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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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21

Implementing Adaptive Dose Finding Studies using Sequential Monte Carlo

James M. McGree, Christopher C. Drovandi and Anthony N. Pettitt

Queensland University of Technology, Brisbane, Australia

21.1 Introduction

In sequential optimal design, data are observed temporally, which allows a design to be adjusted at certain stages of an experiment. Such an approach is particularly useful when nonlinear models are of consideration as an optimal design may be dependent upon the assumed prior information about, say, the true model and parameter values. As more data are observed, an informative experiment is achieved through well-informed interventions. The experimental conditions are determined by what the data reveal, removing a total reliance on elicited or prior information.

Bayesian statistics provide the methodology for incorporating uncertainty about the true model and parameter values when designing an experiment. All inferences about the unknown parameter are based on the posterior, a target distribution that can be difficult to sample from directly. Typically, Markov chain Monte Carlo (MCMC) techniques are employed to sample from such distributions. Unfortunately, MCMC techniques can be computationally inefficient in sequential design.

We propose to use a sequential Monte Carlo (SMC) approach to sample from target distributions in deriving experimental conditions. SMC algorithms have been shown to be useful for sampling from a sequence of target distributions that are in some ...

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