### 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

1. Berger, J.O. (1985). “ Statistical Decision Theory & Bayesian Analysis”, Springer Verlag.
2. Lindgren, B.W.(1971). “Elements of Decision Theory, Macmillan”, New York.
3. 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

Description of system of Evaluation

Exam: Mid (30%), Final (50%), Sessional (20%): Assignments, Presentations, Class Participation, Quizzes

Time Table:

 M.Sc (4th Regualr) Day Time monday 11:00 AM to 12:00 AM thursday 8:00 AM to 9:00 AM friday 10:00 AM to 11:00 AM