Standard statistical practice ignores model uncertainty. Data analysts typically select a model from some class of models and then proceed as if the selected model had generated the data. This approach ignores the uncertainty in model selection, leading to over-con dent inferences and decisions that are more risky than one thinks they are. Bayesian model averaging (BMA) provides a coherent mechanism for accounting for this model uncertainty. Several methods for implementing BMA haverecently emerged. We discuss these methods and present anumber of examples. In these examples, BMA provides improved out-of-sample predictive performance. We also provide a catalogue of

There is a trend in recent OCR development to improve system performance by combining recognition results of several complementary algorithms. This thesis examines the classifier combination problem under strict separation of the classifier and combinator design. None other than the fact that every classifier has the same input and output specification is assumed about the training, design or implementation of the classifiers. A general theory of combination should possess the following properties. It must be able to combine anytype of classifiers regardless of the level of information contents in the outputs. In addition, a general combinator must be able to combine any mixture of classifier types and utilize all information available. Since classifier independence is difficult to achieve and to detect, it is essential for a combinator to handle correlated classifiers robustly. Although the performance of a robust (against correlation) combinator can be improved by adding classifiers indiscriminantly, it is generally of interest to achieve comparable performance with the minimum number of classifiers. Therefore, the combinator should have the ability to eliminate redundant classifiers. Furthermore, it is desirable to have a complexity control mechanism for the combinator. In the past, simplifications come from assumptions and constraints imposed by the system designers. In the general theory, there should be a mechanism to reduce solution complexity by exercising non-classifier-specific constraints. Finally, a combinator should capture classifier/image dependencies. Nearly all combination methods have ignored the fact that classifier performances (and outputs) depend on various image characteristics, and this dependency is manifested in classifier output patterns in relation to input imag...

Measures of surprise refer to quantifications of the degree of incompatibility of data with some hypothesized model H 0 without any reference to alternative models. Traditional measures of surprise have been the p-values, which are however known to grossly overestimate the evidence against H 0 . Strict Bayesian analysis calls for an explicit specification of all possible alternatives to H 0 so Bayesians have not made routine use of measures of surprise. In this report we CRITICALLY REVIEw the proposals that have been made in this regard. We propose new modifications, stress the connections with robust Bayesian analysis and discuss the choice of suitable predictive distributions which allow surprise measures to play their intended role in the presence of nuisance parameters. We recommend either the use of appropriate likelihoodratio type measures or else the careful calibration of p-values so that they are closer to Bayesian answers. Key words and phrases. Bayes factors; Bayesian p-values; Bayesian robustness; Conditioning; Model checking; Predictive distributions. 1.

Elements of Bayesian nonparametric statistical thought are explored in a series of case studies. Interpretation of a measurement as continuous, ordered, polychotomous, or dichotomous provides a framework in which examples are presented. Bayesian analogues to frequentist nonparametrics and overt Bayesian techniques are employed. Examples included are as follows: (1) averaging over families of distributions, (2) estimation of a single distribution function, (3) comparing several distribution functions, (4) estimating the coefficient of a concomitant variable affecting a distribution function, (5) monitoring compliance with a dichotomous measurement, and (6) using the multinomial for a categorization of any measurement's range. Lindley (1972, §12.2) provides an intitial sketch. Hill's (1968) nonparametric Bayesian construct and Berliner and Hill's (1988) application to survival are also reviewed. A commonality in the mechanics of these examples is the calculation of a marginal distribution over model parameters. Many are predictive distributions, resulting from an average over a likelihood and vague prior, and leaving observables for the calculations, as described by Roberts (1965) and advocated by Geisser (1971). Other specific observations from these efforts include the following