Unbiased Bayesian inference for population Markov jump processes via random truncations

Research output: Contribution to journalArticlepeer-review

Abstract

We consider continuous time Markovian processes where populations of individual agents interact stochastically according to kinetic rules. Despite the increasing prominence of such models in fields ranging from biology to smart cities, Bayesian inference for such systems remains challenging, as these are continuous time, discrete state systems with potentially infinite state-space. Here we propose a novel efficient algorithm for joint state / parameter posterior sampling in population Markov Jump processes. We introduce a class of pseudo-marginal sampling algorithms based on a random truncation method which enables a principled treatment of infinite state spaces. Extensive evaluation on a number of benchmark models shows that this approach achieves considerable savings compared to state of the art methods, retaining accuracy and fast convergence. We also present results on a synthetic biology data set showing the potential for practical usefulness of our work.
Original languageEnglish
Pages (from-to)991–1002
Number of pages12
JournalStatistics and Computing
Volume27
Issue number4
Early online date2 Jun 2016
DOIs
Publication statusPublished - 1 Jul 2017

Keywords

  • Markov Jump Processes
  • Markov Chain Monte Carlo
  • Pseudo-marginal methods
  • Parameter estimation
  • Stochastic processes

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