Bayesian sampling without tears

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Following a question on Stack Overflow trying to replicate a figure from the paper written by Alan Gelfand and Adrian Smith (1990) for The American Statistician, Bayesian sampling without tears, which precedes their historical MCMC papers, I looked at the R code produced by the OP and could not spot an issue as to why their simulation did not fit the posterior produced in the paper. Which proposes acceptance-rejection and sampling-importance-resampling as two solutions to approximately simulate from the posterior. The later being illustrated by simulations from the prior being weighted by the likelihood… The illustration is made of 3 observations from the sum of two Binomials with different success probabilities, θ¹ and θ². With a Uniform prior on both.

for (i in 1:N)
  for (k in 1:3){
    for (j in max(0,n2[k]-y[k]):min(y[k],n1[k]))

To double-check, I also wrote a Gibbs version:

for(t in 1:(T-1)){
   for(j in 1:3){

which did not show any difference with the above. Nor with the likelihood surface.

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