Bayesian_Notes_520.R

#Inference for Binomial with Beta Prior
BBB<-function(n,p,alpha,beta)
{
  require(ggplot2)
  require(reshape2)
  xx<-rbinom(1,n,p)
  p_hat<-xx/n
  print("Observed Proportion, Posterior Mean")
  p_hat_Post<-(alpha+xx)/(n+alpha+beta)
  print(c(p_hat,p_hat_Post))
  x  <- seq(0, 1, 0.01)
  Prior <- dbeta(x,alpha,beta)
  Posterior <- dbeta(x,alpha+xx,n+beta-xx)

  df <- data.frame(x, Prior, Posterior)
  
  # melt the data to a long format
  df2 <- reshape2::melt(data = df, id.vars = "x")
  
  # plot, using the aesthetics argument 'colour'
  ggplot(data = df2, aes(x = x, y = value, colour = variable)) + geom_line() + geom_vline(xintercept=p_hat)

 
}

n<-1
p<-0.3
alpha<-1
beta<-1

BBB(n,p,alpha,beta)
#Inference for Normal with Normal Prior
BNN<-function(n,mu,sigma,theta,tau)
{
  require(ggplot2)
  require(reshape2)
  xx<-rnorm(n,mu,sigma)
  xbar<-mean(xx)
  theta_post<-(theta*sigma^2+n*xbar*tau^2)/(sigma^2+n*tau^2)
  tau_post<-(sigma^2*tau^2)/(sigma^2+n*tau^2)
  print("Observed Mean, Posterior Mean")
  xbar_Post<-theta_post
  print(c(xbar,xbar_Post))
  a<-min(xx)-1
  b<-max(xx)+1
  x  <- seq(a, b, 0.01)
  Prior <- dnorm(x,theta,tau)
  Posterior <- dnorm(x,theta_post,tau_post)

  df <- data.frame(x, Prior, Posterior)
  
  # melt the data to a long format
  df2 <- reshape2::melt(data = df, id.vars = "x")
  
  # plot, using the aesthetics argument 'colour'
  ggplot(data = df2, aes(x = x, y = value, colour = variable)) + geom_line() + geom_vline(xintercept=xbar)
  
  
}

BNN(10,20,5,12,4)