Geometric ergodicity of Rao and Teh's algorithm for Markov jump processes

TL;DR

This paper proves that Rao and Teh's MCMC algorithm for Markov jump processes converges rapidly by establishing its geometric ergodicity, ensuring reliable sampling from the posterior distribution.

Contribution

The paper demonstrates the geometric ergodicity of Rao and Teh's algorithm, providing theoretical guarantees of its convergence rate for Markov jump processes.

Findings

The Markov chain is geometrically ergodic.

A geometric drift condition towards a small set is established.

The results ensure reliable posterior sampling.

Abstract

Rao and Teh (2013) introduced an efficient MCMC algorithm for sampling from the posterior distribution of a hidden Markov jump process. The algorithm is based on the idea of sampling virtual jumps. In the present paper we show that the Markov chain generated by Rao and Teh's algorithm is geometrically ergodic. To this end we establish a geometric drift condition towards a small set.