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An Omnibus Test for Univariate and Multivariate Normality
, 1994
"... this paper are based on random samples. In practice, however, the tests will also be applied to regression residuals and residuals from time series models. ..."
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Cited by 53 (3 self)
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this paper are based on random samples. In practice, however, the tests will also be applied to regression residuals and residuals from time series models.
When Can Association Graphs Admit A Causal Interpretation?
, 1993
"... This paper provides conditions and procedures for deciding if patterns of independencies found in covariance and concentration matrices can be generated by a stepwise recursive process represented by some directed acyclic graph. If such an agreement is found, we know that one or several causal proce ..."
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Cited by 18 (4 self)
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This paper provides conditions and procedures for deciding if patterns of independencies found in covariance and concentration matrices can be generated by a stepwise recursive process represented by some directed acyclic graph. If such an agreement is found, we know that one or several causal processes could be responsible for the observed independencies, and our procedures could then be used to elucidate the graphical structure common to these processes, so as to evaluate their compatibility against substantive knowledge of the domain. If we find that the observed pattern of independencies does not agree with any stepwise recursive process, then there are a number of different possibilities. For instance,  some weak dependencies could have been mistaken for independencies and led to the wrong omission of edges from the covariance or concentration graphs.  some of the observed linear dependencies reflect accidental cancellations or hide actual nonlinear relations, or  the process responsible for the data is nonrecursive, involving aggregated variables, simultenous reciprocal interactions, or mixtures of several causal processes. In order to recognize accidental independencies it would be helpful to conduct several longitudinal studies under slightly varying conditions. In such studies the covariances for the same set of variables is estimated under different conditions and the variations in the conditions would typically affect the numerical values of the parameters. But, if the data were generated by a causal process represented by some directed acyclic graph, then the basic structural properties reflected in the missing edges of that graph should remain unchanged. Under such assumptions, the pattern of independencies that is "implied" by the dag (see Definitio...
Interpretation of interaction: A review
 Annals of Applied Statistics
"... Several different types of statistical interaction are defined and distinguished, primarily on the basis of the nature of the factors defining the interaction. Illustrative examples, mostly epidemiological, are given. The emphasis is primarily on interpretation rather than on methods for detecting i ..."
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Cited by 3 (0 self)
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Several different types of statistical interaction are defined and distinguished, primarily on the basis of the nature of the factors defining the interaction. Illustrative examples, mostly epidemiological, are given. The emphasis is primarily on interpretation rather than on methods for detecting interactions. 1. Introduction. Interaction
A Graphical Chain Model Derived From a Model Selection Strategy for the Sociologists Graduates Study
, 1997
"... This paper objects to the arising problems due to fitting graphical chain models to multidimensional data sets. This multivariate statistical tool is used to cope with complex research questions concerning not only direct, but also indirect associations between the variables of interest. Due to this ..."
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Cited by 2 (0 self)
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This paper objects to the arising problems due to fitting graphical chain models to multidimensional data sets. This multivariate statistical tool is used to cope with complex research questions concerning not only direct, but also indirect associations between the variables of interest. Due to this high complexity sensible strategies for fitting such models are required. Here, a datadriven selection strategy is discussed. Its application is illustrated for an empirical data example in detail. 1 Introduction In empirical studies, typically a large number of different variables is collected for each individual. Often the researcher has a certain idea concerning the underlying association structure which implies direct as well as indirect influences on the main responses. Such influences cannot be captured by conventional regression models. Here, graphical chain models are the adequate tool since they allow for intermediate variables additional to the pure explanatories and pure respo...
Blauth, Pigeot: GraphFitI A computer program for graphical chain
"... Fitting a graphical chain model to a multivariate data set consists of di erent steps some of which being rather tedious. The paper outlines the basic features and overall architecture of the computer program GraphFitI which provides the application of a selection strategy for tting graphical chain ..."
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Fitting a graphical chain model to a multivariate data set consists of di erent steps some of which being rather tedious. The paper outlines the basic features and overall architecture of the computer program GraphFitI which provides the application of a selection strategy for tting graphical chain models and for visualising the resulting models as a graph. It additionally supports the user at the di erent steps of the analysis by an integrated help system.
An Omnibus Test for Univariate and
"... this paper are based on random samples. In practice, however, the tests will also be applied to regression residuals and residuals from time series models ..."
