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215
Bayesian Data Analysis
, 1995
"... I actually own a copy of Harold Jeffreys’s Theory of Probability but have only read small bits of it, most recently over a decade ago to confirm that, indeed, Jeffreys was not too proud to use a classical chisquared pvalue when he wanted to check the misfit of a model to data (Gelman, Meng and Ste ..."
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Cited by 1230 (47 self)
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I actually own a copy of Harold Jeffreys’s Theory of Probability but have only read small bits of it, most recently over a decade ago to confirm that, indeed, Jeffreys was not too proud to use a classical chisquared pvalue when he wanted to check the misfit of a model to data (Gelman, Meng and Stern, 2006). I do, however, feel that it is important to understand where our probability models come from, and I welcome the opportunity to use the present article by Robert, Chopin and Rousseau as a platform for further discussion of foundational issues. 2 In this brief discussion I will argue the following: (1) in thinking about prior distributions, we should go beyond Jeffreys’s principles and move toward weakly informative priors; (2) it is natural for those of us who work in social and computational sciences to favor complex models, contra Jeffreys’s preference for simplicity; and (3) a key generalization of Jeffreys’s ideas is to explicitly include model checking in the process of data analysis.
ModelBased Clustering, Discriminant Analysis, and Density Estimation
 JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
, 2000
"... Cluster analysis is the automated search for groups of related observations in a data set. Most clustering done in practice is based largely on heuristic but intuitively reasonable procedures and most clustering methods available in commercial software are also of this type. However, there is little ..."
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Cited by 260 (24 self)
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Cluster analysis is the automated search for groups of related observations in a data set. Most clustering done in practice is based largely on heuristic but intuitively reasonable procedures and most clustering methods available in commercial software are also of this type. However, there is little systematic guidance associated with these methods for solving important practical questions that arise in cluster analysis, such as \How many clusters are there?", "Which clustering method should be used?" and \How should outliers be handled?". We outline a general methodology for modelbased clustering that provides a principled statistical approach to these issues. We also show that this can be useful for other problems in multivariate analysis, such as discriminant analysis and multivariate density estimation. We give examples from medical diagnosis, mineeld detection, cluster recovery from noisy data, and spatial density estimation. Finally, we mention limitations of the methodology, a...
Efficient approximations for the marginal likelihood of Bayesian networks with hidden variables
 Machine Learning
, 1997
"... We discuss Bayesian methods for learning Bayesian networks when data sets are incomplete. In particular, we examine asymptotic approximations for the marginal likelihood of incomplete data given a Bayesian network. We consider the Laplace approximation and the less accurate but more efficient BIC/MD ..."
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Cited by 178 (10 self)
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We discuss Bayesian methods for learning Bayesian networks when data sets are incomplete. In particular, we examine asymptotic approximations for the marginal likelihood of incomplete data given a Bayesian network. We consider the Laplace approximation and the less accurate but more efficient BIC/MDL approximation. We also consider approximations proposed by Draper (1993) and Cheeseman and Stutz (1995). These approximations are as efficient as BIC/MDL, but their accuracy has not been studied in any depth. We compare the accuracy of these approximations under the assumption that the Laplace approximation is the most accurate. In experiments using synthetic data generated from discrete naiveBayes models having a hidden root node, we find that (1) the BIC/MDL measure is the least accurate, having a bias in favor of simple models, and (2) the Draper and CS measures are the most accurate. 1
A Guide to the Literature on Learning Probabilistic Networks From Data
, 1996
"... This literature review discusses different methods under the general rubric of learning Bayesian networks from data, and includes some overlapping work on more general probabilistic networks. Connections are drawn between the statistical, neural network, and uncertainty communities, and between the ..."
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Cited by 172 (0 self)
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This literature review discusses different methods under the general rubric of learning Bayesian networks from data, and includes some overlapping work on more general probabilistic networks. Connections are drawn between the statistical, neural network, and uncertainty communities, and between the different methodological communities, such as Bayesian, description length, and classical statistics. Basic concepts for learning and Bayesian networks are introduced and methods are then reviewed. Methods are discussed for learning parameters of a probabilistic network, for learning the structure, and for learning hidden variables. The presentation avoids formal definitions and theorems, as these are plentiful in the literature, and instead illustrates key concepts with simplified examples. Keywords Bayesian networks, graphical models, hidden variables, learning, learning structure, probabilistic networks, knowledge discovery. I. Introduction Probabilistic networks or probabilistic gra...
Probabilistic independence networks for hidden Markov probability models
, 1996
"... Graphical techniques for modeling the dependencies of random variables have been explored in a variety of different areas including statistics, statistical physics, artificial intelligence, speech recognition, image processing, and genetics. Formalisms for manipulating these models have been develop ..."
