Topics will include the value and importance of Bayesian non-parametric (BNP) methods in data science; Dirichlet-Process (DP) and Polya-Tree (PT) priors for CDFs; the stick-breaking algorithm; DP mixture modeling; and the value of the frequentist bootstrap as an approximate BNP method, and how this opens up BNP for data science with enormous data sets.

The case studies will be drawn from work I did at eBay Research Labs on large-scale A/B testing (randomized controlled trials) and large-scale observational studies.

Through one or more practicals (computer labs), the course will liberally illustrate user-friendly implementations of MCMC sampling via the freeware programs WinBUGS (for Windows platforms), R and rjags (for all platforms) when closed-form solutions are not possible.

The course is intended mainly for people who often use statistics in their research or other work in academia, government or industry; as noted above, a first, second and third course in Bayesian analysis equivalent to the content of day 4 of this five-day course will provide sufficient background for participants.

He is a Fellow of the American Association for the Advancement of Science, the American Statistical Association (ASA), the Institute of Mathematical Statistics, and the Royal Statistical Society; from 2001 to 2003 he served as the President-Elect, President, and Past President of the International Society for Bayesian Analysis (ISBA).

He is the author or co-author of about 140 contributions to the methodological and applied statistical literature, including articles in the Journal of the Royal Statistical Society (Series A, B and C), the Journal of the American Statistical Association, the Annals of Applied Statistics, Bayesian Analysis, Statistical Science, the New England Journal of Medicine, and the Journal of the American Medical Association; his 1995 JRSS-B article on assessment and propagation of model uncertainty has been cited more than 1,400 times, and taken together his publications have been cited about 13,200 times.

His research is in the areas of Bayesian inference and prediction, model uncertainty and empirical model-building, hierarchical modeling, Markov Chain Monte Carlo methods, and Bayesian nonparametric methods, with applications mainly in medicine, health policy, education, environmental risk assessment and data science.

His short courses have received Excellence in Continuing Education Awards from the American Statistical Association on two occasions. He has won or been nominated for major teaching awards everywhere he has taught (the University of Chicago; the RAND Graduate School of Public Policy Studies; the University of California, Los Angeles; the University of Bath (UK); and the University of California, Santa Cruz).

He has a particular interest in the exposition of complex statistical methods and ideas in the context of real-world applications.

• 9.00-9.10: Registration and coffee
• 9.10-9.25: Introductions
• 9.25-10.25: Lecture 1: Bayesian non-parametric (BNP) methods as an important approach to data science
• 10.25-10.40: Short break
• 10.40-11.40: Lecture 2: Introduction to Dirichlet-Process (DP) and Polya-Tree (PT) priors for CDFs; the stick-breaking algorithm; DP mixture modeling
• 11.40-11.55: Coffee break
• 11.55-12.55 Practical 1: Simulating from DP and PT prior and posterior distributions and fitting DP mixture models in R
• 12.55-13.40: Lunch
• 13.40-14.40 Lecture 3: The frequentist bootstrap as a fast and accurate approximation to stick-breaking; BNP for data science with enormous data sets
• 14.40-14.55: Short break
• 14.55-15.55: Practical 2: Data science case study 1: A/B testing with 24 million observations
• 15.55-16.10: Tea break
• 16.10-17.10: Lecture 4: Data science case studies 2 and 3: causal inference in an observational study with 10 million observations; estimation of heterogeneous treatment effects with 21 million observations
• 17.10-17.40: Overview and summary (of the entire 5-day course)
• 17.40: Close of day

• Lecture notes: Part 1 (Building a Non-Parametric Prior)
• Lecture notes: Part 2 (BNP Implementation Details)
• Lecture notes: Part 3 (Bayesian Non-Parametric Case Studies)
• Lecture notes: Part 4 (Optimal Bayesian Analysis in Digital Experimentation)
• Lecture notes: Part 5 (Big-Data Bayesian Data Science)
• Krnajajic M, Kottas A, Draper D (2008). Parametric and nonparametric Bayesian model specification: A case study involving models for count data. Computational Statistics and Data Analysis, 52, 2110-2128.
• Draper D (2013). Bayesian model specification: heuristics and examples, in Damien P, Dellaportas P, Polson NG, Stephens DA (2013, editors): Bayesian Theory and Applications, Oxford: University Press, 409-431 (gives a worked example of Calibration Cross Validation and shows that Bayesian nonparametric analyses with fully diffuse priors can lead to some surprises)

• Bayesian nonparametric modeling R code: part 1 (Dirichlet process (DP) priors), part 2 (Polya tree (PT) priors), part 3 (fitting BNP models to the NB10 data set), part 4 (Tim Hanson's WinBUGS Polya tree code for monitoring the population median), part 5 (ditto Tim Hanson but monitoring the population mean), part 6 (Thanasis Kottas's R code for fitting location-normal Dirichlet-process mixture models), part 7 (information about how to use Thanasis's code), part 8 (a simulated data set for testing Thanasis's code), part 8 (R code to run Thanasis's example)
• eBay A/B test: data from the control and treatment groups; R code for descriptive analysis and R code for bootstrap analysis