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this paper are based on random samples. In practice, however, the tests will also be applied to regression residuals and residuals from time series models
Graphical chain models for the analysis of complex genetic diseases: an application to hypertension
"... A crucial task in modern genetic medicine is the understanding of complex genetic diseases. The main complicating features are that a combination of genetic and environmental risk factors is involved, and the phenotype of interest may be complex. Traditional statistical techniques based on lodscore ..."
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A crucial task in modern genetic medicine is the understanding of complex genetic diseases. The main complicating features are that a combination of genetic and environmental risk factors is involved, and the phenotype of interest may be complex. Traditional statistical techniques based on lodscores fail when the disease is no longer monogenic and the underlying disease transmission model is not defined. Different kinds of association tests have been proved to be an appropriate and powerful statistical tool to detect a “candidate gene ” for a complex disorder. However, statistical techniques able to investigate direct and indirect influences among phenotypes, genotypes and environmental risk factors, are required to analyse the association structure of complex diseases. In this paper we propose graphical models as a natural tool to analyse the multifactorial structure of complex genetic diseases. An application of this model to primary hypertension data set is illustrated.
Sequences of regressions and their dependences
"... ABSTRACT: In this paper, we study sequences of regressions in joint or single responses given a set of context variables, where a dependence structure of interest is captured by a regression graph. These graphs have nodes representing random variables and three types of edge. Their set of missing ed ..."
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ABSTRACT: In this paper, we study sequences of regressions in joint or single responses given a set of context variables, where a dependence structure of interest is captured by a regression graph. These graphs have nodes representing random variables and three types of edge. Their set of missing edges defines the independence structure of the graph provided two properties are used that are not common to all probability distributions, named the intersection and the composition property. We derive the additionally needed properties for tracing the effects of single active paths and for excluding any canceling of effects due to several paths connecting the same pair of nodes. For this, we use the notion of a generating process for the joint distribution and derive new properties of an edge matrix calculus for transforming graphs. One key is the Mmatrix property of each regularized square edge matrix, others are the proposed notions of traceable regressions and of singleton transitivity.
International Statistical Review (2012), 80, 3, 415–438 doi:10.1111/j.17515823.2012.00195.x Traceable Regressions
"... In this paper, we define and study the concept of traceable regressions and apply it to some examples. Traceable regressions are sequences of conditional distributions in joint or single responses for which a corresponding graph captures an independence structure and represents, in addition, conditi ..."
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In this paper, we define and study the concept of traceable regressions and apply it to some examples. Traceable regressions are sequences of conditional distributions in joint or single responses for which a corresponding graph captures an independence structure and represents, in addition, conditional dependences that permit the tracing of pathways of dependence. We give the properties needed for transforming these graphs and graphical criteria to decide whether a path in the graph induces a dependence. The much stronger constraints on distributions that are faithful to a graph are compared to those needed for traceable regressions. Key words: Chain graphs; edgematrix calculus; faithfulness of graphs; graphical Markov models; independence axioms; regression graphs. 1
BIOINFORMATICS An Empirical Bayes Approach to Inferring LargeScale Gene Association Networks
, 2003
"... Motivation: Genetic networks are often described statistically by graphical models (e.g. Bayesian networks). However, inferring the network structure offers a serious challenge in microarray analysis where the sample size is small compared to the number of considered genes. This renders many standar ..."
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Motivation: Genetic networks are often described statistically by graphical models (e.g. Bayesian networks). However, inferring the network structure offers a serious challenge in microarray analysis where the sample size is small compared to the number of considered genes. This renders many standard algorithms for graphical models inapplicable, and inferring genetic networks an “illposed” inverse problem. Methods: We introduce a novel framework for smallsample inference of graphical models from gene expression data. Specifically, we focus on socalled graphical Gaussian models (GGMs) that are now frequently used to describe gene association networks and to detect conditionally dependent genes. Our new approach is based on (i) improved (regularized) smallsample point estimates of partial correlation, (ii) an exact test of edge inclusion with adaptive estimation of the degree of freedom, and (iii) a heuristic network search based on false discovery rate multiple testing. Steps (ii) and (iii) correspond to an empirical Bayes estimate of the network topology. Results: Using computer simulations we investigate the sensitivity (power) and specificity (true negative rate) of the proposed framework to estimate GGMs from microarray data. This shows that it is possible to recover the true network topology with high accuracy even for smallsample data sets. Subsequently, we analyze gene expression data from a breast cancer tumor study and illustrate our approach by inferring a corresponding largescale gene association network for 3,883 genes. Availability: The authors have implemented the approach in the R package “GeneTS ” that is freely available from