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Cited by 167 (12 self)
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Graphical techniques for modeling the dependencies of random variables have been explored in a variety of different areas including statistics, statistical physics, artificial intelligence, speech recognition, image processing, and genetics. Formalisms for manipulating these models have been developed relatively independently in these research communities. In this paper we explore hidden Markov models (HMMs) and related structures within the general framework of probabilistic independence networks (PINs). The paper contains a selfcontained review of the basic principles of PINs. It is shown that the wellknown forwardbackward (FB) and Viterbi algorithms for HMMs are special cases of more general inference algorithms for arbitrary PINs. Furthermore, the existence of inference and estimation algorithms for more general graphical models provides a set of analysis tools for HMM practitioners who wish to explore a richer class of HMM structures. Examples of relatively complex models to handle sensor fusion and coarticulation in speech recognition are introduced and treated within the graphical model framework to illustrate the advantages of the general approach.
On Comparing Classifiers: Pitfalls to Avoid and a Recommended Approach
 Data Mining and Knowledge Discovery
, 1997
"... Abstract. An important component of many data mining projects is finding a good classification algorithm, a process that requires very careful thought about experimental design. If not done very carefully, comparative studies of classification and other types of algorithms can easily result in stati ..."
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Cited by 155 (0 self)
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Abstract. An important component of many data mining projects is finding a good classification algorithm, a process that requires very careful thought about experimental design. If not done very carefully, comparative studies of classification and other types of algorithms can easily result in statistically invalid conclusions. This is especially true when one is using data mining techniques to analyze very large databases, which inevitably contain some statistically unlikely data. This paper describes several phenomena that can, if ignored, invalidate an experimental comparison. These phenomena and the conclusions that follow apply not only to classification, but to computational experiments in almost any aspect of data mining. The paper also discusses why comparative analysis is more important in evaluating some types of algorithms than for others, and provides some suggestions about how to avoid the pitfalls suffered by many experimental studies.
Comparing Dynamic Causal Models
 NEUROIMAGE
, 2004
"... This article describes the use of Bayes factors for comparing Dynamic Causal Models (DCMs). DCMs are used to make inferences about effective connectivity from functional Magnetic Resonance Imaging (fMRI) data. These inferences, however, are contingent upon assumptions about model structure, that is, ..."
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Cited by 81 (34 self)
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This article describes the use of Bayes factors for comparing Dynamic Causal Models (DCMs). DCMs are used to make inferences about effective connectivity from functional Magnetic Resonance Imaging (fMRI) data. These inferences, however, are contingent upon assumptions about model structure, that is, the connectivity pattern between the regions included in the model. Given the current lack of detailed knowledge on anatomical connectivity in the human brain, there are often considerable degrees of freedom when defining the connectional structure of DCMs. In addition, many plausible scientific hypotheses may exist about which connections are changed by experimental manipulation, and a formal procedure for directly comparing these competing hypotheses is highly desirable. In this article, we show how Bayes factors can be used to guide choices about model structure, both with regard to the intrinsic connectivity pattern and the contextual modulation of individual connections. The combined use of Bayes factors and DCM thus allows one to evaluate competing scientific theories about the architecture of largescale neural networks and the neuronal interactions that mediate perception and cognition.
A Bayesian Approach to Causal Discovery
, 1997
"... We examine the Bayesian approach to the discovery of directed acyclic causal models and compare it to the constraintbased approach. Both approaches rely on the Causal Markov assumption, but the two differ significantly in theory and practice. An important difference between the approaches is that t ..."
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Cited by 79 (1 self)
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We examine the Bayesian approach to the discovery of directed acyclic causal models and compare it to the constraintbased approach. Both approaches rely on the Causal Markov assumption, but the two differ significantly in theory and practice. An important difference between the approaches is that the constraintbased approach uses categorical information about conditionalindependence constraints in the domain, whereas the Bayesian approach weighs the degree to which such constraints hold. As a result, the Bayesian approach has three distinct advantages over its constraintbased counterpart. One, conclusions derived from the Bayesian approach are not susceptible to incorrect categorical decisions about independence facts that can occur with data sets of finite size. Two, using the Bayesian approach, finer distinctions among model structuresboth quantitative and qualitativecan be made. Three, information from several models can be combined to make better inferences and to better ...
Analyzing Developmental Trajectories: A Semiparametric, GroupBased Approach
 Psychological Methods
, 1999
"... A developmental trajectory describes the course of a behavior over age or time. A groupbased method for identifying distinctive groups of individual trajectories within the population and for profiling the characteristics of group members is demonstrated. Such clusters might include groups of " ..."
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Cited by 56 (1 self)
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A developmental trajectory describes the course of a behavior over age or time. A groupbased method for identifying distinctive groups of individual trajectories within the population and for profiling the characteristics of group members is demonstrated. Such clusters might include groups of "increasers. " "decreasers," and "no changers. " Suitably defined probability distributions are used to handle 3 data types—count, binary, and psychometric scale data. Four capabilities are demonstrated: (a) the capability to identify rather than assume distinctive groups of trajectories, (b) the capability to estimate the proportion of the population following each such trajectory group, (c) the capability to relate group membership probability to individual characteristics and circumstances, and (d) the capability to use the group membership probabilities for various other purposes such as creating profiles of group members. Over the past decade, major advances have been made in methodology for analyzing individuallevel developmental trajectories. The two main branches of methodology are hierarchical modeling (Bryk &