5.3 Settng up a problem in R.txt

#5.3 Setting up a Bayesian problem in R

#1. It is not necessary to include any normalizing constants that 
#don't involve the paremeters.

#2. REPARAMETERIZE all paremeters so they are ALL real-valued
#A positive parameter such as variance SHOULD be transformed using log function
#A proportion papameter can be transformed to the real line by the logit function.

#the GOAL is to express the porterior density using tansformed papameters
#to summarize THIS posterior density, write an R function defining
# the logarithm of the joint posterior density.

library('LearnBayes')

#here theta is asumed to be a vector with k components
#note the 'exp' in sigma=exp(theta[2])
#(so theta was transformed to log first but exp is used to convert it back?)

#the use of log=TRUE option in dnorm computes the logarithm of the density

mylogposterior=function(theta,data)
{
n=length(data)
mu=theta[1]; sigma=exp(theta[2])
logf = function(y, mu, sigma)
	dnorm(y, mean=mu, sd=sigma, log=TRUE)
val=dnorm(mu, mean=10, sd=20, log=TRUE)+sum(logf(data,mu,sigma))
return(val)
}
x=c(3,4,1,5,6,4,5,6,7,8,9,2,2,3,1,4,5)
theta=c(13, 23)

mylogposterior(theta,x)