Bayesian Statistics

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See also: Daily Schedule Term 2

Daily Schedule Term 3

Week 8 — Building Your Intuition with More Examples with Mutually-Exclusive Hypotheses: Hamilton vs. Madison and a Mudslide with Pollen

• Tuesday, Oct. 29 — Study Chapter 5 of Bayesian Statistics for Beginners — Do the Assignment for Tuesday — Preparatory discussion for Chapter 6
• Friday, Nov. 1 — Study Chapter 6 of Bayesian Statistics for Beginners — Do the Assignment for Friday — Preparatory discussion for Chapters 8 and 9: A Continuum of Hypotheses — NOTE: We skipped Chapter 7 because it introduced too little that is new

Week 9 — Bayesian Statistics with Probability Distributions

• Tuesday, Nov. 5 — Dive in at the last half of Chapter 8, pp. 95-107 (if you also try to read pp. 88-94 of Chapter 8, I think you will find it to be a mind-numbing review of what we covered in Young) — Continue in Chapter 9, pp. 108-122 (this is yet more review of Young but in this case the review is useful) — Do the Assignment for Tuesday — We reviewed Bernoulli and Binomial Distributions, including the “n choose k” prefactor in the binomial distribution — We looked at the etymology of the terms “probability mass function (PMF)” (an example of which is the Poisson distribution) as Donovan and Mickey use the term in Chapter 8, and “probability density function (PDF)” (an example of which is the Gaussian distribution) as Donovan and Mickey use the term in Chapter 9 — We started the Assignment for Friday
• Friday, Nov. 8 — Finish Chapter 9 and the Assignment for Friday — We are not starting any new material — Instead, let’s consolidate — People asked for additional practice problems, which we started in class

Week 10 — Exam 2 — Start Bayesian Conjugates

• Tuesday, Sept. 24 — Exam 2 on Frequentist and Bayesian Statistics (covers Problem Sets 6 to 12 and Donovan and Mickey Chapters 1 to 9), including linear regression and χ-squared — See also the quick summary of Problem Sets 10, 10, 11, and 12
• Friday, Nov. 15 — Study Chapter 10 — Introduce Bayesian Conjugates — Please examine the Assignment for Friday which is not to be turned in — Instead it just contains ideas for how you could approach Chapter 10

Week 11 — Finish Bayesian Conjugates — Start Monte Carlo, Simple Applications

• Tuesday, Nov. 19 — You can study Chapter 11, which introduces gamma functions which are conjugate to Poisson distributions, or alternatively, you can just study my handout on Bayesian Conjugates — Please come with questions about Chapters 11 or my summary in the handout of Chapter 11: Bayesian Conjugates — Do the Assignment for Tuesday — An Advanced Idea from Chapter 12: A Multi-Dimensional Continuum of Hypotheses — For completeness, here are Michael I. Jordan’s Stat260 notes
• Friday, Nov. 22 — While you are doing the Assignment for Friday on Chapter 11, I have been working on a Monte Carlo Methods Introduction and on a Monte Carlo Playground and Program that we will use in class — Rather than you diving in to Chapter 13 already, wait until that for the next class, and instead start by reading The Beginning of the Monte Carlo Method

Week 12 — Continue Monte Carlo, Simple Applications — The Metropolis Algorithm

• Tuesday, Nov. 26 — Study Chapter 13 — Do the Assignment for Tuesday — Look ahead to the remainder of the course — Describe the various Monte Carlo methods and the Hepatitis B vaccination study
• Friday, Nov. 29 — No class - Shakespeare Festival

Week 13 — The Metropolis-Hastings Algorithm

• Tuesday, Dec. 3 — See Monte Carlo Methods - Why Do They Work? - Part I for my proof that the Metropolis algorithm works — Introducing Metropolis-Hastings
• Friday, Dec. 6 — Study Chapter 15 to p. 229 — More directions for Friday are in the Assignment for Friday — See also Monte Carlo Methods - Why Do They Work? - Part II for my proof that the Metropolis-Hastings algorithm works

Week 14 — The Gibbs Sampling Algorithm — Exam 3

• Tuesday, Dec. 10 — Our final subject before Exam 3 is Gibbs sampling, and I am not going to have you look at Donovan and Mickey Chapter 16, because they have obscured what is almost laughably simple — Instead, in class we’ll go through my Monte Carlo Methods - Why Do They Work? - Part III — Here is the In-Class Exercise for Tuesday
• Friday, Dec. 13 — Exam 3 covering Chapters 10 and 11 of Donovan and Mickey on Bayesian Conjugates and Chapters 13, 15, and 16 on Markov Chain Monte Carlo — For understanding the theory of chapters 13, 15, and 16, I’d recommend you use my “Monte Carlo Methods - Why do They Work?” write-ups, linked above and my quick summary of Problem Sets 14 to 18

Week 15 — A Case Study Using Gibbs Sampling

• Tuesday, Dec. 17 — We will work through this Monte Carlo Methods Case Study

Spiegelhalter, Best, Gilks, and Inskip use this graphic as a summary of the 217-parameter Hepatitis B model