Hi, I have a quick question about the video. 1. What does support mean in video's context? 2. For target and proposal distributions, we assume that we know functional forms of BOTH distributions? Can we use importance sampling using proposal distribution of our CHOICE with an abstract target distribution which maybe UNKNOWN?
I think Support means generally that the proposed distribution is high where the product of h(x) and pi(x) is large. This idea is mentioned in this video at the timestamp: czcams.com/video/C3p2wI4RAi8/video.html
Well, I am still not quite convinced about the superiority of the imp sampling over the naive MC. Since all the calculations are strickly depends on random sampling, I found some results in naive MC which gave me better approximation comparing to the imp sampling case aftter running the same loop several times.
Very nice video, just one question, let's say we can sample infinite times, then will using importance sampling make any difference, will 3 line be the same (at 7:00)?
Thank you for this video! I was wondering if this (or other technique) could be used to get samples of the target distribution from the proposed distribution where not only the moments are estimated, but the distribution itself... I would like to confront a theoretical distribution with, say, an ECDF of measured samples. But the measured samples are very difficult to obtain. Can I estimate an ECDF of my target distribution, but by sampling another (of course intrinsically related) one?
Why is the pink function equal to exp(1)? I don't get it. Exp(1) is just = e = 2.7... and is a constant. What you are plotting is f(x) = exp(x), or am I wrong? Also, I always thought MC methods help you for integration, but you only talk about means and variance, so no integrals can be calculated with this?
Good question, Here exp() refers to the exponential distribution (en.wikipedia.org/wiki/Exponential_distribution) and not the exponential function. Also the mean that is being calculated is the expected value of a function. The expected value of a function is an integral usually, but sometimes the expected value function can be simplified to the average function. Here is a mathematical overview including discussion of using IS to evaluate integrals: czcams.com/video/C3p2wI4RAi8/video.html
great video! my confusion with Importance Sampling has vanished after watching this. thank you!
thank u 😊
this is a perfect video! I am troubling this problem in the statistical computing course! thanks!
Thank you so much! good video, a rich explanation!
Awesome explanation! Thank you so much!
Gran explicación!!
Great demo!! Thank you!
Nice video, thank you
Hi, I have a quick question about the video.
1. What does support mean in video's context?
2. For target and proposal distributions, we assume that we know functional forms of BOTH distributions?
Can we use importance sampling using proposal distribution of our CHOICE with an abstract target distribution which maybe UNKNOWN?
I think Support means generally that the proposed distribution is high where the product of h(x) and pi(x) is large. This idea is mentioned in this video at the timestamp: czcams.com/video/C3p2wI4RAi8/video.html
Another meaning of support is an area of a function which is not mapped to 0 (en.wikipedia.org/wiki/Support_(mathematics))
Well explained
Well, I am still not quite convinced about the superiority of the imp sampling over the naive MC. Since all the calculations are strickly depends on random sampling, I found some results in naive MC which gave me better approximation comparing to the imp sampling case aftter running the same loop several times.
Very nice video, just one question, let's say we can sample infinite times, then will using importance sampling make any difference, will 3 line be the same (at 7:00)?
Thank you for this video! I was wondering if this (or other technique) could be used to get samples of the target distribution from the proposed distribution where not only the moments are estimated, but the distribution itself... I would like to confront a theoretical distribution with, say, an ECDF of measured samples. But the measured samples are very difficult to obtain. Can I estimate an ECDF of my target distribution, but by sampling another (of course intrinsically related) one?
Thanks for the video, I want to use one of your examples but giving the credit. Who do I have to cite?
Go for it 👍🏻👍🏻 no need to cite or you can cite the video
Why is the pink function equal to exp(1)? I don't get it. Exp(1) is just = e = 2.7... and is a constant. What you are plotting is f(x) = exp(x), or am I wrong? Also, I always thought MC methods help you for integration, but you only talk about means and variance, so no integrals can be calculated with this?
Exp(lambda=1)= lambda * exp (-lambda*x) , according to the pdf of exp(1)
Good question, Here exp() refers to the exponential distribution (en.wikipedia.org/wiki/Exponential_distribution)
and not the exponential function.
Also the mean that is being calculated is the expected value of a function. The expected value of a function is an integral usually, but sometimes the expected value function can be simplified to the average function.
Here is a mathematical overview including discussion of using IS to evaluate integrals: czcams.com/video/C3p2wI4RAi8/video.html
Thank you
Brilliant explanation! Thank you!