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Bayesian Statistics
Bayesian asymptotic theory (see under asymptotic theory of statistical inference). Bayesian methodology and computation. Various aspects of generalised regression models, such as approximate analysis of data from location-scale regression models (Biometrika, 1987, for example). Applications of this work include the analysis of censored survival data arising in the medical and biological sciences, and of failure-time data arising in reliability studies. Work on likelihood and Bayesian inference for ratios of regression coefficients in linear models appeared in Ann. Inst. Stat. Math. (2006). The analysis of transformations in regression models (for example, Bayesian Statistics 2, 1985) has interesting links with parameter orthogonality (see my discussion of D. R. Cox and N. Reid. J. R. Statist. Soc. B, 1987). Parameterisation issues more generally have been addressed. An invited paper on Bayesian computation based on directed likelihood appeared in Bayesian Statistics 5 (1996). Other papers on this topic and related hybrid computational schemes include Statistics & Computing, 2005, Test, 2003 and current work includes hybrid asymptotic/Monte Carlo strategies that allow the fine-tuning of higher-order asymptotic formulae via simulation. A current topic of research is nonparametric hierarchical Bayesian clustering using Dirichlet Process Mixture models, with application to brand segmentation (in conjunction with a research student). Objective Bayes. Based on coverage probability bias and probability matching priors (Biometrika, 2001, 2005, Handbook of Statistics, 2005, IMS Collections, 2008) and relative entropy loss for prediction (Ann. Statist., 2006). The latter topic quantifies the predictive performance of prior distributions and can be used as a tool for objective Bayes or for the study of robust prediction (the latter in conjunction with a research student). Some promising new results on weakly admissible invariant prior classes for prediction were presented at OBayes6 in 2007.
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