
Course information

Academic year: 2017/2018

Local code:

919 
Course:

DECISION THEORY 
Syllabus:


Centre:


Course type:

Elective

Total credits:

9 
Theoretical:

6 
Practical:

3 
Cycle:

2nd 
Year:


Terms:

2nd TERM. 
Lecturers:


Goals:

Students should receive a general view on the decision problems and the basic methods to solve the elementary problems, with a clear distinction between the problems with and without experimentation. Special attention is given to the subjective approach to probability and how to determine subjetive probabilities.
The comparison between classical and Bayesian inferential techniques will be a crucial topic to discuss about (the second one being applicable when the problem is viewed as a special decision problem with experimentation) . Advantages, inconveniences and similarities of the two inferential approaches are analyzed. 
Content:

Theme 1. INTRODUCTION TO DECISION THEORY. Aims and elements in a decision problem.
Theme 2. INTRODUCTION TO BAYESIAN INFERENCE. Different approaches to probability; subjective probability: determination. Prior and posterior distributions, and their role in Bayesian Inference. Practical determination of the prior distribution. Conjugate distributions. Noninformative distributions. Bayesian Inference: essential connections and differences between the Classical and the Bayesian Inference; Bayesian Point Estimation; Bayesian Interval Estimation; Bayesian Hypothesis Testing.
Theme 3. DECISION PROBLEMS (WITHOUT EXPERIMENTATION). Scheme of a general decision problem: certainty, risk and uncertainty environments; basic concepts. Criteria to choose among pure and among mixed actions: nonprobabilistic cretria; Bayes probabilistic criterion. Geometrical interpretation of some criteria; admisibility and completeness concepts. Determining the loss function in a decision problem: standar functions and functions derived from Utility Theory.
Theme 4. STATISTICAL DECISION PROBLEMS (WITH EXPERIMENTATION). Scheme of a general decision problem involving associated experimentation; basic concepts. Some decision criteria: Bayes criterion. The Expected Value of Sample Information. Introduction to the comparison of experiments.
5. DECISION THEORY AND STATISTICAL INFERENCE. Handling estimation problems as special decision problems. Viewing the parameter estimation as a particular statistical decision problem: Bayes estimators for special loss functions. Viewing testing hypothesis as a decision problem: Bayes methods to test hypothesese with a general loss function.
6. COMPLEMENTARY STUDIES. Graphical methods to represent decision problems: decision trees and influence diagrams.

Bibliography:

Berger, J. O. (1985). Statistical Decision Theory and Bayesian Analysis. SpringerVerlag. New York.
Blackwell, D. and Girshick, M. A (1954). Theory of Games and Statistical Decisions. Dover Pub. Inc.. New York.
Chernoff, J. and Moses, L. (1974). Elementary Decision Theory. Wiley, New York.
DeGroot, M.H. (1970). Optimal Statistical Decisions. McGraw Hill. New York.
Ferguson, T. S. (1967). Mathematical Statistics: A Decision Theoretic Approach. Academic Press. New York.
French, S. and Ríos Insua, D. (2000). Statistical Decision Theory, Arnold, London.
Lindley, D.V. (1970). lntroduction to Probability and Statistics from a Bayesian Viewpoint. (2 volúmenes). Cambridge University Press.
Lindley, D.V. (1985). Making Decisions. Wiley. New York.
Pardo, L. and Valdés, T. (1987). Decisiones Estratégicas. Ed. Díaz de Santos, Madrid.
Raiffa, H. and Schlaifer, R. (1977). Applied Statistical Decision Theory. The MIT Press. Massachusetts.
Ríos, S. (1976). Análisis de Decisiones. Paraninfo. Madrid.
Ríos, S., RíosInsua, S. and RíosInsua, M.J. (1989). Procesos de decisión multicriterio. Eudema, Madrid.
Smith, J. Q. (1988). Decision Analysis: a Bayesian Approach. Chapman & Hall. New York.
U.N.E.D. (1978). Teoría de la Decisión. Ediciones de la Universidad Nacional de Educación a Distancia. Madrid.
Wald, A (1950). Statistical Decision Functions. Wiley. New York.
Winkler, R. L. (1972). lntroduction to Bayesian lnference and Decision. Holt, Rinehart & Winston. New York.
Winkler, R. L. and Hays, W.L. (1975). Statistics: Probability, lnference and Decision. Holt, Rinehart & Winston. New York.
Zacks, S. (1971). The Theory ofStatistical lnference. Wiley. New York.

Metodology and Assessment system:

The course can be approved by either passing two partial exams or a final one.

ECTS information 
ECTS code:

ELSUD3MATH308DT

ECTS credits:

7.2 
Theoretical:

4.8 
Practical:

2.4 
Teaching method:

Lectures Course practicum 
Assessment system:

Written exam 

