Thank yor for a great explanation. I have a question. At th-cam.com/video/bZ2sCqj3ACU/w-d-xo.html , mean(new.weights) should be close to 1 because F(5, 25) is already normalized. If the target distribution is normalized, can we always get the mean being equal to 1? I cannot get the intutition of it as clear as other points you make in this video.
This is not related to SIR, this is a property of both distributions. F is related to chi-square, in the following : if you have (chi2/m)/(chi2/n)~F_(m,n) (See here en.wikipedia.org/wiki/F-distribution#Characterization) . If you then take a R.V. that distributes F with 5,25, and divide it by chi2_5, the numerator cancels, and you are left with 25/chi2_25. The mean of chi2_25 is 25. So the mean of this will be close to 25/25 = 1.
I think it might have different names. The literature I read refers to this as Sampling-Importance-Resampling. Check "Bayesian Statistics without Tears: A Sampling-Resampling Perspective" by Smith and Gelfand, they refer to Rubin (1988) who apparently coined the term.
Thanks man for this knowldge
Great video! Thanks for the effort.
Can you please upload the R script again? It's unavailable right now.
Thank you!
fixed
Thank yor for a great explanation. I have a question. At th-cam.com/video/bZ2sCqj3ACU/w-d-xo.html , mean(new.weights) should be close to 1 because F(5, 25) is already normalized. If the target distribution is normalized, can we always get the mean being equal to 1? I cannot get the intutition of it as clear as other points you make in this video.
This is not related to SIR, this is a property of both distributions. F is related to chi-square, in the following : if you have (chi2/m)/(chi2/n)~F_(m,n) (See here en.wikipedia.org/wiki/F-distribution#Characterization) . If you then take a R.V. that distributes F with 5,25, and divide it by chi2_5, the numerator cancels, and you are left with 25/chi2_25. The mean of chi2_25 is 25. So the mean of this will be close to 25/25 = 1.
@@MeerkatStatistics Thank you. :) I clearly understand it now.
Thanks, but I think it's Sequential Importance Resampling(SIR)
I think it might have different names. The literature I read refers to this as Sampling-Importance-Resampling. Check "Bayesian Statistics without Tears: A Sampling-Resampling Perspective" by Smith and Gelfand, they refer to Rubin (1988) who apparently coined the term.
@@MeerkatStatistics I understand, thanks for the reference