{"title":"Particle Methods for Stochastic Differential Equation Mixed Effects Models","authors":"Imke Botha, R. Kohn, C. Drovandi","doi":"10.1214/20-ba1216","DOIUrl":null,"url":null,"abstract":"Parameter inference for stochastic differential equation mixed effects models (SDEMEMs) is a challenging problem. Analytical solutions for these models are rarely available, which means that the likelihood is also intractable. In this case, exact inference is possible using the pseudo-marginal method, where the intractable likelihood is replaced by its nonnegative unbiased estimate. A useful application of this idea is particle MCMC, which uses a particle filter estimate of the likelihood. While the exact posterior is targeted by these methods, a naive implementation for SDEMEMs can be highly inefficient. We develop three extensions to the naive approach which exploits specific aspects of SDEMEMs and other advances such as correlated pseudo-marginal methods. We compare these methods on real and simulated data from a tumour xenography study on mice.","PeriodicalId":8446,"journal":{"name":"arXiv: Computation","volume":"6 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2019-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"17","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: Computation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1214/20-ba1216","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 17
Abstract
Parameter inference for stochastic differential equation mixed effects models (SDEMEMs) is a challenging problem. Analytical solutions for these models are rarely available, which means that the likelihood is also intractable. In this case, exact inference is possible using the pseudo-marginal method, where the intractable likelihood is replaced by its nonnegative unbiased estimate. A useful application of this idea is particle MCMC, which uses a particle filter estimate of the likelihood. While the exact posterior is targeted by these methods, a naive implementation for SDEMEMs can be highly inefficient. We develop three extensions to the naive approach which exploits specific aspects of SDEMEMs and other advances such as correlated pseudo-marginal methods. We compare these methods on real and simulated data from a tumour xenography study on mice.