We present an importance sampling algorithm that can produce realisations of Markovian epidemic models that exactly match observations, taken to be the number of a single event type over a period of time. The importance sampling can be used to construct an efficient particle filter that targets the states of a system and hence estimate the likelihood to perform Bayesian parameter inference. When used in a particle marginal Metropolis Hastings scheme, the importance sampling provides a large speed-up in terms of the effective sample size per unit of computational time, compared to simple bootstrap sampling. The algorithm is general, with minimal restrictions, and we show how it can be applied to any discrete-state continuous-time Markov chain where we wish to exactly match the number of a single event type over a period of time.
Bounds on $R_0$ and final epidemic size when the next-generation matrix $M$ is only partially known
Health Emergencies Center, Bruno Kessler Foundation（布鲁诺·凯瑟勒基金会紧急事件中心）；Department of Mathematics, University of Trento（特伦托大学数学系）；School of Mathematical Sciences, University of Nottingham（诺丁汉大学数学科学学院）；Department of Mathematics, Stockholm University（斯德哥尔摩大学数学系）
Bayesian Inference of Reproduction Number from Epidemiological and Genetic Data Using Particle MCMC
Nuffield Department of Medicine, University of Oxford（牛津大学纳菲尔德医学系）；School of Mathematics, Statistics and Physics, Newcastle University（纽卡斯尔大学数学、统计与物理学院）；Department of Statistics, University of Warwick（华威大学统计学系）；School of Life Sciences, University of Warwick（华威大学生命科学学院）；The Zeeman Institute for Systems Biology and Infectious Disease Epidemiology Research, University of Warwick（华威大学泽曼系统与传染病流行病学研究学院）
