Robust Bayesian Analysis (Lecture Notes in Statistics, 152)

Robust Bayesian analysis aims at overcoming the traditional objection to Bayesian analysis of its dependence on subjective inputs, mainly the prior and the loss. Its purpose is the determination of the impact of the inputs to a Bayesian analysis (the prior, the loss and the model) on its output when the inputs range in certain classes. If the impact is considerable, there is sensitivity and we should attempt to further refine the information the incumbent classes available, perhaps through additional constraints on and/ or obtaining additional data; if the impact is not important, robustness holds and no further analysis and refinement would be required. Robust Bayesian analysis has been widely accepted by Bayesian statisticians; for a while it was even a main research topic in the field. However, to a great extent, their impact is yet to be seen in applied settings. This volume, therefore, presents an overview of the current state of robust Bayesian methods and their applications and identifies topics of further in­ terest in the area. The papers in the volume are divided into nine parts covering the main aspects of the field. The first one provides an overview of Bayesian robustness at a non-technical level. The paper in Part II con­ cerns foundational aspects and describes decision-theoretical axiomatisa­ tions leading to the robust Bayesian paradigm, motivating reasons for which robust analysis is practically unavoidable within Bayesian analysis. Front Matter....Pages i-xiii Front Matter....Pages 1-1 Bayesian Robustness....Pages 1-32 Front Matter....Pages 33-33 Topics on the Foundations of Robust Bayesian Analysis....Pages 33-44 Front Matter....Pages 45-45 Global Bayesian Robustness for Some Classes of Prior Distributions....Pages 45-70 Local Robustness in Bayesian Analysis....Pages 71-88 Global and Local Robustness Approaches: Uses and Limitations....Pages 89-108 On the Use of the Concentration Function in Bayesian Robustness....Pages 109-126 Front Matter....Pages 127-127 Likelihood Robustness....Pages 127-143 Front Matter....Pages 145-145 Ranges of Posterior Expected Losses and ε-Robust Actions....Pages 145-159 Computing Efficient Sets in Bayesian Decision Problems....Pages 161-186 Stability of Bayes Decisions and Applications....Pages 187-196 Front Matter....Pages 197-197 Robustness Issues in Bayesian Model Selection....Pages 197-222 Bayesian Robustness and Bayesian Nonparametrics....Pages 223-240 Γ-Minimax: A Paradigm for Conservative Robust Bayesians....Pages 241-259 Front Matter....Pages 261-261 Linearization Techniques in Bayesian Robustness....Pages 261-272 Methods for Global Prior Robustness under Generalized Moment Conditions....Pages 273-293 Efficient MCMC Schemes for Robust Model Extensions Using Encompassing Dirichlet Process Mixture Models....Pages 295-315 Front Matter....Pages 317-317 Sensitivity Analysis in IctNeo....Pages 317-334 Sensitivity of Replacement Priorities for Gas Pipeline Maintenance....Pages 335-350 Robust Bayesian Analysis in Medical and Epidemiological Settings....Pages 351-372 A Robust Version of the Dynamic Linear Model with an Economic Application....Pages 373-383 Front Matter....Pages 317-317 Prior Robustness in Some Common Types of Software Reliability Model....Pages 385-400 Back Matter....Pages 401-424

This edited volume will present an overview of robust Bayesian methods and their applications. Chapters will explore both foundational and computational aspects together with applications. Chapters concerning foundations will describe decision theoretical axiomatisations leading to the robust Bayesian paradigm and motivate reasons for which robust analyses are practically unavoidable within Bayesian analysis.