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February 2016 A Comparison of Inferential Methods for Highly Nonlinear State Space Models in Ecology and Epidemiology
Matteo Fasiolo, Natalya Pya, Simon N. Wood
Statist. Sci. 31(1): 96-118 (February 2016). DOI: 10.1214/15-STS534


Highly nonlinear, chaotic or near chaotic, dynamic models are important in fields such as ecology and epidemiology: for example, pest species and diseases often display highly nonlinear dynamics. However, such models are problematic from the point of view of statistical inference. The defining feature of chaotic and near chaotic systems is extreme sensitivity to small changes in system states and parameters, and this can interfere with inference. There are two main classes of methods for circumventing these difficulties: information reduction approaches, such as Approximate Bayesian Computation or Synthetic Likelihood, and state space methods, such as Particle Markov chain Monte Carlo, Iterated Filtering or Parameter Cascading. The purpose of this article is to compare the methods in order to reach conclusions about how to approach inference with such models in practice. We show that neither class of methods is universally superior to the other. We show that state space methods can suffer multimodality problems in settings with low process noise or model misspecification, leading to bias toward stable dynamics and high process noise. Information reduction methods avoid this problem, but, under the correct model and with sufficient process noise, state space methods lead to substantially sharper inference than information reduction methods. More practically, there are also differences in the tuning requirements of different methods. Our overall conclusion is that model development and checking should probably be performed using an information reduction method with low tuning requirements, while for final inference it is likely to be better to switch to a state space method, checking results against the information reduction approach.


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Matteo Fasiolo. Natalya Pya. Simon N. Wood. "A Comparison of Inferential Methods for Highly Nonlinear State Space Models in Ecology and Epidemiology." Statist. Sci. 31 (1) 96 - 118, February 2016.


Published: February 2016
First available in Project Euclid: 10 February 2016

zbMATH: 06946214
MathSciNet: MR3458595
Digital Object Identifier: 10.1214/15-STS534

Rights: Copyright © 2016 Institute of Mathematical Statistics


Vol.31 • No. 1 • February 2016
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