PROJECT GUIDELINE PSTAT 160B Winter 2015 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 (or Abstract), Motivation, Methods, Results, Discussion (and Future Questions). Due : Final Exam Date. Group Policy : you can work together during the project but the report should be your own. Choose one of the following. 1. Projects more on theoretical questions Read a research paper with applications (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 continuoustime stochastic processes (Markov Chains, Brownian motion, Renewal 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 : Pinsky, M.A. (2001).``Brownian continuity models via series expansion\". Journal of Theoretical Probability 14 261-266 van Dijk, N.M. (1992). ``Approximate uniformization for continuous time Markov chains with an application to performability analysis\". Stochastic Processes and their Applications 40:2 339-357. Bratko, A., Cormack, G. V., Filipic, B., Lynam, T., and Zupan, B. (2006). ``Spam Filtering Using Statistical Data Compression Models". Journal of Machine Learning Research 7: 2673-2698. Jones, B.L. (1994). ``Actuarial Calculations using a Markov Model\". 2. Implementing with Numerical 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 Output process of an infinite server Poisson queue (Chapter 5) Machine repair model (Chapter 6) Queuing system with renewal arrivals (Chapter 7) Ornstein-Uhlenbeck process, (Chapter 10)