python

PROJECT GUIDELINE PSTAT 160A Winter 2018

Idea : The purpose of this project is to use the ideas and computational skills that you learn in the class for your own problem. Have a fun and enjoy the project to fulfill your intellectual curiosity. The report can be short but it should contain your own creative work.

Report format : PDF (at most 3 pages) includes Summary, Motivation, Methods, Results, Discussion (and Future Questions). Due : Upload it in gauchospace by the end of Final Exam Date.

Group Policy : you can work together during the project but the report should be your own. Grading Policy : This is optional. It should be your own work, that is, if there is identical or almost identical one (in the class or anywhere), the grade must be zero.

Choose one of the following.

1. Projects more on theoretical questions

Read a research paper (for the choice of the paper, try to find an interesting paper and discuss with the instructor before you write the project report) related to Markov Chains or discrete-time stochastic processes, summarize the results in the paper, and write your own discussions about the paper (for instance, numerically implement the results in the paper in Python as an example, or extend the theorems and propositions therein, etc.).

Examples of papers :

M. R. Segal (2007) ``Chess, Chance and Conspiracy ” Statistical Science 22 98–108 P. K. Newton and J. B. Keller (2005) ``Probability of Winning at Tennis I. Theory and Data” Studies in Applied Mathematics 114 241-269

2. Implementing Markov Chain Methods

Review the class material and the textbook and write Python codes for some of the examples discussed in the class or textbook (for the choice of the examples, discuss with the instructor before you write the project report), simulate it, compute meaningful quantities and discuss your results.

Examples Markov Decision Processes. Markov Chain Monte Carlo. Hidden Markov Models. Branching Processes. Random Walk in Z^d.