No this is not yet another post-Christmas/NY ‘Og entry about food! Ian Murray, Ryan Adams and David MacKay posted a small piece on arXiv on Tuesday where they advocate a new type of slice sampler in cases when the posterior distribution on the parameter is associated with a Gaussian prior,
and where the update in the Markov chain is based on an elliptic update,
except that is also updated at each MCMC step by a slice sampler. The resulting algorithm is a slice sampler in that it does not reject new values of .
I find the proposal interesting, especially because it incorporates a “cyber-parameter” like within the Markov chain, but I wonder how widely the efficiency of the algorithm persists. Indeed, simulating from the prior cannot be very efficient when the likelihood strongly differs from the Gaussian prior. A lack of rejection is not a positive property per se and Gibbs sampling (incl. slice sampling) is notoriously slow for this very lack…