Time series analysis via mechanistic models

Carles Bretó, Daihai He, Edward L. Ionides, Aaron A. King

Research output: Journal article publicationJournal articleAcademic researchpeer-review

113 Citations (Scopus)

Abstract

The purpose of time series analysis via mechanistic models is to reconcile the known or hypothesized structure of a dynamical system with observations collected over time. We develop a framework for constructing nonlinear mechanistic models and carrying out inference. Our framework permits the consideration of implicit dynamic models, meaning statistical models for stochastic dynamical systems which are specified by a simulation algorithm to generate sample paths. Inference procedures that operate on implicit models are said to have the plug-and-play property. Our work builds on recently developed plug-and-play inference methodology for partially observed Markov models. We introduce a class of implicitly specified Markov chains with stochastic transition rates, and we demonstrate its applicability to open problems in statistical inference for biological systems. As one example, these models are shown to give a fresh perspective on measles transmission dynamics. As a second example, we present a mechanistic analysis of cholera incidence data, involving interaction between two competing strains of the pathogen Vibrio cholerae.
Original languageEnglish
Pages (from-to)319-348
Number of pages30
JournalAnnals of Applied Statistics
Volume3
Issue number1
DOIs
Publication statusPublished - 1 Mar 2009
Externally publishedYes

Keywords

  • Cholera
  • Filtering
  • Maximum likelihood
  • Measles
  • Sequential Monte Carlo
  • State space model

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • Statistics, Probability and Uncertainty

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