Archive for book chapter

Le bayésianisme aujourd’hui

Posted in Books, Statistics with tags , , , , , , , on September 19, 2016 by xi'an

A few years ago, I was asked by Isabelle Drouet to contribute a chapter to a multi-disciplinary book on the Bayesian paradigm, book that is now soon to appear. In French. It has this rather ugly title of Bayesianism today. Not that I had hear of Bayesianism or bayésianime previously. There are chapters on the Bayesian notion(s) of probability, game theory, statistics, on applications, and on the (potentially) Bayesian structure of human intelligence. Most of it is thus outside statistics, but I will certainly read through it when I receive my copy.

beta HPD

Posted in Books, R, Statistics, Uncategorized, University life with tags , , , , , , , on October 17, 2013 by xi'an

While writing an introductory chapter on Bayesian analysis (in French), I came by the issue of computing an HPD region when the posterior distribution is a Beta B(α,β) distribution… There is no analytic solution and hence I resorted to numerical resolution (provided here for α=117.5, β=115.5):

f=function(p){

  # find the symmetric
  g=function(x){return(x-p*((1-p)/(1-x))^(115.5/117.5))}
  return(uniroot(g,c(.504,.99))$root)}

ff=function(alpha){

  # find the coverage
  g=function(x){return(x-p*((1-p)/(1-x))^(115.5/117.5))}
  return(uniroot(g,c(.011,.49))$root)}

and got the following return:

> ff(.95)
[1] 0.4504879
> f(ff(.95))
[1] 0.5580267

which was enough for my simple book illustration… Since (.450,558) is then the HPD region at credible level 0.95.