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.

Ruriko Yoshida, Assistant Professor of Statistics

- Office: 805A POT
- Phone: (859) 257-5698
- E-mail:
*ruriko.yoshida@uky.edu* - Office Hours: MW 2:10 PM - 3:00 PM

- MWF 1:00 PM - 1:50 PM, CB309

www.polytopes.net/courses/Stat624S08

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.

**Exam 1**Fri February 29.**Exam 2**Fri April 18th.**Final**April 30th. 1pm to 3pm. ROOM CB 309.

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.

- Basic Probability (PDF)
- Probability review part 1 (PDF)
- Probability review part 2 (PDF)
- MATLAB Exercise (PDF). Matlab code for LU decomposition (ZIP file). Templete file (Change this file name to LUsolve.m). Test file.
- MATLAB Tutorial 1 (PDF)
- MATLAB Tutorial 2 (PDF)
- MATLAB Tutorial 3 (PDF)
- MATLAB Tutorial 4 (PDF)
- MATLAB Tutorial 5 (PDF)
- MATLAB Tutorial 6 (PDF)

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.

**Exam 1**February 29. Review PDF. Practice exam PDF. mean = 94.25. STD = 5.2764.**Exam 2**April 18. Review PDF. Practice exam PDF. mean = 94.727. STD = 3.1652. Highest = 100.**Final**April 30. 1pm to 3pm.**Common Exam Practice**Practice problems for DTMC for the exam (PDF). Also I found a nice problem set on the website..... Here is a PDF file.

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.

The deadline for redo HWs is April 23rd, Wed. HW session is held at 4pm to 5pm on Tue at CB217.

- Homework 0 (PDF) Due: January 11th, Fri.
- Homework 1 (UPDATED) (PDF) Due: January 18th, Fri.
- Homework 2 (PDF) Due: January 25th, Fri.
- Homework 3 (PDF) Due: February 1st, Fri.
- Homework 4 (PDF) Due: February 8th, Fri.
- Homework 5 (PDF) Due: February 15th, Fri.
- Homework 6 (PDF) Due: February 22nd, Fri (UPDATED).
- EXTRA CREDIT: Due: March 7th, Fri. Write a brief summary of Dr Bathke's talk at a student seminar on Feb 27th. Describe (1) his problems, (2) methods he uses, (3) benefits over other methods, (4) difficulties, and (5) open problems. (2 points credits for regular HW scale).
- Homework 7 (PDF) Due: March 17th, Mon.
- Homework 8 (PDF) Due: March 21st Fri.
- EXTRA CREDIT: Due: March 28th, Fri. Write the summary of Dr. Zheng Qi's talk at the statistics seminar on March 21st, Fri.. Include: (1) What is the Luria-Delbruck distribution? (2) What are applications of this distribution and why do we care? (3) What are similarities and dissimilarities between Poisson distributions and the Luria-Delbruck distribution? (4) Can you characterize the Luria-Delbruck distribution in terms of a continuous time Markov chain? (5) Summarize new methods developed during this six years for estimating microbial mutation rates.
- Homework 9 (PDF) Due: March 28th Fri.
- Homework 10 (PDF) Due: April 4th Fri.