################################
# Section 2.4 Using a Beta Prior
#############################
library(LearnBayes)
quantile2=list(p=.9,x=.5)
quantile1=list(p=.5,x=.3)
ab=beta.select(quantile1,quantile2)
a = ab[1]
b = ab[2]
s = 11
f = 16
curve(dbeta(x,a+s,b+f), from=0, to=1,
xlab="p",ylab="Density",lty=1,lwd=4)
curve(dbeta(x,s+1,f+1),add=TRUE,lty=2,lwd=4)
curve(dbeta(x,a,b),add=TRUE,lty=3,lwd=4)
legend(.7,4,c("Prior","Likelihood","Posterior"),
lty=c(3,2,1),lwd=c(3,3,3))
1 - pbeta(0.5, a + s, b + f)
qbeta(c(0.05, 0.95), a + s, b + f)
ps = rbeta(1000, a + s, b + f)
if (.Platform$OS.type == "unix") x11() else windows()
hist(ps,xlab="p")
sum(ps >= 0.5)/1000
quantile(ps, c(0.05, 0.95))
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