## Causal Interpretation and Identification of Conditional
Independence Structures

Short Courses

**LINEAR STRUCTURAL EQUATIONS AND GRAPHICAL
MODELS**

September 20- October 1, 1999

*Lecturer: Jan Koster, Erasmus University*

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).*

September 20-October 22, 1999

**GRAPHICAL MARKOV MODELS AND RELATED TOPICS IN MULTIVARIATE STATISTICAL
ANALYSIS**

Lecturer: Steen Andersson, Deptartment of Mathematics, Indiana University

**THE AIM OF THE COURSE:**

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.*

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.

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.