Trans-Dimensional Markov Chain Simulation for both Bayesian and Classical Model Determination

Lead Research Organisation: University of Cambridge
Department Name: Pure Maths and Mathematical Statistics

Abstract

The proposed programme of research is intended to construct, investigate, develop and apply a range of novel model exploration techniques that can be used to either select or average over competing models. These methods will be based upon the idea of simulating Markov chains capable of moving between states of different dimensions corresponding to competing models under consideration. Whether the aim is to locate modes or explore model space more generally, these methods will be applicable under any statistical philosophy and will facilitate investigation of the increasingly complex (yet realistic) models required by modern science.Under the proposed programme of research, we will demonstrate the utility of these new simulation methods over a wide range of application areas that will be used to motivate and direct methodological developments. Particular areas of application include time series modelling of archaeological and geological data; analysis of epidemiological data associated with a variety of diseases of political, economic and biological importance; and variable selection in economic modelling. In each of these areas, it is intended that our work will provide significant advances in the scientific understanding of the stochastic processes under study.

Publications

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Broderick T (2011) Classification and Categorical Inputs with Treed Gaussian Process Models in Journal of Classification

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Franzke CL (2012) Robustness of estimators of long-range dependence and self-similarity under non-Gaussianity. in Philosophical transactions. Series A, Mathematical, physical, and engineering sciences

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Gramacy R (2008) Importance tempering in Statistics and Computing

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Gramacy R (2012) Simulation-based Regularized Logistic Regression in Bayesian Analysis

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Gramacy R (2010) Cases for the nugget in modeling computer experiments in Statistics and Computing

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Lawrence J (2013) The importance of prior choice in model selection: a density dependence example in Methods in Ecology and Evolution

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Taddy M (2011) Dynamic Trees for Learning and Design in Journal of the American Statistical Association