SPRING 2020 - Stochastic Models and Simulation (STAT 753) - Course Website

Office Hours: Wednesdays 3-4pm, Thursdays 2:30-3:30pm, or by appointment (DMSC 219)
Lectures: Tues/Thurs 10:30-11:45pm, DMS 106

Syllabus: Click here to download (PDF)

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Announcements: Get feedback on project rough drafts by Tuesday 5/5/20. See project guidlines below.
Note: The chapters/sections below refer to the Probability Models book unless otherwise specified.

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Course Information

• Week 1: Jan 21, 23
  
  • Introduction and getting started with R: [Intro PDF] [R Practice Exercises] [R Practice Solutions]
    
  • Review of Probability Theory (Models Ch. 1-2): Lec 2
    Probability Distribution Chart
    Homework 1 - due Thursday Feb 6 - Solutions
    
  
  
• Week 2: Jan 28, 30
  
  • Review of Probability Theory (Ch. 2-3): Lec 3-4
    
  • R practice: [LLN-v1] [LLN-v2] [CLT]
    Homework 2 - due Thursday Feb 13 - Solutions
    
  
  
• Week 3: Feb 4, 6
  
  • Simulation basics (Sections 11.1-11.2, 11.4 OR Chapters 3-5 in Simulation): Lec 5, Lec 6
    
  • R practice: [Inverse Transform: Discrete Distributions] [Inverse Transform: Continuous Distributions] [Solutions]
    
  
  
• Week 4: Feb 11, 13
  
  • Stochastic processes (Section 2.9): Lec 7
    
  • Markov Chains I (Sections 4.1-4.2): Lec 8
    
  • R practice: [Markov chains I]
    Homework 3 - due Thursday Feb 20 - Solutions, (R markdown file)
    
  
  
• Week 5: Feb 18, 20
  
  • Markov Chains II (Sections 4.3-4.4): Lec 9, Lec 10
    
  • R practice: [Markov chains II,A] [Markov chains II,B]
    
  
  
• Week 6: Feb 25, 27
  
  • Markov Chains III (Sections 4.5-4.6): Lec 11
    
  • Branching Processes (Section 4.7): Lec 12
    Homework 4 - due Thursday Mar 5 - Solutions
    
  
  
• Week 7: Mar 3, 5
  
  • MCMC Methods (Section 4.9, Simulation ch. 12): Lec 13, Lec 14
    
  • R practice: [Metropolis-Hastings] [MH solns] [Gibbs Sampler], [For more info] - see Myxomatosis example via MH and Gibbs
    
  
  
• Week 8: Mar 10, 12
  
  • TAKE-HOME EXAM - due Tuesday Mar 24 -- Solutions posted on Canvas
  • Poisson Processes I (Sections 5.1-5.4): Lec 15-16
    
  • R practice: [Poisson process]
    
  
  
• SPRING BREAK
  
  
• Week 9: Mar 24, 26
  
  • Poisson Processes II (Sections 5.4-5.5): Lec 17
    
  • Continuous time Markov chains I (Sections 6.1-6.2): Lec 18
    
  • R practice: [Nonhomogeneous Poisson process]
    
  • Discuss Projects
    
  
  
• Week 10: Mar 31, Apr 2
  
  • CTMC II (Sections 6.3-6.4): Lec 19, Lec 20
    Project Guidelines, LaTeX file
    Homework 5 - due Tuesday Apr 16
  
  
• Week 11: Apr 7, 9
  
  • CTMC III (Section 6.4-6.5): Lec 21
    
  • Renewal Theory I (Sections 7.1-7.2): Lec 22
    
  • R practice: [Gillespie SSA] [Gillespie Ref 1] [Gillespie Ref 2]
    
  
  
• Week 12: Apr 14, 16
  
  • Renewal Theory II (Sections 7.3-7.4): Lec 23, Lec 24
    
  • R practice: [Renewal process]
    
  
  
• Week 13: Apr 21, 23
  
  • Brownian Motion (Sections 10.1-10.3, 10.7): Lec 25, Lec 26
    
  • R practice: [Brownian Motion]
    
  
  
• Week 14: Apr 28, 30
  
  • Gaussian Processes and SDEs I: Lec 27, Lec 28, Extra Notes - comprehensive SDE notes posted to Canvas
    
  • R practice: [SDEs - updated] [Numerically solving SDEs - Euler Method]
    
  
  
• Week 15: May 5 (Last Day of Class)
  
  • Gaussian Processes and SDEs II: Lec 29 - more on numerically solving SDEs on Canvas, see SDEs_Hurtado.pdf
  • R practice: [Numerically solving SDEs - Runge-Kutta Method]
    
  
  
• Week 16: May 12
  
  • Final projects due!
    
  • Project Presentations (5-10 minutes each)
    
  
  

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