Showing papers by "James O. Berger published in 2009"

The formal definition of reference priors

Abstract: Reference analysis produces objective Bayesian inference, in the sense that inferential statements depend only on the assumed model and the available data, and the prior distribution used to make an inference is least informative in a certain information-theoretic sense. Reference priors have been rigorously defined in specific contexts and heuristically defined in general, but a rigorous general definition has been lacking. We produce a rigorous general definition here and then show how an explicit expression for the reference prior can be obtained under very weak regularity conditions. The explicit expression can be used to derive new reference priors both analytically and numerically.

The formal definition of reference priors

Abstract: Reference analysis produces objective Bayesian inference, in the sense that inferential statements depend only on the assumed model and the available data, and the prior distribution used to make an inference is least informative in a certain information-theoretic sense. Reference priors have been rigorously defined in specific contexts and heuristically defined in general, but a rigorous general definition has been lacking. We produce a rigorous general definition here and then show how an explicit expression for the reference prior can be obtained under very weak regularity conditions. The explicit expression can be used to derive new reference priors both analytically and numerically.

Modularization in Bayesian analysis, with emphasis on analysis of computer models

Abstract: Bayesian analysis incorporates different sources of information into a single analysis through Bayes theorem. When one or more of the sources of information are suspect (e.g., if the model assumed for the information is viewed as quite possibly being significantly flawed), there can be a concern that Bayes theorem allows this suspect information to overly influence the other sources of information. We consider a variety of situations in which this arises, and give methodological suggestions for dealing with the problem. After consideration of some pedagogical examples of the phenomenon, we focus on the interface of statistics and the development of complex computer models of processes. Three testbed computer models are considered, in which this type of issue arises.

Using Statistical and Computer Models to Quantify Volcanic Hazards

Abstract: Risk assessment of rare natural hazards, such as large volcanic block and ash or pyroclastic flows, is addressed. Assessment is approached through a combination of computer modeling, statistical modeling, and extreme-event probability computation. A computer model of the natural hazard is used to provide the needed extrapolation to unseen parts of the hazard space. Statistical modeling of the available data is needed to determine the initializing distribution for exercising the computer model. In dealing with rare events, direct simulations involving the computer model are prohibitively expensive. The solution instead requires a combination of adaptive design of computer model approximations (emulators) and rare event simulation. The techniques that are developed for risk assessment are illustrated on a test-bed example involving volcanic flow.

Predicting Vehicle Crashworthiness: Validation of Computer Models for Functional and Hierarchical Data

Abstract: The CRASH computer model simulates the effect of a vehicle colliding against different barrier types. If it accurately represents real vehicle crashworthiness, the computer model can be of great value in various aspects of vehicle design, such as the setting of timing of air bag releases. The goal of this study is to address the problem of validating the computer model for such design goals, based on utilizing computer model runs and experimental data from real crashes. This task is complicated by the fact that (i) the output of this model consists of smooth functional data, and (ii) certain types of collision have very limited data. We address problem (i) by extending existing Gaussian process-based methodology developed for models that produce real-valued output, and resort to Bayesian hierarchical modeling to attack problem (ii). Additionally, we show how to formally test if the computer model reproduces reality. Supplemental materials for the article are available online.

Natural induction: an objective Bayesian approach

Abstract: The statistical analysis of a sample taken from a finite population is a classic problem for which no generally accepted objective Bayesian results seem to exist. Bayesian solutions to this problem may be very sensitive to the choice of the prior, and there is no consensus as to the appropriate prior to use.

Special Issue on Computer Modeling

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