0.234: The Myth of a Universal Acceptance Ratio for Monte Carlo Simulations

Two well-known papers by Gelman, Roberts, and Gilks have proposed the application of the results of an interesting mathematical proof to practical optimizations of Markov Chain Monte Carlo computer simulations. In particular, they advocated tuning the simulation parameters to select an acceptance ratio of 0.234. In this paper, we point out that although the proof is valid, its significance is questionable, and its application to practical computations is not advisable. The simulation algorithm considered in the proof is very inefficient and produces poor results under all circumstances.