Rate optimality of Random walk Metropolis algorithm in high-dimension with heavy-tailed target distribution

Understand

The choice of the increment distribution is crucial for the random-walk Metropolis-Hastings (RWM) algorithm.

• In this paper we study the optimal choice in high-dimension setting among all possible increment distributions.
• The conclusion is rather counter intuitive, but the optimal rate of convergence is attained by the usual choice, the normal distribution as the increment distribution.
• In particular, no heavy-tailed increment distribution can improve the rate.