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.
Organisations
Publications
Gramacy R
(2012)
Simulation-based Regularized Logistic Regression
in Bayesian Analysis
Gramacy R
(2010)
Cases for the nugget in modeling computer experiments
in Statistics and Computing
Gramacy R
(2011)
Particle Learning of Gaussian Process Models for Sequential Design and Optimization
in Journal of Computational and Graphical Statistics
Gramacy R
(2010)
Simulation-based Regularized Logistic Regression
Gramacy R
(2010)
Categorical Inputs, Sensitivity Analysis, Optimization and Importance Tempering with tgp Version 2, an R Package for Treed Gaussian Process Models
in Journal of Statistical Software
Gramacy R
(2010)
Shrinkage regression for multivariate inference with missing data, and an application to portfolio balancing
in Bayesian Analysis
Gramacy R
(2010)
Optimization Under Unknown Constraints
Gramacy R
(2008)
Importance tempering
in Statistics and Computing
Franzke C
(2012)
Robustness of estimators of long-range dependence and self-similarity under non-Gaussianity
in Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences