STA 624 Applied Stochastic Processes

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).

Spring Semester 2016


Introduction to Stochastic Processes 2nd edit G. F. Lawler.


Ruriko Yoshida, Associate Professor of Statistics

Time and Place for STA624, Spring Semester 2016

  • Tue and Thurs 11:00 AM - 12:15 PM, 335 MDS

Course Website

Syllabus For STA 624

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 Thurs March 10th.
  • Exam 2 Thurs April 21st.
  • Final Wed. May 4th at 10:30AM to 12:30PM.


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.

STA 624 Handout



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.

Homework for STA 624, Spring Semester 2016

  • Due on Jan 26th Tues 2016: HW0
  • Due on Feb 4th Thurs 2016: HW1
  • Due on Feb 11th Thurs 2016: HW2
  • Due on Feb 18th Thurs 2016: HW3
  • Due on Feb 25th Thurs 2016: HW4
  • Due on March 3rd Thurs 2016: HW5
  • Due on March 24th Thurs 2016: HW6
  • Due on April 5th Tues 2016: HW7
  • Due on April 14th Thurs 2016: HW8


  • Notes on Jan 19th Tues PDF and pdf.
  • Notes on Jan 21st Thurs txt.
  • Code for Feb 4th Thurs txt.

Sample topics for Final topics for STA 624.

  • Study Phylogenetic tree models, such as the Jukes-Cantor model, the kimura 2 or 4 parameter models, or the general time reversible (GTR) model (and how to compute the Maximum likelihood estimations).
  • Study the paper [Evans/Speed, Annals of Statistics 1993] on the 3-PARAMETER KIMURA MODEL for trees.
  • Study computing the exact p-value from a multi-dimansional contingency tables and Markov bases.
  • Study enumeration methods of contingency tables.
  • Study how to generate phylogenetic trees and DNA sequences via the birth-and-death process.
  • Study the pairwise Hidden Markov model (HMM) and its application to the pairwise alignment problem.
  • Study HMM and its application to the GpC island problem.
  • Study HMM and its application to gene-finding problem.
  • Study a generalized profile hidden markov model.
  • Study The Coalescent And Population Structure.
  • Study the codon based model for phylogenetic trees suggested by Ziheng Yang.
  • Study Stochastic optimization and its applications to Financial economics.
  • Study the the Ergodic Behavior of Stochastic Processes of Economic Equilibria by Blume, Lawrence.
  • Read the survey paper by David J. Aldous.