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Case Studies in Bayesian Statistical Modelling and Analysis by Anthony N. Pettitt, Kerrie L. Mengersen, Clair L. Alston

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22

Likelihood-Free Inference for Transmission Rates of Nosocomial Pathogens

Christopher C. Drovandi and Anthony N. Pettitt

Queensland University of Technology, Brisbane, Australia

22.1 Introduction

A Bayesian statistician is interested in obtaining the posterior distribution, π(θ|y), given by

equation

where θ is the parameter of interest, y is observed data assumed to be drawn from f(.|.) and π(.) is the prior. Thus, Bayesian inferences are still heavily reliant on the availability of the likelihood function. However, it is becoming increasingly apparent that there are many statistical models that do not provide a computationally tractable likelihood function.

Fortunately a class of simulation methodologies popularly termed approximate Bayesian computation (ABC) can produce statistically valid inferences about the posterior distribution when the likelihood function is not computationally tractable.

Although ABC approaches do not necessitate the evaluation of the likelihood function, it is paramount that simulating data from the statistical model is relatively straightforward to perform. The initial need for a likelihood function is alleviated by simulating data from the model and searching for parameter values that produce simulated data close to the observed data. This assessment of closeness typically involves comparing a set of summary statistics.

Also often referred to as likelihood-free ...

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