Biostat - 276
Bayesian Computation
Biostat 276 - UCLA - Winter 2023 - Syllabus.pdf
Instructor: Donatello Telesca
Lecture: TR - 3:00pm -4:50pm, PUB HLT 61-263 - (Zoom)
Office Hours: TR - 4:30 - 4:50 in class or by appointment
In case you are not cleared to be on campus due to covid symptoms, remote attendance is encouraged via zoom.
Schedule of Lectures
(1/10) Introduction to Bayesian inference [Lecture.pdf - recording]
(1/12) Quadrature and Asymptotic approximations [Lecture.pdf - recording]
(1/17) Introduction to Monte Carlo methods - ARS [Lecture.pdf - recording]
(1/19) Controlling Monte Carlo variance - Importance Sampling [Lecture.pdf - Lecture.Rmd - recording]
(1/24) Project 1 Due - Example s+ Introduction to MCMC [Lab1.Rmd - Lecture.pdf - recording]
(1/26) Review of Project 1 [recording]
(1/31) More on Metropolis Hastings and Gibbs Sampling [Lecture.Rmd - Lecture.pdf - recording]
(2/02) Proposal Strategies for MH Implementations [Lecture.Rmd - Lecture.pdf - recording]
(2/07) Project 2 Due - Auxiliary Variables and Data Augmentation [Lecture.pdf - recording - (Book Chapter)]
(2/09) Review of Project 2 [recording]
(2/14) Tempering strategies and Population MCMC [Lecture.pdf - Recording] (Book Chapter)
(2/16) Lecture Cancelled
(2/21) Trans Dimensional Problems [Lecture.pdf - Recording] (Book Chapter)
(2/23) Introduction to HMC [Lecture.pdf - Recording - Zoom Only]
(2/28) Project 3 Due - Review of Project 3 [Lecture.pdf - Recording]
(3/02) HMC in practice [Lecture.pdf - Lecture.Rmd - Recording]
(3/07) Introduction to INLA [Lecture.pdf - Recording]
(3/09) Introduction to Variational Bayes [Lecture.pdf - Recording]
(3/14) Introduction to ABC [Lecture.pdf]
(3/16) Review of Project 4 - Project 4 Due
Coursework
Three projects each worth 1/4 of your class grade
Reading List
(Recommended) Brooks, Gelman, Jones and Meng. Handbook of Markov Chain Monte Carlo. Chapman and Hall/CRC
(Optional) Liang F et. Al. Advanced Markov Chain Monte Carlo Methods. Wiley.
(Optional) Robert, CP, Casella, G (2004). Monte Carlo Statistical Methods. New York: Springer.
(Optional) Gelman, A, Carlin, JB, Stern, HS, and Rubin, DB (2003). Bayesian Data Analysis, Second Edition. New York: Chapman and Hall.
(Optional) Marin, J-M and Robert C (2007). Bayesian Core. New York: Springe-Verlag. (Available online for UCLA students)
(Optional) Hoff, P (2009). A First Course in Bayesian Statistical Methods. New York: Springer. (Available online for UCLA students)
(Optional) Carlin, BP, Louis, TA (2000). Bayes and Empirical Bayes Methods for Data Analysis, Second Edition. New York: Chapman and Hall.
Manuscripts
Lindley, DV, and Smith, AFM, "Bayes Estimates for the Linear Model". Journal of the Royal Statistical Society. Series B (Methodological), Vol. 34, No. 1. (1972), pp. 1-41. (basics for Bayesian hierarchical models).
Tanner, MA, and Wong, WH, "The Calculation of Posterior Distributions by Data Augmentation". Journal of the American Statistical Association, Vol. 82, No. 398. (Jun., 1987), pp. 528-540. (demonstration that two block Gibbs sampling works).
Gelfand, AE, and Smith, AFM, "Sampling-Based Approaches to Calculating Marginal Densities". Journal of the American Statistical Association, Vol. 85, No. 410. (Jun., 1990), pp. 398-409. (one of the most cited papers in statistics).
Gelfand, AE, Hills, SE, Racine-Poon, A, and Smith, AFM, "Illustration of Bayesian Inference in Normal Data Models Using Gibbs Sampling". Journal of the American Statistical Association, Vol. 85, No. 412. (Dec., 1990), pp. 972-985. (good example list).
Tierney L. (1994). Markov Chains for Exploring Posterior Distributions. Annals of Statistics, 22 (4), 1701-1728 (Convergence Results)
Liu JS. and Wu YN (1999). Parameter Expansion for Data Augmentation. JASA, 94, 448, pp 1264-1274.
Green P.J. (1995). Reversible jump Markov Chain Monte Carlo Computation and Bayesian Model Determination. Biometrika, 82 (4), pp 711-32.
Di Matteo I, et. Al (2001). Bayesian Curve-Fitting Using Free-Knot Splines. Biometrika, 88, pp 1055-1071. (Curve Fitting using RJ-MCMC)
Rue H, Martino S and Chopin N. (2009) Approximate Bayesian Inference for Latent Gaussian Models by Using Integrated Nested Laplace Approximations. JRSS-B, 71, 319-392.
Omerod JT and Wand MP (2010). Explaining Variational Approximations. The American Statistician, 64, 140-153.
More to come! ....
Computing
Computing for Biostat 276 will be based on the R and C++ programming languages. The use of platforms like JAGS or STAN is only allowed to check your work. You may use other programming languages of your liking, but all labs and support will be only provided in R.