# Edps 590BAY
# Fall 2019
# C.J.Anderson
#
# Function to plot cases of normal:  posterior <- likelihood*prior
# Input:
# mu0  = prior mean
# tau0 = prior standard deviation
# m.y  = mean for likelihood, would typically be sample mean of y
# sigma= standard deviations for likelihood
#
# Output: figures
#

normalPriorLike <- function(mu0,tau0,m.y,sigma) {

   y <- seq(from=-12, to=12, length.out=1000)    # you can change if want larger ********
                                                 # range
   prior <- dnorm(y,mean=mu0,sd=tau0)            # density of prior
   likelihood <- dnorm(y,m.y,sd=sigma)           # likelihood using "data"
   posterior <- prior*likelihood                 # proportional to posterior

   p1 <- max(prior)                   # to get comparable limits for y-axis
   p2 <- max(likelihood)              #  in plots of prior and likelihood
   y.lim <- max(p1,p2)

# Indicates coorinadates to place figure on page 
   layout(matrix(c(1,1,0,0,1,1,3,3,2,2,3,3,2,2,0,0),4,4,byrow=FALSE))
     
   plot(y,prior, type='l', lwd=2, col="blue", 
     main=paste("N(",mu0,",",tau0,") Prior"), ylim=c(0,y.lim),     
     xlab="Possible theta", ylab="f(theta)")

   plot(y,likelihood, type='l', lwd=2, col="blue", 
     main=paste("N(",m.y,",",sigma,") Likelihood"), ylim=c(0,y.lim),
     xlab="Possible theta", ylab="f(y|theta,100)")

   plot(y,posterior, type='l', lwd=2, col="blue", 
     main="Posterior:  N(mu_n,tau_n) ",
     xlab="Possible theta", ylab="f(theta|tau_n,y)")
}