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    ABSTRACT: Several Monte Carlo methods have been proposed for computing marginal likelihoods in Bayesian analyses. Some of these involve sampling from a sequence of intermediate distributions between the prior and posterior. A difficulty arises if the support in the posterior distribution is a proper subset of that in the prior distribution. This can happen in problems involving latent variables whose support depends upon the data and can make some methods inefficient and others invalid. The correction required for models of this type is derived and its use is illustrated by finding the marginal likelihoods in two examples. One concerns a model for competing risks. The other involves a zero-inflated over-dispersed Poisson model for counts of centipedes, using latent Gaussian variables to capture spatial dependence.
    Full-text · Article · Mar 2014 · Computational Statistics & Data Analysis
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    ABSTRACT: Crossover clinical trials can provide substantial benefits by eliminating inter-patient variation from treatment comparisons and by allowing multiple observations of each patient. They are particularly useful when sample sizes are necessarily small. These advantages proved particularly valuable in an assessment of clot prevention in children undergoing haemodialysis. Only small numbers of children are treated at any given time in any single dialysis unit, but each patient is obliged to attend two or three times each week, suggesting the use of a crossover trial with many periods. Standard crossover trials described in the literature (i) typically have fewer than 10 periods and (ii) are based on a model of questionable applicability to this study. This paper describes the derivation of an optimal crossover trial with 30 periods, which was used to compare two anticoagulants using nine patients. There is also a discussion of the analysis of the data obtained in the trial, which had a distribution markedly different from that anticipated when the study was designed. Copyright © 2013 John Wiley & Sons, Ltd.
    Preview · Article · Feb 2014 · Statistics in Medicine
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    ABSTRACT: A growing realization of the importance of stochasticity in cell and molecular processes has stimulated the need for statistical models that incorporate intrinsic (and extrinsic) variability. In this chapter we consider stochastic kinetic models of reaction networks leading to a Markov jump process representation of a system of interest. Traditionally, the stochastic model is characterized by a chemical master equation. While the intractability of such models can preclude a direct analysis, simulation can be straightforward and may present the only practical approach to gaining insight into a system's dynamics. We review exact simulation procedures before considering some efficient approximate alternatives.
    No preview · Article · May 2013 · Methods in molecular biology (Clifton, N.J.)
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