Probability and Statistics Reading Group
Department of Mathematics
Washington University in St. Louis
Spring 2017
Spring 2017 Information: Volunteers will present each week in one of two formats: (i) volunteers will give a brief introduction (maximum of 30 minutes) to their area of research which is accessible to non-specialists; (ii) volunteers will practice presenting a recent paper in applied statistics, such as from the list below. This is primarily intended for Ph.D. students to practice explaining their research area to a general statistics audience.

Meeting Time and Location: See schedule below. All meetings will be 2:30-3:30pm, Room 199 in Cupples I
Contact: Professor Todd Kuffner ( kuffner followed by @ followed by math dot wustl dot edu )

February 2
Guanshengrui Hao
Ph.D. student, Dept. of Mathematics
Estimating the size of social networks
February 16
Min Hee Seo
Ph.D. student, Dept. of Political Science
Can a synthetic panel do as well as a true panel?
February 23
Wei Wang
Ph.D. student, Dept. of Mathematics
High-dimensional precision matrix estimation
March 2
Tian Wang
Ph.D. student, Dept. of Mathematics
Introduction to registration problem for functional data
March 30
Liqun Yu
Ph.D. student, Dept. of Mathematics
Divide-and-combine strategies for large-scale statistical model fitting

Big data has imposed both opportunities and challenges for statisticians. Distributed statistical model fitting is required when the data are too big for a single computer to process and/or when data are stored in different machines. Besides subsampling methods, there are typically two approaches to large-scale statistical model fitting. One is to resort to distributed numerical algorithms that solve statistical optimization problems in parallel. And the other is to derive statistical aggregation methods that aggregate subset estimations in a way that preserves asymptotical efficiency. In this talk, I will give a brief overview of both approaches. Throughout the talk, I will be using the penalized quantile regression as a motivation example.
April 13
Luis Garcia German
Ph.D. student, Dept. of Mathematics
A review of the Gaussian correlation inequality

In 2014 Thomas Royen, a retired statistician, provided a proof of the Gaussian correlation inequality. Since then this proof has gone unnoticed up until recently when Rafal Latala (Warsaw, Poland) and one of his students called attention to it. In this talk I will discuss the history of the problem, the proof, and applications of the inequality.

Some suggested papers:

Spring 2015 Semester

Spring 2015 Information: We will focus on MCMC. Volunteers will present each week.

We will start with Chapter 1 of the Handbook of Markov Chain Monte Carlo, edited by Brooks, Gelman, Jones and Meng, published by Chapman & Hall/CRC. Some information is here.

You can find the first chapter of the Handbook here:

When logged in from WashU, you can access all chapters of the book through the libary by this link:

Professor Stanley Sawyer (emeritus professor of mathematics at WashU) authored a great set of notes available here:

Meeting Time and Location: Tuesdays, 1-2pm in Room 115 of Cupples I
Contact: Professor Todd Kuffner ( kuffner followed by @ followed by math dot wustl dot edu )

Spring 2015 Schedule:
Topic/Section of Book
HB 1.8-1.10
Han Liang Gan
HB 1.11-1.12
Guanshengrui Hao
HB 1.17
Liqun Yu
Chib, S. and E. Greenberg (1995), ``Understanding the Metropolis-Hastings Algorithm," The American Statistician, 49 (4), 327-335.
Ed Greenberg
Reversible jump MCMC; Suggested reading: HB Chapter 3, or Green and Hastie (2009), or Green (1995, Biometrika)
Tian Wang
Random Walk Metropolis-Hastings and Adaptive MCMC (time permitting); Suggested reading: HB Chapter 4 (must be logged in from WashU)
Todd Kuffner
Chan, JCC and I. Jeliazkov (2009), ``MCMC estimation of restricted covariance matrices," Journal of Computational and Graphical Statistics, 18 (2), 457-480.
Wei Wang
Convergence diagnostics for MCMC. Suggested reading: Cowles and Carlin (1996), ``Convergence diagnostics for MCMC: A Comparative Review," JASA, 91 (434), 883-904.
Michelle Torres Pacheco and Jonathan Homola
Simulated annnealing; also Gill and Casella (2004), ``Dynamic Tempered Transitions for Exploring Multimodal Posterior Distributions," Political Analysis, 12, 425-443.
Jeff Gill
Tailored randomized block Metropolis-Hastings; Chib and Ramamurthy (2010), ``Tailored randomized block MCMC methods with application to DSGE models," Journal of Econometrics, 155, 19-38.
Sid Chib

HB: Handbook of MCMC

Fall 2014 Semester
Fall 2014 Information: We will focus on articles of interest to the group, including both recent and classic contributions, as well as surveys. Occassionally, we may also invite a presentation from a student or outside speaker on a topic of interest. Articles will be chosen from leading journals in probability, such as:

Annals of Applied Probability
Annals of Probability
Probability Theory and Related Fields
Advances in Applied Probability
Electronic Journal of Probability
Journal of Applied Probability
L'Institut Henri Poincare. Annales (B). Probabilites et Statistiques
Probability Surveys
Theory of Probability and Its Applications

Meeting Time and Location:  Fridays, 12:30-1:30pm, Cupples I, Room 6

Contact: Professor Todd Kuffner ( kuffner followed by @ followed by math dot wustl dot edu )

Incentive for graduate students:  Pizza, generously provided by the Department of Mathematics

Fall 2014 Schedule
19th September
Ross, Nathan F. ``Fundamentals of Stein's method." Probability Surveys, Volume 8, 2011. Han Liang Gan
26th September
Jones, Galin L. ``On the Markov chain central limit theorem." Probability Surveys, Volume 1, 2004. Jeff Gill
3rd October
Le Gall, Jean-Francois. ``Random trees and applications." Probability Surveys, Volume 2, 2005. Todd Kuffner
10th October
Roberts and Rosenthal. ``Coupling and ergodicity of adaptive Markov chain Monte Carlo algorithms." Journal of Applied Probability 44 (2), 2007.   Han Liang Gan
17th October

24th October
Ramsey, F.P. ``Truth and Probability", in Ramsey, 1931, The Foundations of Mathematics and other Logical Essays, Ch. VII, p. 156-198, edited by R.B. Braithwaite, New York: Harcourt, Brace and Company.

31st October
Special Topic: The Dirichlet Process
Suggested Reading: Ferguson, Thomas S. (1973). ``A Bayesian Analysis of Some Nonparametric Problems." Annals of Statistics, 1 (2), 209-230.
Jeff Gill
7th November
Two Essays of Bruno de Finetti:
1. ``Probabilism" in Erkenntnis, September 19989, 31 (2-3), p. 169-223. [Translation by Maria Concetta Di Maio, Maria Carla Galavotti and Richard C. Jeffrey of  `Probabilismo', 1931.]
2. ``The logic of probability" in Philosophical Studies, 77 (1), p. 181-190, 1995. [Translation by R.B. Angell from `La logique de la probabilite", 1935.]

14th November
Robert, Christian P., Nicolas Chopin and Judith Rousseau. ``Harold Jeffreys's Theory of Probability Revisited." Statistical Science, Volume 24 (2), 141-172, 2009.

Suggested Recent Survey Articles:
Suggested Recent Highly-Cited Papers: (Scopus citation count as of Sep. 9, 2014)

Suggested Topics for Presentation: law of the iterated logarithm, the mathematics of MCMC, limit theorems for dependent processes, Dirichlet processes, ergodic theorems, the Kalman filter