This is a course on stochastic processes, which involve collections of random variables indexed by time or by space. In this course you will learn the nomenclature and techniques needed for understanding the major types of stochastic processes, how to apply these processes in mathematical modeling, and how to effectively compute and simulate using these processes. We will cover materials including (not limited to) discrete-time and continurous-time Markov Chain, Reversible Markov Chain, hidden Markov Model (HMM) (see more details at a sylabus). For computing I will be teaching the basics of MATLAB, although you may utilize any environment you are familiar with for completing the assignments.
Introduction to Stochastic Processes 2nd edit G. F. Lawler.
We will cover Chapter 1, 2, 3, and 5. In addition, We will cover Hidden Markov Model and also applications to computational Biology (especially, to alignment problems and also evolutional model). For more details see PDF.
There will be two in-class exams, graded homeworks, programming assignments, and a final exam: these will count 40%, 20%, 15%, and 25% of your grade, respectively.
Students with excused absences will be given a make-up exam. No homework will be made up for credit, but it's important to make it up for your own benefit. The lowest scored HW will be discarded. Late homework will not be accepted. No make up final.
Write each problem neatly. If you have any question about grading, you must prove why you think so. Regrading will be in 7 days after returning. After 7 days, regrading will NOT be accepted. All exams will be in class. Calculator is allowed. They are closed book exams.
For computing problems, I recommend you to use MATLAB. But if you want to use R or SAS it is fine if you do not use pre-existing functions. Please show me what you have before hand in if you are using R or SAS. If you do not get my permission then you will get no credits.