APP MTH 7090 - Stochastic Decision Theory
North Terrace Campus - Semester 2 - 2015
General Course Information
Course Code APP MTH 7090 Course Stochastic Decision Theory Coordinating Unit Applied Mathematics Term Semester 2 Level Postgraduate Coursework Location/s North Terrace Campus Units 3 Contact Up to 3 hours per week Available for Study Abroad and Exchange Y Prerequisites MATHS 2103 or APP MTH 3001 Assumed Knowledge Knowledge of linear programming such as would be obtained from APP MTH 2105 Course Description People make decisions everyday: whether to take an umbrella to work; to take an available park for their car of continue to search for a better one; which of several possible methods to implement to attempt to save a species from extinction; and, which people in the population to give a vaccine to. All of these decisions are being made under uncertainty: there exists a certain chance of rain today; a certain chance all of the car parks are used; uncertainty about how many individuals of the species exist and how they will respond to each of the possible interventions; and, the actual dynamics of the infection and the uptake of the vaccine by the population. This course will focus on formulating problems of this type in a mathematical framework and provide methods for making the best decision possible taking into account the uncertainty.
Topics covered are: stochastic linear programming - the extension of linear programming to account for uncertainty; Markov decision processes (MDP) and dynamic programming - the framework for solving problems in which the state of the process up to the time of decision is known but the behaviour of the process is governed by a Markov chain; Hidden Markov models, and Partially-observable MDPs - the extension of MDPs where we can only observe a `noisy' version of the state of the system.
Course Coordinator: Dr David Green
The full timetable of all activities for this course can be accessed from Course Planner.
Course Learning Outcomes
1 Be able to formulate Deterministic Equivalent Problems (DEPs) for Stochastic Linear Programs and solve them under certain assumptions. 2 Understand the Principle of Optimality and Dynamic Programming and be able to use Dynamic Programming to solve appropriate problems. 3 Be able to specify a Markov Decision Chain (MDC). 4 Be able to formulate and solve Finite Horizon MDC Programs, simple Infinite Horizon MDC Programs with Discounting, simple Positive MDC Programs, simple Negative MDC Programs and simple Average-Cost MDC Programs. 5 Understand Value-Iteration and Policy-Improvement Algorithms, be able to identify and specify a Hidden Markov Chain (HMC) model and to evaluate quantities of interest. 6 Demonstrate skills in communicating mathematics both orally and in writing.
University Graduate Attributes
This course will provide students with an opportunity to develop the Graduate Attribute(s) specified below:
University Graduate Attribute Course Learning Outcome(s) Knowledge and understanding of the content and techniques of a chosen discipline at advanced levels that are internationally recognised. 1,2,3,4,5 The ability to locate, analyse, evaluate and synthesise information from a wide variety of sources in a planned and timely manner. 1,2,3,4,5,6 An ability to apply effective, creative and innovative solutions, both independently and cooperatively, to current and future problems. 1,2,3,4,5,6 Skills of a high order in interpersonal understanding, teamwork and communication. 6 A proficiency in the appropriate use of contemporary technologies. 1,2,3,4,5 A commitment to continuous learning and the capacity to maintain intellectual curiosity throughout life. 1,2,3,4,5,6 An awareness of ethical, social and cultural issues within a global context and their importance in the exercise of professional skills and responsibilities. 1,2,3,4,5,6
Recommended ResourcesThere are many good books on Stochastic Decision Theory in the Barr Smith Library, with the following texts and articles being recommended for this course (many of which should be available electronically).
1. "Statistical Modelling and Computation", by D.P. Kroese and J.C.C. Chan (Springer, 2014).
2. "Probability and Random Processess", by G. Grimmett and D. Stirzaker (Oxford University Press, 2001).
3. "Stochastic Programming", by P. Kall and S.W. Wallace (John Wiley & Sons, 1994).
4. "Stochastic Linear Programming", by P. Kall and J. Mayer (Springer, 2011).
5. "Markov Decision Processes: Discrete Stochastic Dynamic Programming", by M.L. Puterman (John Wiley & Sons).
