An introduction to importance sampling

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An introduction to importance sampling

Рет қаралды 58,050

Күн бұрын

This video explains what is meant by importance sampling, and how this method can be used to provide estimates of a distribution's characteristics, even if we are unable to sample from that distribution.
This video is part of a lecture course which closely follows the material covered in the book, "A Student's Guide to Bayesian Statistics", published by Sage, which is available to order on Amazon here: www.amazon.co....
For more information on all things Bayesian, have a look at: ben-lambert.co.... The playlist for the lecture course is here: • A Student's Guide to B...

Пікірлер: 46

@vladislavstankov1796 3 жыл бұрын

you are amazing! Every time when i have troubles understanding some concept and need to search the web, if i see that you have a video on this topic, is already solved for me.

@carloszarzar 2 жыл бұрын

Professor Ben Lambert congratulations on the videos. Great didactics. My suggestion is to always keep the footer of videos clean (no written information). Because a lot of people watch their videos with subtitles, it often gets confused the subtitles and their writing and makes it difficult to learn. Again, I congratulate you on the initiative to democratize information here on KZfaq.

@lexparsimoniae2107 3 жыл бұрын

Ben, you are a life saver.

@inothernews 6 жыл бұрын

Hi, thanks for the great video series. Question: for importance sampling, do we already assume we know what g is, such that given some x, we can compute g(x)? If we do, then couldn't we compute its mean analytically? If not, how do we resolve g(x) in the g(x)/f(x) term?

@SpartacanUsuals 6 жыл бұрын

Hi, thanks for your comment. Yes, you’re right that we need to know g(x) (at least up to a constant of proportionality). The beauty of importance sampling is that even if g(x) is unnormalised, however - and so we cannot compute the particular expectation - we can still use importance sampling to estimate it. Also, whilst I’ve illustrated how importance sampling works for a 1D example (where computing integrals is typically quite straightforward), importance sampling can be used in higher dimensional integration where it is usually not possible to compute integrals analytically. Hope that helps! Best, Ben

@inothernews 6 жыл бұрын

Right, that cleared things up a lot. Thank you for your time!

@lesterknome 4 жыл бұрын

@@SpartacanUsuals If we cannot compute the integral of g analytically, in general are we able to compute the integral of f?

@robinranabhat3125 4 жыл бұрын

@@SpartacanUsuals can you give an concrete example though . If you know ..

@robinranabhat3125 4 жыл бұрын

@@ianpan0102 hi genius. I meant concrete example for multivariate problem. I meant an actual case where he actually does a freaking sampling without knowing the other distribution. And not just talk on how it's useful there. Even an 8 year old would understand that first part. If you have nothing informative to say, don't comment as if you know it.

@shoryaagarwal561 3 жыл бұрын

This would really help for someone to understand why importance sampling is used for sampling rays in ray tracing. Thanks!!

@sivad1025 3 жыл бұрын

You saved my life. Thanks.

@Hecklit 5 жыл бұрын

I really like the way you explain things. Thanks a lot.

@mystonefeel 4 жыл бұрын

The best explain on importance sampling... good animation

@alexanderl.2689 5 жыл бұрын

Thank you so much, with the help of your video I finally understand the idea behind IS

@emmanuelameyaw6806 4 жыл бұрын

Hi Lambert, it would be great to include sequential importance sampling in the series.

@jorgepereiradelgado7492 5 жыл бұрын

Great video! Thanks for putting effort into this, it really helped! Greetings from Spain.

@kleemc6267 6 жыл бұрын

Well done ! I like the graphics that shows convergence.

@maurocamaraescudero1062 5 жыл бұрын

Great series of videos, complements very well the book by Casella! Would you please be able to add a link to the Mathematica animation code for both importance and rejection sampling? They would be tremendously useful!

@violinplayer7201 4 жыл бұрын

Well and very clearly explained! Thank you!

@huxixi4120 4 жыл бұрын

But how we get or calculate the ratio between f and g? the true distribution f is unknown right?

@alikassem812 3 жыл бұрын

As he explained, we have f(x) but we don't have g(x), so we will approximate it by sampling from other distribution which is h(x)/z. Then we will compute W

@thidmg 3 жыл бұрын

@@alikassem812 i think we have g(x), but sometimes is very difficult to do the math of g(x), so we use importance sampling. In this case g(x) is simple, but in bayesian statistics in general is a very complex function

@alikassem812 3 жыл бұрын

@@thidmg yea, you are right. Thanks

@alexmtbful Жыл бұрын

@@thidmg agree- seems too easy and useless at the first look but I guess it's more a numerical issue why importance sampling has its right to exist and then it gets super useful

@YChen-ut1dw 4 жыл бұрын

this is perfect, thank you

@aishikpyne Жыл бұрын

I'm still a little confused on why, if we know the ratio of g(x)/f(x) then we can compute E_g[x] directly? Can you give an concrete example/illustration of a multivariate continuous/discrete case?

@peaelle42 8 ай бұрын

but what happens if i actually wanna sample from that difficult-to-sample distribution instead of computing things like expectation etc etc? like, i want the points themselves.

@omid_tau 5 жыл бұрын

dude it would be really helpful if you could reference the page in your book that the video refers too .

@emmanuelameyaw6806 4 жыл бұрын

what if we are interested in another statistic like the median (r(x)) or quantile (h(x)) of g(x)? we just change 'x' in the derivation to 'h(x)' or 'r(x)'?

@distrologic2925 2 жыл бұрын

at 9:18 there is an f(x) missing in the sum, isn't there? Because it is the expectation of f..?

@AndriyDrozdyuk 5 жыл бұрын

Beautiful video.

@zeeshan008x52 5 жыл бұрын

you are a genius

@songlinyang9248 5 жыл бұрын

nice explained,thank you

@user-cc8kb 5 жыл бұрын

great video

@hossein_haeri Жыл бұрын

You actually lost many people at 4:00 when you said "we only have access to the fair dice and somehow we want to work out the mean of the biased dice". Well... If we don't have access to the dice and it's probability distribution how do we even know what kind of dice are we dealing with? If we have its distribution then why are we bothering using the other ones samples???

@lisaka2951 4 жыл бұрын

Hi, I really enjoyed that video. But why is the expectation value of 1 always equal to 1?

@thidmg 4 жыл бұрын

hi, the expectation of a constant is always that constant, "the constant is constant" it does not varies anytime, it's always that constant number, in this example is 1 but can be any constant number like 1, 2, 3, 4...

@lisaka2951 4 жыл бұрын

@@thidmg Ohh.. thank you very much. That explanation did not come to my mind. Thank you and stay healthy!

@chenyang1896 4 жыл бұрын

is there anybody knows the software's name which is the uploader was using?

@jaylenjames322 3 жыл бұрын

The part where he was showing the automatically plotting graphs is called Mathematica. It's made by Wolfram.

@allenkalalu6006 5 жыл бұрын

Hi! I am trying to work out model selection trough information criterion, please can you help in explaining the intuition behind Akaike Information criterion (AIC) also Bayesian Information criterion(BIC) and if you could start from Kullback Leibler divergence and how to derive AIC(or BIC) from it , and how AIC/BIC pick the best model,it will be deeply appreciate. Thanks in advance!!