# Example, prior and posterior beta ----
makepdf = F
fname = '../pdftex/img/class20-stopping.pdf'
if (makepdf)
{
  wd = 5.5
  ht = 3
  scale = .8
  pdf(fname, width=wd*scale,height= ht*scale)
}
par(mar=c(3.5,2.5,.4,.3))
txtxpos = .43
txtwd = .02
linewd = .13
cex.txt = 1.1

x = seq(0,1,.01)
# Set up limits etc, plot type ='n'
plot(c(0,1),c(0,3.5), type='n', mgp=c(2.5,1,0), ylab='', xaxt='n', xlab=expression(theta),
     cex.lab=2)
axis(1, at=c(0,.25, .50, .75, 1.0), labels=c('0','.25','.50','.75','1.0'), cex.axis=1.2)
prior.a = 3; prior.b = 3
col = 'cyan'
txtht = 3
lines(x,dbeta(x,prior.a, prior.b), col=col, lwd=2)
s = sprintf('Prior Beta(%d,%d)', prior.a, prior.b)
text(txtxpos, txtht, s, pos=2, cex=cex.txt)
lines(c(txtxpos+txtwd,txtxpos+txtwd+linewd),c(txtht,txtht), col=col,lwd=3)

posterior.a = 8; posterior.b = 4
col = 'red'
txtht = 2.5
lines(x,dbeta(x, posterior.a, posterior.b), col=col, lwd=2)
s = sprintf('Posterior Beta(%d,%d)', posterior.a, posterior.b)
text(txtxpos, txtht, s, pos=2, cex=cex.txt)
lines(c(txtxpos+txtwd,txtxpos+txtwd+linewd),c(txtht,txtht), col=col,lwd=3)

# 50% probability interval
col = 'blue'
probInt.50 = qbeta(c(.25,.75),posterior.a,posterior.b)
ht = .15
lines(probInt.50,c(ht,ht), col=col, lwd=3)

ht = 0
probInt.90 = qbeta(c(.05,.95),posterior.a,posterior.b)
lines(probInt.90,c(ht,ht), col=col, lwd=3)

s = sprintf("50%% probabilitly interval [%.2f, %.2f]", probInt.50[1], probInt.50[2])
print(s)
s = sprintf("90%% probabilitly interval [%.2f, %.2f]", probInt.90[1], probInt.90[2])
print(s)
s = sprintf("P(theta > .5) = %.2f", 1- pbeta(.5,posterior.a,posterior.b))
print(s)
if (makepdf)
  dev.off()