A0513
Title: Haar-Weave-Metropolis kernel
Authors: Kengo Kamatani - ISM (Japan) [presenting]
Xiaolin Song - Osaka University (Japan)
Abstract: Recently, many Markov chain Monte Carlo methods have been developed with deterministic reversible transform proposals inspired by the Hamiltonian Monte Carlo method. The deterministic transform is relatively easy to reconcile with the local information (gradient etc.) of the target distribution. However, as the ergodic theory suggests, these deterministic proposal methods seem to be incompatible with robustness and lead to poor convergence, especially in the case of target distributions with heavy tails. On the other hand, the Markov kernel using the Haar measure is relatively robust since it learns global information about the target distribution by introducing global parameters. However, it requires a density preserving condition, and many deterministic proposals break this condition. We carefully select deterministic transforms that preserve the value of the density function and create a Markov kernel, the Weave-Metropolis kernel, using the deterministic transforms. By combining with the Haar measure, we also introduce the Haar-Weave-Metropolis kernel.
