THEMATIC PROGRAMS

Causal Interpretation and Identification of Conditional Independence Structures
Short Courses

Linear structural equation models (LSEMs) are used frequently in the social sciences for the analysis of observational data. Their main attractiveness derives from the fact that they allow the substantive theory (i) to contain both manifest and latent variables, (ii) to specify interdependence 'reciprocal causation' among variables, and (iii) to define structural relationships between latent variables. LSEMs include many well-known types of multivariate analysis, such as regression analysis, factor analysis, path analysis and simultaneous equations. The first objective of this course is to give students a graduate level introduction to LSEMs. Besides discussion of topics such as model specification, identification, estimation, etc., particular attention will be paid to the structural interpretation of LSEMs, i.e. their meaning as causal model, as opposed to their content as statistical model. The theory on LSEMs will be illustrated by examples which are estimated using the LISREL 8 statistical software (students need [3] in order to perform these analyses). The second objective of the course is to make clear the relationship between LSEMs and graphical models. The theory on graphical models will be presented so far as necessary to obtain the main result (consistency theorem) stating that a LSEM satisfies the Markov properties implied by its path diagram. Literature for this part of the course is in the form of Lecture notes [4] which will be distributed at the beginning of the course.

Prerequisites: Students are assumed to be acquainted with introductory level linear algebra, and with the essentials of inferential statistics (including OLS regression and ML estimation).

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September 20-October 22, 1999
GRAPHICAL MARKOV MODELS AND RELATED TOPICS IN MULTIVARIATE STATISTICAL ANALYSIS

Lecturer: Steen Andersson, Deptartment of Mathematics, Indiana University

One of the most central ideas of statistical science is the assessment of dependencies among a set of stochastic variables. The familiar concepts of correlation, regression, and prediction are manifestations of this idea, and many aspects of causal relationships rest on representations of multivariate dependence.

Graphical Markov Models (GMM) use graphs, either directed, undirected, or mixed, to represent multivariate dependencies in an economical and computationally efficient way. A GMM is constructed by specifying local dependencies for each variable = node of the graph in terms of its immediate neighbours, parents, or both, yet represents a complex system of dependencies by means of the global structure of the graph. The local specification permits efficiencies in modeling, inference, and probabilistic calculations.

GMMs based on undirected graphs (= Markov random fields) are used to represent spatial dependencies in such applications as statistical mechanics and image analysis, while GMMs based on directed graphs (= path diagrams) occur as structural equation models (SEM) in psychometrics, econometrics, and similar fields. In statistics, the use of GMMs for both continuous and categorical data accelerated in the late 1970s, beginning with work by Darroch, Lauritzen, Speed, Wermuth and others on graphical log-linear models and recursive SEMs, then continued in work by Dawid, Spiegelhalter, Frydenberg, Cox and others with applications in medical diagnosis, epidemiology, etc. At the same time, separate but convergent developments of these ideas occurred in computer science, decision analysis, management science, and philosophy, where GMMs have been called influence diagrams or Bayesian belief networks and are used for the construction of expert systems, neural networks, and causal models. The application of GMMs to expert systems has proved hugely successful - the vibrant Uncertainty in Artificial Intelligence community currently focuses much of its effort on GMM methodology.

Prerequisites: Students are assumed to be acquainted with the basics in the following areas and subjects within mathematics and statistics: linear, algebra, group and group action, likelihood inference (estimation and test), probability theory, univariate distributions, conditional distributions, the multivariate normal distribution, multivariate analysis of variance (MANOVA), and contingency tables.

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October 27-29, 1999
DIAGNOSING AND PLANNING WITH BAYESIAN NETWORKS AND INFLUENCE DIAGRAMS
(A PRACTICAL GUIDE)

Lecturers:
Uffe Kjærulff, Aalborg University and Kristian Olesen, Aalborg UniversityThe Aim of this Short Course:Bayesian networks are graphical models of non-deterministic impact between variables and events. These relations are described by conditional probability tables. If decisions are added to the models they are known as influence diagrams. The formalisms rely on a coherent probability theoretic foundation, thus they are particular well suited for systems where uncertainty plays an important role. The graphical representation makes models easy to understand and enable immediate investigation of the effects of information and intervention. These effects are displayed as updated posterior distributions for unknown variables given the states of some other variables. As effective algorithms exist for automatic updating of models, users need not worry much about details. Methods for automatic adaptation of the conditional probability tables are available, as are semi-automatic methods for identifying the structure of models. The technology has matured to a stage where it has been applied to various practical problems, such as forecasting, diagnosing and planning. In this three day course the basics of Bayesian networks and influence diagrams will be presented, including examples of applications in agriculture, medicine, genetics and fault repair in computer equipment. The course includes hands-on experience with HUGIN, an automated tool for construction and execution of models. During these sessions the participants will be given the opportunity to work on their own problems.

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Short Course 2:
GRAPHICAL MARKOV MODELS: THEIR ROLE IN STATISTICAL ANALYSIS
Monday, November 15, 1999 to Tuesday, November 16, 1999

Lecturers:
David Cox, Nuffield College, Oxford and Nanny Wermuth, ZUMA - Center for Survey Research, Mannheim

The Aim of this Short Course:The course will provide a systematic discussion of a basis for the analysis and interpretation of complex multivariate data. As well as core material a number of specific research questions will be discussed in detail; the corresponding data can be obtained via Internet. The course is designed both for statisticians and for those in the health and social sciences making extensive use of statistical methods in their research. The course is intended for those concerned with the analysis and interpretation of complex data, especially but not entirely observational data. The applications from the social and health sciences are wide-ranging including, for example, studies of medical interventions and of sociological or psychological development. While the primary emphasis will be on statistical methods for direct use in applications, some issues of theoretical interest will also be addressed. One central theme will be the role of independence graphs and on processes by which the data could have been generated. No software presentations will be given, the emphasis being largely on methods which can be implemented within standard packages. While the course is based in part on the presentrs' book "Multivariate Dependencies - Models, Analysis and Interpretation" (London: Chapman and Hall, 1996), a number of important developments since the book will be described.