6. "Stochastic Dynamics Programming and the Control of Queueing Systems", by L.I. Sennott (John Wiley & Sons).
7."What HMMs Can Do", by J.A. Bilmes, Bilmes, J. A. (2006), IEICE - Transactions on Information and Systems E89-D(3), 869–891.
8. "A Tutorial on Hidden Markov Models and Selected Applications in Speech Recognition", by L.R. Rabiner (1989), Proceedings of the IEEE 77(2), 257–286.
9. "Hidden Markov Models: Estimation and Control", by R.J. Elliott, L. Aggoun and J.B. Moore (Springer-Verlag).
Online LearningA version of the course notes will available online for those whowish to download and print prior to attending lectures. The format (either as two or one slide per page) is the same as the presentation slides used in the lectures, with room for you to annotate during lectures.
All assignments, tutorials, handouts and solutions, where appropriate, will be made available on the course website as the course ensues.
Please don't hesitate to e-mail the lecturer should anything be missing.
Learning & Teaching Activities
Learning & Teaching ModesThis course relies on lectures as the primary delivery mechanism for the material. The lecturer will guide the students through the material presented in this course in a total of 33 lectures. Downloading and prereading the online notes will enable the students to more actively engage the material and interact during lectures.
Tutorials supplement the lectures by providing exercises and example problems to enhance the understanding obtained through lectures. A sequence of written assignments provides assessment opportunities for students to gauge their progress and understanding.
The information below is provided as a guide to assist students in engaging appropriately with the course requirements.
Activity Quantity Workload hours Lectures 33 99 Tutorials 5 25 Assignments 5 30 Total 154
Learning Activities SummaryLecture outline
Introduction to Stochastic Decision Theory (1 Lecture)
Revision of Basic Probability, Discrete-time Markov chains, Linear Programming and Convexity (5 Lectures) Stochastic Linear Programming (9 Lectures), including
-General Formulation (1 Lecture)
-Recourse Deterministic Equivalent Problems (DEPs) (5 Lectures)
-Chance Constrained DEPs (3 Lectures)
Markov Decision Chains (10 Lectures), including
-The Principle of Optimality and Dynamic Programming (1 Lecture)
-Introduction to Markov Decision Chains and Finite Horizon Programming (1 Lecture)
-Infinite Horizon Programming, with Discounting (1 Lecture)
-Positive Programming and the Value Iteration Algorithm (2 Lectures)
-Negative Programming and Optimal Stopping (2 Lectures)
-Average Cost Programming and the Policy Improvement Algorithm (3 Lectures)
Hidden Markov Chains (7 Lectures), including
-Introduction to Hidden Markov Chains (1 Lecture)
-Smoothing and the Forward-Backward Algorithm (2 Lectures)
-Optimal State Sequence and the Viterbi Algorithm (2 Lectures)
-Estimation of Parameters and the Baum-Welch Algorithm (2 Lectures)
Summary (1 Lecture)
The first tutorial in Week 3 covers material from the previous two weeks and other material that should be considered revision. Tutorials in Weeks 5, 7, 9 and 11 cover the material of the previous few weeks.
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Assessment task Task type When due Weighting Learning outcomes Examination Summative Examination period 70% All Assignments Formative and summative Weeks 4, 6, 8, 10 and 12 30% All
Assessment task Set Due Weighting Assignment 1 week 3 week 4 6% Assignment 2 week 5 week 6 6% Assignment 3 week 7 week 8 6% Assignment 4 week 9 week 10 6% Assignment 5 week 11 week 12 6%
SubmissionAssignments must be submitted on time to the designated hand-in box in the School of Mathematical Sciences with a signed assessment cover sheet attached to the assignment.
Late assignments will not be accepted.
Assignments will normally be returned within two weeks.
Students may be excused from an assignment for medical or compassionate reasons. In such cases, documentation is required and the lecturer must be notified as soon as possible.
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M10 (Coursework Mark Scheme) Grade Mark Description FNS Fail No Submission F 1-49 Fail P 50-64 Pass C 65-74 Credit D 75-84 Distinction HD 85-100 High Distinction CN Continuing NFE No Formal Examination RP Result Pending
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