Simulation based sequential Monte Carlo methods for discretely observed Markov processes

TL;DR

This paper introduces a novel sequential Monte Carlo algorithm leveraging coupled simulations and importance sampling to efficiently estimate parameters of discretely observed Markov processes, demonstrated on ecological and genetic models.

Contribution

The paper presents two innovations—coupled simulations and an importance sampling scheme—that significantly enhance the efficiency of SMC algorithms for Markov process parameter estimation.

Findings

Improved efficiency of SMC algorithms for Markov processes

Successful application to ecological and genetic models

Minimal impact on simulation speed

Abstract

Parameter estimation for discretely observed Markov processes is a challenging problem. However, simulation of Markov processes is straightforward using the Gillespie algorithm. We exploit this ease of simulation to develop an effective sequential Monte Carlo (SMC) algorithm for obtaining samples from the posterior distribution of the parameters. In particular, we introduce two key innovations, coupled simulations, which allow us to study multiple parameter values on the basis of a single simulation, and a simple, yet effective, importance sampling scheme for steering simulations towards the observed data. These innovations substantially improve the efficiency of the SMC algorithm with minimal effect on the speed of the simulation process. The SMC algorithm is successfully applied to two examples, a Lotka-Volterra model and a Repressilator model.