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March 2009 Time series analysis via mechanistic models
Carles Bretó, Daihai He, Edward L. Ionides, Aaron A. King
Ann. Appl. Stat. 3(1): 319-348 (March 2009). DOI: 10.1214/08-AOAS201

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.

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Carles Bretó. Daihai He. Edward L. Ionides. Aaron A. King. "Time series analysis via mechanistic models." Ann. Appl. Stat. 3 (1) 319 - 348, March 2009. https://doi.org/10.1214/08-AOAS201

Information

Published: March 2009
First available in Project Euclid: 16 April 2009

zbMATH: 1160.62080
MathSciNet: MR2668710
Digital Object Identifier: 10.1214/08-AOAS201

Keywords: cholera , Filtering , maximum likelihood , measles , sequential Monte Carlo , state space model

Rights: Copyright © 2009 Institute of Mathematical Statistics

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Vol.3 • No. 1 • March 2009
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