title: Model choice problems using approximate Bayesian computation with applications to pathogen transmission data sets.
abstract: Analytically or computationally intractable likelihood functions can arise in complex statistical inferential problems making them inaccessible to standard Bayesian inferential methods. Approximate Bayesian computation (ABC) methods address such inferential problems by replacing direct likelihood evaluations with repeated sampling from the model. ABC methods have been predominantly applied to parameter estimation problems and less to model choice problems due to the added difficulty of handling multiple model spaces. The ABC algorithm proposed here addresses model choice problems by extending Fearnhead and Prangle (2012, Journal of the Royal Statistical Society, Series B 74, 1-28) where the posterior mean of the model parameters estimated through regression formed the summary statistics used in the discrepancy measure. An additional stepwise multinomial logistic regression is performed on the model indicator variable in the regression step and the estimated model probabilities are incorporated into the set of summary statistics for model choice purposes. A reversible jump Markov chain Monte Carlo step is also included in the algorithm to increase model diversity for thorough exploration of the model space. This algorithm was applied to a validating example to demonstrate the robustness of the algorithm across a wide range of true model probabilities. Its subsequent use in three pathogen transmission examples of varying complexity illustrates the utility of the algorithm in inferring preference of particular transmission models for the pathogens.
authors.affiliation: School of Mathematical Sciences, Queensland University of Technology, Brisbane, Queensland, 4000, Australia.
authors.forename: Xing Ju
authors.initials: XJ
authors.lastname: Lee
authors.affiliation: School of Mathematical Sciences, Queensland University of Technology, Brisbane, Queensland, 4000, Australia.
authors.forename: Christopher C
authors.initials: CC
authors.lastname: Drovandi
authors.affiliation: School of Mathematical Sciences, Queensland University of Technology, Brisbane, Queensland, 4000, Australia.
authors.forename: Anthony N
authors.initials: AN
authors.lastname: Pettitt
mesh_terms: D001499:Bayes Theorem; D003141:Communicable Diseases / Q000453:epidemiology* / Q000635:transmission*; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D004196:Disease Outbreaks / Q000706:statistics & numerical data*; D004812:Epidemiologic Methods; D006801:Humans; D015233:Models, Statistical; D011159:Population Surveillance / Q000379:methods*; D015995:Prevalence; D018570:Risk Assessment / Q000379:methods
keywords: Approximate Bayesian computation; Hagelloch measles; MRSA; Model choice; Tristan da Cunha cold outbreak