Decision theory (STAT-6226)

Program: M.Sc

Course Code STAT-6226

Credit Hours 3 CR

Course Coordinator Qasim Ramzan

Introduction

This course will introduce the basic concept to a set of quantitative methods for reaching optimal decisions. A solvable decision problem must be capable of being tightly formulated in terms of initial conditions and choices or courses of action, with their consequences. In general, such consequences are not known with certainty but are expressed as a set of probabilistic outcomes. An optimal decision, following the logic of the theory, is one that maximizes the expected utility. Thus, the ideal of decision theory.

Pre requisites: -

Learning outcomes

Provide rational bases for decision making.
Utilize the logic of the theory to provide an optimal decision.
Dealing with complex situations and improving quantitative decisions.

Textbooks

Berger, J.O. (1985). “ Statistical Decision Theory & Bayesian Analysis”, Springer Verlag.
Lindgren, B.W.(1971). “Elements of Decision Theory, Macmillan”, New York.
Blackwell, D. and Graphic, M.A.(1996).”Theory of gGames and Statistical Decision “, John Wiley, New York.

Week	Topics	Books
1	The nature and concepts of loss functions	Statistical Decision Theory & Bayesian Analysis.(5-7),
2	parameters, decisions and sample spaces.	Statistical Decision Theory & Bayesian Analysis.(8-12),
3	Risk and average loss.	Statistical Decision Theory & Bayesian Analysis.(55-57),
4	Admissibility and the class of admissible decisions.	Statistical Decision Theory & Bayesian Analysis.(111-117),
5	Minimax principle and its application to simple decision problems	Statistical Decision Theory & Bayesian Analysis.(122-126),
7	linear and quadratic losses and their uses in problem of estimation and testing hypothesis.	Statistical Decision Theory & Bayesian Analysis.(502-507),
8	Asymptotically minimax procedure.	Assignment
9	A prior distribution and conjugate priors.	Statistical Decision Theory & Bayesian Analysis.(313-317),
10	Bayes’ decision procedure	Statistical Decision Theory & Bayesian Analysis.(323-329),
11	admissibility of Bayes’ and minimax procedure.	Statistical Decision Theory & Bayesian Analysis.(350-361),
12	Risk and average loss using software	Mathematica Software
13	Bayes’ decision procedure using software	Mathematica Software
14	Risk and average loss using software	R Software
	Bayes’ decision procedure using software	R Software
16	Risk and average loss using software	Assignment