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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 ..."
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Cited by 270 (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
Probabilistic Reasoning in Decision Support Systems: From Computation to Common Sense
, 1993
"... Most areas of engineering, science, and management use important tools based on probabilistic methods. The common thread of the entire spectrum of these tools is aiding in decision making under uncertainty: the choice of an interpretation of reality or the choice of a course of action. Although the ..."
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Cited by 25 (14 self)
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Most areas of engineering, science, and management use important tools based on probabilistic methods. The common thread of the entire spectrum of these tools is aiding in decision making under uncertainty: the choice of an interpretation of reality or the choice of a course of action. Although the importance of dealing with uncertainty in decision making is widely acknowledged, dissemination of probabilistic and decisiontheoretic methods in Artificial Intelligence has been surprisingly slow. Opponents of probability theory have pointed out three major obstacles to applying it in computerized decision aids: (1) the counterintuitiveness of probabilistic inference, which makes it hard for system builders, experts, and users to translate knowledge into probabilistic form, create knowledge bases, and to interpret results; (2) the quantitative character of probability theory, which implies collection or assessment of vast quantities of numbers and, since these are not always readily available, raises questions about their quality; and (3) closely related to its quantitative character, the computational complexity of probabilistic inference. Its proponents, on the other hand, point
Graphical Models for Multivariate Time Series from Intensive Care Monitoring
, 2000
"... In critical care extremely high dimensional time series are generated by clinical information systems. This yields new perspectives of data recording and also causes a new challenge for statistical methodology. Recently graphical correlation models have been developed for analysing the partial assoc ..."
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Cited by 9 (3 self)
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In critical care extremely high dimensional time series are generated by clinical information systems. This yields new perspectives of data recording and also causes a new challenge for statistical methodology. Recently graphical correlation models have been developed for analysing the partial associations between the components of multivariate time series. We apply this technique to the hemodynamic system of critically ill patients monitored in intensive care. We appraise the practical value of the procedure by reidentifying known associations between the variables. From separate analyses for different pathophysiological states we conclude that distinct clinical states can be characterised by distinct partial correlation structures.
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
Sequences of regressions and their independences
, 2012
"... Ordered sequences of univariate or multivariate regressions provide statistical modelsfor analysingdata fromrandomized, possiblysequential interventions, from cohort or multiwave panel studies, but also from crosssectional or retrospective studies. Conditional independences are captured by what we ..."
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Cited by 4 (1 self)
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Ordered sequences of univariate or multivariate regressions provide statistical modelsfor analysingdata fromrandomized, possiblysequential interventions, from cohort or multiwave panel studies, but also from crosssectional or retrospective studies. Conditional independences are captured by what we name regression graphs, provided the generated distribution shares some properties with a joint Gaussian distribution. Regression graphs extend purely directed, acyclic graphs by two types of undirected graph, one type for components of joint responses and the other for components of the context vector variable. We review the special features and the history of regression graphs, prove criteria for Markov equivalence anddiscussthenotion of simpler statistical covering models. Knowledgeof Markov equivalence provides alternative interpretations of a given sequence of regressions, is essential for machine learning strategies and permits to use the simple graphical criteria of regression graphs on graphs for which the corresponding criteria are in general more complex. Under the known conditions that a Markov equivalent directed acyclic graph exists for any given regression graph, we give a polynomial time algorithm to find one such graph.
Model Selection using Sparse Data and Backward Sequential Search
, 1996
"... This paper presents an empirical comparison of a variety of model evaluation criteria used in backwards sequential search (BSS). Both information criteria (IC) and significance tests are compared when applied to the problem of word sense disambiguation. We present experimental results that show the ..."
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This paper presents an empirical comparison of a variety of model evaluation criteria used in backwards sequential search (BSS). Both information criteria (IC) and significance tests are compared when applied to the problem of word sense disambiguation. We present experimental results that show the evaluation criteria that selects the most accurate models for classification. When the degrees of freedom of the model are adjusted the Loglikelihood ratio G2 and Akaike's Information Criteria (AIC) select the most accurate models. If the degrees of freedom are not adjusted then the most accurate evaluation criteria for word sense disambiguation is IC =
Undirected Graphical Models
, 2006
"... This note proposes a novel approach for assessing the balancing hypothesis that underlies propensity score matching methods based on using an informationtheoretic approach to fit undirected graphical models. Graphical models are parametric statistical models for multivariate random variables whose ..."
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This note proposes a novel approach for assessing the balancing hypothesis that underlies propensity score matching methods based on using an informationtheoretic approach to fit undirected graphical models. Graphical models are parametric statistical models for multivariate random variables whose conditional independence structure can be displayed in a mathematical graph. Specialized software packages for estimating graphical models have recently become readily available, and a detailed illustrative example using MIM is provided to show how this approach can be implemented in practice.
Computational
 Computational Statistics
, 1992
"... CoCo 1 , a highly advanced program for analysis of complete and incomplete contingency tables, is presented. In the paper a short presentation of CoCo is given. Incremental search by backward elimination and forward selection and the global search procedure from Edwards & Havr'anek (1985 ..."
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CoCo 1 , a highly advanced program for analysis of complete and incomplete contingency tables, is presented. In the paper a short presentation of CoCo is given. Incremental search by backward elimination and forward selection and the global search procedure from Edwards & Havr'anek (1985) is considered. By incremental search a single minimal acceptable model is identified. By the principles of weak acceptance and weak rejection the class of minimal acceptable models are found in the global search procedure. In CoCo each of the model searches can be done by a single command, or CoCo can be guided through the search in a highly user controlled model selection. 1 CoCo CoCo works especially effectively on graphical models, and some of the commands in CoCo are designed to handle graphical models. Graphical models are for contingency tables loglinear interaction models that can be represented by a simple undirected graph with as many vertices as the table has dimension (Darroch, Lauritz...