Introductory description

This module runs in Term 1 and is available for students on a course where it is a listed option and as an Unusual Option for students who have taken the pre-requisites.

Pre-requisites:
ST119 Probability 2 OR ST120 Introduction to Probability.

Module web page

Module aims

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

This module introduces the use of decision theory for making rational decisions in the face of uncertainty

1. Introduction. Motivating examples. What is decision theory?
2. Normative decision theory: elicitation and calculation, actions and outcomes, games.
3. Review of Probability. Frequentist vs subjective.
4. Frequentist approach to assigning probabilities to real-world events as long-run frequencies.
5. Elicitation. Calibration and coherence.
6. Decisions. Decision spaces and decision rules.
7. Decision trees.
8. Preferences. Axioms of preference, utility functions, risk.
9. Normative game theory: Games, payoffs.
10. Separability, dominance, iterated strict domination.
11. Mixed and pure strategies. Von Neumann minimax theorem.
12. Pareto optimality.
13. Nash equilibrium, Nash solvable.

Learning outcomes

By the end of the module, students should be able to:

• analyse and compare the underlying mathematical and philosophical basis for a number of alternative approaches to probability including subjective probability.
• describe the main features of normative decision theory and analyse models of decision-making in practical examples from a wide range of applications.
• use mathematical game theory to analyse mathematical toy example games as well as to understand the limits of game theory when used on 'real world' scenarios.
• communicate  solutions  to problems  accurately with  structured  and  coherent  arguments.

Indicative reading list

Peterson “An introduction to decision theory”. CUP, 2017.
Parmigiani & Inoue “Decision Theory”. Wiley, 2009.
Karlin & Peres “Game Theory, Alive”. AMS, 2016.

View reading list on Talis Aspire

Subject specific skills

Demonstrate knowledge of key mathematical and statistical concepts, both explicitly and by applying them to the solution of mathematical problems.

Create structured and coherent arguments communicating them in written form.

Analyse problems, abstracting their essential information formulating them using appropriate mathematical language to facilitate their solution.

Transferable skills

Written communication skills: Students complete written assessments that require precise and unambiguous communication in the manner and style expected in mathematical sciences.

Verbal communication skills: Students are encouraged to discuss and debate formative assessment and lecture material within small-group tutorials sessions. Students can continually discuss specific aspects of the module with the module leader. This is facilitated by statistics staff office hours.

Problem-solving skills: The module requires students to solve problems with complex solutions and this requirement is embedded in the module’s assessment.