Section ##################################################################
# 6.7 Learning about a Normal Population from Grouped Data
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library(LearnBayes)
d=list(int.lo=c(-Inf,seq(66,74,by=2)),
int.hi=c(seq(66,74,by=2), Inf),
f=c(14,30,49,70,33,15))
y=c(rep(65,14),rep(67,30),rep(69,49),rep(71,70),rep(73,33), rep(75,15))
start = c( mean(y), log(sd(y)))
fit=laplace(groupeddatapost,start,d)
fit
modal.sds=sqrt(diag(fit$var))
proposal=list(var=fit$var,scale=2)
fit2=rwmetrop(groupeddatapost,proposal,start,10000,d)
post.means=apply(fit2$par,2,mean)
fit2$accept
post.sds=apply(fit2$par,2,sd)
cbind(c(fit$mode),modal.sds)
cbind(post.means,post.sds)
mycontour(groupeddatapost,c(69,71,.6,1.3),d, xlab="mu",ylab="log sigma")
points(fit2$par[5001:10000,1],fit2$par[5001:10000,2])
# Try a bad choice of proposal distribution
start.bad = array(c(65,1)...