A New Framework for Inference on Markov Population Models

TL;DR

This paper introduces a novel inference framework for Markov population models using a joint Gaussian likelihood derived from a deterministic limit of stochastic differential equations, improving predictive accuracy without stochastic infill.

Contribution

The paper develops the Joint Gaussian Deterministic Limiting Approximation (JGDLA) for Markov population models, enabling inference solely through deterministic equations and outperforming existing stochastic schemes.

Findings

JGDLA provides improved predictive power over Euler-Maruyama.

Method requires no stochastic infill, simplifying computations.

Successfully applied to COVID-19 cruise ship data.

Abstract

In this work we construct a joint Gaussian likelihood for approximate inference on Markov population models. We demonstrate that Markov population models can be approximated by a system of linear stochastic differential equations with time-varying coefficients. We show that the system of stochastic differential equations converges to a set of ordinary differential equations. We derive our proposed joint Gaussian deterministic limiting approximation (JGDLA) model from the limiting system of ordinary differential equations. The results is a method for inference on Markov population models that relies solely on the solution to a system deterministic equations. We show that our method requires no stochastic infill and exhibits improved predictive power in comparison to the Euler-Maruyama scheme on simulated susceptible-infected-recovered data sets. We use the JGDLA to fit a stochastic susceptible-exposed-infected-recovered system to the Princess Diamond COVID-19 cruise ship data set.