gif_example

setwd("C:/Users/psa33/Dropbox/Work/Blog/gifs/increasingN")

binWidth <- 0.005

# define parameter space
x <- seq(from = binWidth / 2, to = 1 - binWidth / 2, by = binWidth)

# what rate of fairness is the coin?
rate <- 0.5

# how many flips to go up to?
n <- 100

# declare the prior
prior <- c(9, 1)
priorDensity <- dbeta(x, prior[1], prior[2])

# get a matrix to store all data likelihoods & posteriors
likelihood <- matrix(0, nrow = length(x), ncol = n)
posterior <- matrix(0, nrow = length(x), ncol = n)

for(i in 1:n){
  
  likelihood[, i] <- dbeta(x, 1 + i * rate, 1 + i * rate)
  posterior[, i] <- dbeta(x, prior[1] + i * rate, prior[2] + i * rate)
  
}

# loop over number of heads 1 to n and store a plot (in png) for each step
for(i in 1:n){
  
  # set up the file
  currFile <- paste(getwd(), "/plot_", i, ".png", sep = "")
  
  # initiate the png file
  png(file = currFile, width = 1200, height = 1000, res = 200)
  
  # initiat
  
  
  # do the plot
  plot(x, posterior[, i], type = "l", 
       ylim = c(0, max(c(likelihood, posterior, priorDensity))), lty = 1, 
       lwd = 3, col = "skyblue", xlab = bquote(theta), ylab = "Density", 
       las = 1, main = paste("Number of Flips = ", i, sep = ""))
  lines(x, likelihood[, i], type = "l", lty = 2, col = "red")
  lines(x, priorDensity, type = "l", lty = 2, col = "gray48")
  legend("topleft", c("Prior", "Likelihood", "Posterior"), lty = c(2, 2, 1), 
         col = c("gray48", "red", "skyblue"), lwd = c(1, 1, 4), bty = "n")
  
  dev.off()
  
}