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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)
 0.4504879
> f(ff(.95))
 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()  