We consider the problem of model selection and accounting for model uncertainty in high-dimensional contingency tables, motivated by expert system applications. The approach most used currently is a stepwise strategy guided by tests based on approximate asymptotic P-values leading to the selection of a single model; inference is then conditional on the selected model. The sampling properties of such a strategy are complex, and the failure to take account of model uncertainty leads to underestimation of uncertainty about quantities of interest. In principle, a panacea is provided by the standard Bayesian formalism which averages the posterior distributions of the quantity of interest under each of the models, weighted by their posterior model probabilities. Furthermore, this approach is optimal in the sense of maximising predictive ability. However, this has not been used in practice because computing the posterior model probabilities is hard and the number of models is very large (often greater than 1011). We argue that the standard Bayesian formalism is unsatisfactory and we propose an alternative Bayesian approach that, we contend, takes full account of the true model uncertainty byaveraging overamuch smaller set of models. An efficient search algorithm is developed for nding these models. We consider two classes of graphical models that arise in expert systems: the recursive causal models and the decomposable

We discuss a strategy for polychotomous classification that involves estimating class probabilities for each pair of classes, and then coupling the estimates together. The coupling model is similar to the Bradley-Terry method for paired comparisons. We study the nature of the class probability estimates that arise, and examine the performance of the procedure in real and simulated datasets. Classifiers used include linear discriminants, nearest neighbors, adaptive nonlinear methods, and the support vector machine. Department of Statistics, Sequoia Hall, Stanford University, Stanford California 94305; trevor@playfair.stanford.edu y Department of Preventive Medicine and Biostatistics, and Department of Statistics; tibs@utstat.toronto.edu 1 Introduction We consider the discrimination problem with K classes and N training observations. The training observations consist of predictor measurements x = (x 1 ; x 2 ; : : : x p ) on p predictors and the known class memberships. Our goal is...

This paper provides an overview of methods and systems developed for record linkage. Modern record linkage begins with the pioneering work of Newcombe and is especially based on the formal mathematical model of Fellegi and Sunter. In their seminal work, Fellegi and Sunter introduced many powerful ideas for estimating record linkage parameters and other ideas that still influence record linkage today. Record linkage research is characterized by its synergism of statistics, computer science, and operations research. Many difficult algorithms have been developed and put in software systems. Record linkage practice is still very limited. Some limits are due to existing software. Other limits are due to the difficulty in automatically estimating matching parameters and error rates, with current research highlighted by the work of Larsen and Rubin. Keywords: computer matching, modeling, iterative fitting, string comparison, optimization RsSUMs Cet article donne une vue d'ensemble sur les ...

We construct Markov chain algorithms for sampling from discrete exponential families conditional on a sufficient statistic. Examples include generating tables with fixed row and column sums and higher dimensional analogs. The algorithms involve finding bases for associated polynomial ideals and so an excursion into computational algebraic geometry.

An algebra is presented for a simple probabilistic data model that may be regarded as an extension of the standard relational model. The probabilistic algebra is developed in such a way that (restricted to α-acyclic database schemes) the relational algebra is a homomorphic image of it. Strictly probabilistic results are emphasized. Variations on the basic probabilistic data model are discussed. The algebra is used to explicate a commonly used statistical smoothing procedure and is shown to be potentially very useful for decision support with uncertain information.

Ways of obtaining approximate Bayes factors for generalized linear models are described, based on the Laplace method for integrals. I propose a new approximation which uses only the output of standard computer programs such as GUM; this appears to be quite accurate. A reference set of proper priors is suggested, both to represent the situation where there is not much prior information, and to assess the sensitivity of the results to the prior distribution. The methods can be used when the dispersion parameter is unknown, when there is overdispersion, to compare link functions, and to compare error distributions and variance functions. The methods can be used to implement the Bayesian approach to accounting for model uncertainty. I describe an application to inference about relative risks in the presence of control factors where model uncertainty is large and important. Software to implement the

INTRODUCTION Matching has a long history of uses in statistical surveys and administrative data development. A business register consisting of names, addresses, and other identifying information such as total financial receipts might be constructed from tax and employment data bases (see chapters by Colledge, Nijhowne, and Archer). A survey of retail establishments or agricultural establishments might combine results from an area frame and a list frame. To produce a combined estimator, units from the area frame would need to be identified in the list frame (see Vogel-Kott chapter). To estimate the size of a (sub)population via capture-recapture techniques, one needs to accurately determine units common to two or more independent listings (Sekar and Deming 1949; Scheuren 1983; Winkler 1989b). Samples must be drawn appropriately to estimate overlap (Deming and Gleser 1959). Rather than develop a special survey to collect data for policy decisions, it might be more appropriate t

Abstract not found

When the Gibbs sampler is used to estimate posterior distributions (Gelfand and Smith, 1990), the question of how many iterations are required is central to its implementation. When interest focuses on quantiles of functionals of the posterior distribution, we describe an easily-implemented method for determining the total number of iterations required, and also the number of initial iterations that should be discarded to allow for "burn-in". The method uses only the Gibbs iterates themselves, and does not, for example, require external specification of characteristics of the posterior density. Here the method is described for the situation where one long run is generated, but it can also be easily applied if there are several runs from different starting points. It also applies more generally to Markov chain Monte Carlo schemes other than the Gibbs sampler. It can also be used when several quantiles are to be estimated, when the quantities of interest are probabilities rath...

Approximating the joint data distribution of a multi-dimensional data set through a compact and accurate histogram synopsis is a fundamental problem arising in numerous practical scenarios, including query optimization and approximate query answering. Existing solutions either rely on simplistic independence assumptions or try to directly approximate the full joint data distribution over the complete set of attributes. Unfortunately, both approaches are doomed to fail for high-dimensional data sets with complex correlation patterns between attributes. In this paper, we propose a novel approach to histogram-based synopses that employs the solid foundation of statistical interaction models to explicitly identify and exploit the statistical characteristics of the data. Abstractly, our key idea is to break the synopsis into (1) a statistical interaction model that accurately captures significant correlation and independence patterns in data, and (2) a collection of histograms on low-dimensional marginals that, based on the model, can provide accurate approximations of the overall joint data distribution. Extensive experimental results with several real-life data sets verify the effectiveness of our approach. An important aspect of our general, model-based methodology is that it can be used to enhance the performance of other synopsis techniques that are based on data-space partitioning (e.g., wavelets) by providing an effective tool to deal with the “dimensionality curse”. 1.