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73
Model selection and accounting for model uncertainty in graphical models using Occam's window
, 1993
"... We consider the problem of model selection and accounting for model uncertainty in highdimensional contingency tables, motivated by expert system applications. The approach most used currently is a stepwise strategy guided by tests based on approximate asymptotic Pvalues leading to the selection o ..."
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Cited by 342 (48 self)
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We consider the problem of model selection and accounting for model uncertainty in highdimensional contingency tables, motivated by expert system applications. The approach most used currently is a stepwise strategy guided by tests based on approximate asymptotic Pvalues 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
Marginal models for categorical data
, 1997
"... Statistical models defined by imposing restrictions on marginal distributions of contingency tables have received considerable attention recently. This paper introduces a general definition of marginal loglinear parameters and describes conditions for a marginal loglinear parameter to be a smoot ..."
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Cited by 44 (9 self)
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Statistical models defined by imposing restrictions on marginal distributions of contingency tables have received considerable attention recently. This paper introduces a general definition of marginal loglinear parameters and describes conditions for a marginal loglinear parameter to be a smooth parameterization of the distribution, and to be variation independent. Statistical models defined by imposing affine restrictions on the marginal loglinear parameters are investigated. These models generalize ordinary loglinear and multivariate logistic models. Sufficient conditions for a logaffine marginal model to be nonempty, and to be a curved exponential family are given. Standard large sample theory is shown to apply to maximum likelihood estimation of logaffine marginal models for a variety of sampling procedures.
Multidimensional Scaling
 Handbook of Statistics
, 2001
"... eflecting the importance or precision of dissimilarity # i j . 1. SOURCES OF DISTANCE DATA Dissimilarity information about a set of objects can arise in many different ways. We review some of the more important ones, organized by scientific discipline. 1.1. Geodesy. The most obvious application, ..."
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Cited by 38 (2 self)
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eflecting the importance or precision of dissimilarity # i j . 1. SOURCES OF DISTANCE DATA Dissimilarity information about a set of objects can arise in many different ways. We review some of the more important ones, organized by scientific discipline. 1.1. Geodesy. The most obvious application, perhaps, is in sciences in which distance is measured directly, although generally with error. This happens, for instance, in triangulation in geodesy. We have measurements which are approximately equal to distances, either Euclidean or spherical, depending on the scale of the experiment. In other examples, measured distances are less directly related to physical distances. For example, we could measure airplane or road or train travel distances between different cities. Physical distance is usually not the only factor determining these types of dissimilarities. 1 2 J. DE LEEUW<
Soft Evidential Update for Probabilistic Multiagent Systems
 INTERNATIONAL JOURNAL OF APPROXIMATE REASONING
, 2000
"... We address the problem of updating a probability distribution represented by a Bayesian network upon presentation of soft evidence. Our motivation ..."
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Cited by 28 (5 self)
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We address the problem of updating a probability distribution represented by a Bayesian network upon presentation of soft evidence. Our motivation
Network Routing
 Phil. Trans. R. Soc. Lond. A,337
, 1991
"... How should flows through a network be organized, so that the network responds sensibly to failures and overloads? The question is currently of considerable technological importance in connection with the development of computer and telecommunication networks, while in various other forms it has a lo ..."
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Cited by 27 (2 self)
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How should flows through a network be organized, so that the network responds sensibly to failures and overloads? The question is currently of considerable technological importance in connection with the development of computer and telecommunication networks, while in various other forms it has a long history in the fields of physics and economics. In all of these areas there is interest in how simple, local rules, often involving random actions, can produce coherent and purposeful behaviour at the macroscopic level. This paper describes some examples from these various fields, and indicates how analogies with fundamental concepts such as energy and price can provide powerful insights into the design of routing schemes for communication networks.
Computing Maximum Likelihood Estimates in loglinear models
, 2006
"... We develop computational strategies for extended maximum likelihood estimation, as defined in Rinaldo (2006), for general classes of loglinear models of widespred use, under Poisson and productmultinomial sampling schemes. We derive numerically efficient procedures for generating and manipulating ..."
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Cited by 25 (4 self)
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We develop computational strategies for extended maximum likelihood estimation, as defined in Rinaldo (2006), for general classes of loglinear models of widespred use, under Poisson and productmultinomial sampling schemes. We derive numerically efficient procedures for generating and manipulating design matrices and we propose various algorithms for computing the extended maximum likelihood estimates of the expectations of the cell counts. These algorithms allow to identify the set of estimable cell means for any given observable table and can be used for modifying traditional goodnessoffit tests to accommodate for a nonexistent MLE. We describe and take advantage of the connections between extended maximum likelihood
Univariate and Bivariate Loglinear Models for Discrete Test Score Distributions
, 2000
"... The welldeveloped theory of exponential families of distributions is applied to the problem of fitting the univariate histograms and discrete bivariate frequency distributions that often arise in the analysis of test scores. These models are powerful tools for many forms of parametric data smoothi ..."
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Cited by 19 (3 self)
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The welldeveloped theory of exponential families of distributions is applied to the problem of fitting the univariate histograms and discrete bivariate frequency distributions that often arise in the analysis of test scores. These models are powerful tools for many forms of parametric data smoothing and are particularly wellsuited to problems in which there is little or no theory to guide a choice of probability models, e.g., smoothing a distribution to eliminate roughness and zero frequencies in order to equate scores from different tests. Attention is given to efficient computation of the maximum likelihood estimates of the parameters using Newton's Method and to computationally efficient methods for obtaining the asymptotic standard errors of the fitted frequencies and proportions. We discuss tools that can be used to diagnose the quality of the fitted frequencies for both the univariate and the bivariate cases. Five examples, using real data, are used to illustrate the methods of this paper.