Statistical inference for stochastic simulation models - theory and application

• Published in: Ecology letters Vol. 14; no. 8; pp. 816 - 827
• Main Authors: Hartig, Florian, Calabrese, Justin M., Reineking, Björn, Wiegand, Thorsten, Huth, Andreas
• Format: Journal Article
• Language: English
• Published: Oxford, UK Blackwell Publishing Ltd 01.08.2011; Blackwell
• Subjects: Algorithms; Animal and plant ecology; Animal, plant and microbial ecology; Bayes Theorem; Bayesian analysis; Bayesian statistics; Biological and medical sciences; Biological Sciences; Boundary conditions; Computer Simulation; Ecology; Ecosystem; Fundamental and applied biological sciences. Psychology; General aspects; General aspects. Techniques; indirect inference; intractable likelihood; inverse modelling; likelihood approximation; likelihood-free inference; Markov Chains; maximum likelihood; methodology; Methods and techniques (sampling, tagging, trapping, modelling...); model selection; Models, Statistical; Monte Carlo Method; parameter estimation; simulation models; Statistical inference; Statistical models; statistics; Statistics, Nonparametric; Stochastic models; stochastic simulation; Stochastic model; Parameter estimation; Statistical analysis; Theory; indirect inference; likelihood-free inference; model selection; Stochastic simulation; Modeling; Statistics; inverse modelling; likelihood approximation; Bayesian statistics; Maximum likelihood; Simulation model; intractable likelihood
• ISSN: 1461-023X; 1461-0248; 1461-0248
• DOI: 10.1111/j.1461-0248.2011.01640.x

Ecology Letters (2011) 14: 816–827 Statistical models are the traditional choice to test scientific theories when observations, processes or boundary conditions are subject to stochasticity. Many important systems in ecology and biology, however, are difficult to capture with statistical models. Stochastic simulation models offer an alternative, but they were hitherto associated with a major disadvantage: their likelihood functions can usually not be calculated explicitly, and thus it is difficult to couple them to well‐established statistical theory such as maximum likelihood and Bayesian statistics. A number of new methods, among them Approximate Bayesian Computing and Pattern‐Oriented Modelling, bypass this limitation. These methods share three main principles: aggregation of simulated and observed data via summary statistics, likelihood approximation based on the summary statistics, and efficient sampling. We discuss principles as well as advantages and caveats of these methods, and demonstrate their potential for integrating stochastic simulation models into a unified framework for statistical modelling.