[This article was first published on Xi'an's Og » R, and kindly contributed to R-bloggers]. (You can report issue about the content on this page here)
Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.
Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.
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.
Filed under: Books, R, Statistics, Uncategorized, University life Tagged: beta distribution, book chapter, fREN, French paper, HPD region, pbeta(), R, uniroot() 
To leave a comment for the author, please follow the link and comment on their blog: Xi'an's Og » R.
R-bloggers.com offers daily e-mail updates about R news and tutorials about learning R and many other topics. Click here if you're looking to post or find an R/data-science job.
Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.