austerity in MCMC land (#2)

mcmc run with median instead of meanAfter reading the arXiv paper by Korattikara, Chen and Welling, I wondered about the expression of the acceptance step of the Metropolis-Hastings algorithm as a mean of log-likelihoods over the sample. More specifically the long sleepless nights at the hospital led me to ponder the rather silly question of the impact of replacing mean by median. I thus tried running a Metropolis-Hastings algorithm with the substitute and it (of course!) let to a nonsensical answer, as shown by the above graph. The true posterior is the one for a normal model and the histogram indicates a lack of convergence of the Markov chain to this posterior even though it does converge to some posterior. Here is the R code for this tiny experiment:

#data generation

#HM steps
for (t in 2:T){

  if (median(proplike)-median(curlike)>bound/N){
   } else { theta[t]=theta[t-1]}

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