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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 ..."
Abstract

Cited by 266 (46 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
Split models for contingency tables
, 2003
"... A framework for loglinear models with context specific independence structures, i.e. conditional independencies holding only for specific values of the conditioning variables is introduced. This framework is constituted by the class of split models. Also a software package named YGGDRASIL which is ..."
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Cited by 8 (1 self)
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A framework for loglinear models with context specific independence structures, i.e. conditional independencies holding only for specific values of the conditioning variables is introduced. This framework is constituted by the class of split models. Also a software package named YGGDRASIL which is designed for statistical inference in split models is presented. Split models are an extension of graphical models for contingency tables. The treatment of split models includes estimation, representation and a Markov property for reading off independencies holding in a specific context. Two examples, including an illustration of the use of YGGDRASIL are
Relaxing the Local Independence Assumption for Quantitative Learning in Acyclic Directed Graphical Models through Hierarchical Partition Models
 Proceedings of Artificial Intelligence and Statistics ’99
, 1999
"... The simplest method proposed by Spiegelhalter and Lauritzen (1990) to perform quantitative learning in ADG presents a potential weakness: the local independence assumption. We propose to alleviate this problem through the use of Hierarchical Partition Models. Our approach is compared with the previo ..."
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Cited by 6 (0 self)
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The simplest method proposed by Spiegelhalter and Lauritzen (1990) to perform quantitative learning in ADG presents a potential weakness: the local independence assumption. We propose to alleviate this problem through the use of Hierarchical Partition Models. Our approach is compared with the previous one from an interpretative and predictive point of view. 1 INTRODUCTION Spiegelhalter and Lauritzen (1990) (SL) proposed a Bayesian model for Acyclic Directed Graphical Models (ADG) (also known as Bayesian Networks) that has become somewhat standard in the burgeoning literature on learning discrete graphical models. The basic idea is to treat the conditional probabilities of the random variables at each vertex in the graph as unknowns and associate a prior distribution on each one (the conditioning in each case is on the random variables associated with the parent vertices in the graph). The simplest approach of SL introduces strong assumptions on the unknown conditional probabilities ...
YGGDRASIL  A statistical package for learning Split Models
, 2000
"... There are two main objectives of this paper. The first is to present a statistical framework for models with context specific independence structures, i.e. conditional independencies holding only for specific values of the conditioning variables. This framework is constituted by the class of s ..."
Abstract
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There are two main objectives of this paper. The first is to present a statistical framework for models with context specific independence structures, i.e. conditional independencies holding only for specific values of the conditioning variables. This framework is constituted by the class of split models. Split models are an extension of graphical models for contingency tables and allow for a more sophisticated modelling than graphical models. The treatment of split models include estimation, representation and a Markov property for reading off those independencies holding in a specific context. The second objective is to present a software package named YGGDRASIL which is designed for statistical inference in split models, i.e. for learning such models on the basis of data. 1 INTRODUCTION Recently there has been an increased interest in models which explicitly account for conditional independencies holding only for specific values of the variables conditioned upon. ...