up finding the high probability distribution (like the “lightening” from the previous screen) for one of those phase diagrams?
Question about your intuitive description of the algorithm: what happens when you have disconnected regions of high probability? Will MCMC fail to find them?
I understood the intuition. However, I still did not understand how it works. I believe if you used a numerical example, I would understand much better the idea.
The random variable is not just one dimensional but spans across multiple dimensions. Like - Multinomial distribution, Dirchlet distribution, Multivariate Gaussian etc.
what do you do if after one of the iterations the new configuration is not allowed (like two discs intersect). Do you just go back and try again until you step to an allowed configuration? or perhaps reset to some sort of base state?
As I understand, MC jsut sampling data but MCMC use Markov property for sampling. So, you do not just randomly sample data in MCMC but you follow a sampling pattern regarding the previous sampling. That is called Markov property.
I've a MS in Statistics, and I can say that these videos are not helpful. He doesn't explain the algorithms well. I made my own video where I actually have an example: th-cam.com/video/tre4zz7pnlE/w-d-xo.html
Hi man, this is one of the best MCMC introduction I have seen. Just for your information, these big guys who developed MCMC are all physicists. not statisticians. They developed this for attacking real problems not playing math tricks.
Thank you so so much ! So my understanding is MCMC is Monte Carlo simulation for a vector (array) of variables. The number of variables is infinite. Is my understanding correct?
I don't think your variables can be infinitely. You have p-dimensional problem with p-unknown parameters you are trying to estimate via sampling from the marginal distribution. You sample from the marginal distribution by MCMC. See my video: th-cam.com/video/tre4zz7pnlE/w-d-xo.html
fyi, the two authors referred to as "the wives of Rosenbluth and Teller" have names, as well; they are Arianna W. Rosenbluth and Augusta H. Teller
Exactly the comment I wanted to see. Thanks. :)
thanks!
YES!
In general, MC is used by rappers and the evolution of MC have made into pop culture to MC Hammer. Hence when MC Hammer says 'Can't touch this' this means that there is no way to approximate the parameter of the distribution that we want to aim.
Hence MCMC can't touch this.
LOL
Now I know everything about everything.
Your enthusiastic way of teaching is so inspiring. Thank you for sharing this great video!
Fantastic presentation, easy to follow and giving great intuition, thank you.
I still do not understand
"A Markov chain is a sequential model that transitions from one state to another in a probabilistic fashion, where the next state that the chain takes is conditioned on the previous state." -theclevermachine.wordpress,com
Let's apply that to his drawing of the various interconnected green lines. The OP started at a point on the line and progressed along the line. The progression is based on the previous point. The red points as depicted in the drawing are probabilities. Examples in real life are tracking of an aircraft, missile or spacecraft.There is variation and noise in radar. (Actually there is variation and noise in every measuring instrument). Another example can be a missile tracking an aircraft as in a heat seeking missile.
You should watch this for an actual example: th-cam.com/video/tre4zz7pnlE/w-d-xo.html
Agreed, the video introduces the MCMC concept in a rather high-level way so you get the intuition, somewhat, but you can't program the MCMC method by yourself with the help of this video. More details and math would be needed.
A little dissapointed that Arianna Rosenbluth wasn't included in the list of creators. She was also the first to use the method. Great explanation of MCMC!
I like your explanation. My physics background helps me a lot :). Many people learn algorithms just by learning their mathematics without knowing why we need that. Many tricks in MCMC, such as Gib sampling, Metropolis-Hastings algorithm come from solving statistical mechanics problems. And that's physics, not computer science :)
Curious to know how? Can you elaborate a bit on this - algorithm come from solving statistical mechanics problems.
Or maybe refer a source to know more?
@@raghavendrakaushik4871 statistical mechanics is study of a large no of particles by applying probabilistic methods. It's all about applying MCMC simulations to spin hamiltonians. Spin is an intrinsic property of an electron(u can call it a direction of an electron) and these hamiltonian equations are not solvable analytically bcz they are non-linear. That's why we employ the MCMC technique (metropolis, heat bath) to sample configurations from a large ensemble of states and calculate our observables on only these sampled states. If we don't use MCMC simulations, we would have to average over all the possible states which is very impractical since for real systems bcz there might be infinitely large no. of states. My phd was also about applying MCMC to quantum many-body physics.
Thanks for the lecture, great explanation. Nonetheless, "do the wives of Rosenbluth and Teller have names?"
A masterpiece. Thank you so much for sharing the knowledge.
So this is where I go after graduating from Khan Academy! Thanks for posting these videos, very helpful!
This reminds me of simulated annealing in a sense - the fact that the vector of variables was a state of the problem and the algorithm does a sort of hill-climbing to find better states, as well as the fact that annealing has to do with particles...
Excellent tutorial.
Great series of videos. Thank you so much.
The photos used around 7:45 make the physicists look like gangsters
What has the discs to do with the phase diagram? In the moving of the discs, how are Markov chains used?
This is way more accessible than the Hastie and Tibshirani book :) Excellent Stuff
Great video, the initial physics application for MCMC was in modelling neutron diffusion
A very good tutorial ! Thank you !
This was mostly pretty clear. The pace and tone of it are quite easy to listen to. I was a little unclear about how the circles corresponded to the solid/liquid/gas diagram at the end, or what sort of data was (or would need to be) collected to develop the correspondence. Was the idea that those circles would end up finding the high probability distribution (like the “lightening” from the previous screen) for one of those phase diagrams?
Question about your intuitive description of the algorithm: what happens when you have disconnected regions of high probability? Will MCMC fail to find them?
I understood the intuition. However, I still did not understand how it works. I believe if you used a numerical example, I would understand much better the idea.
This is the next 3blue1brown
This is great, thanks.
love it! thank you!
Thank you for this!
Thanks for the videos!
thank you for the excellent lecture. I wonder if you can do about the "Particle filter" (Sequential Monte Carlo Method) as well?
Thank you.
thank you
thanks you very very much great video.........could probably under better than reading
Excellent
what does high-dimensional probability mean when he said here in the introduction? plss someone help me!!
The random variable is not just one dimensional but spans across multiple dimensions.
Like - Multinomial distribution, Dirchlet distribution, Multivariate Gaussian etc.
Way too good explanation...
When you draw a box around a molecule, what is it that you are examine? Presence of a molecule?
So is MCMC just random sampling? Similar to numpy.random but for more complicated distributions?
It was not clear for me at all. :(
❤️🔥
I found SYSTAT 13 is good software for MCMC
what do you do if after one of the iterations the new configuration is not allowed (like two discs intersect). Do you just go back and try again until you step to an allowed configuration? or perhaps reset to some sort of base state?
Thank you :)
If one who not understanding clearly each of two theory will cause confusing when mixing it.
when we use MC ?and MCMC and what is the problem in MC so we use MCMC?
Can you clarify your question? Are you asking for the difference between MC and MCMC?
As I understand, MC jsut sampling data but MCMC use Markov property for sampling. So, you do not just randomly sample data in MCMC but you follow a sampling pattern regarding the previous sampling. That is called Markov property.
voice sounds very similar to sal khan
Can you please add a lecture on Reversible jump MCMC thank you
Bad education is when you over-simplify the stupid and easy parts and hurriedly skip over the hard parts.
Value gained = 0
It's a video series. Watch the other videos for the hard parts
I've a MS in Statistics, and I can say that these videos are not helpful. He doesn't explain the algorithms well. I made my own video where I actually have an example: th-cam.com/video/tre4zz7pnlE/w-d-xo.html
Hi man, this is one of the best MCMC introduction I have seen. Just for your information, these big guys who developed MCMC are all physicists. not statisticians. They developed this for attacking real problems not playing math tricks.
What is the software that you are using?
Thank you so so much !
So my understanding is MCMC is Monte Carlo simulation for a vector (array) of variables. The number of variables is infinite. Is my understanding correct?
I don't think your variables can be infinitely. You have p-dimensional problem with p-unknown parameters you are trying to estimate via sampling from the marginal distribution. You sample from the marginal distribution by MCMC. See my video: th-cam.com/video/tre4zz7pnlE/w-d-xo.html
This was awful
Not a great explanation
terrible video, could hardly watch it despite being very interested in the topic.