STA961: Statistical Stochastic Processes

Prof:Robert L. Wolpert OH: Mon 4:30-5:30pm, 211c Old Chem
TA:Yun Yang  OH: Mon 7:00-9:00pm, 211a Old Chem
Class: Tue/Thu 11:45a-1:00p, Soc Sci 124
Text:Rasmussen & Williams, Gaussian Processes for Machine Learning Free on-line version
Opt'l:Santner, Williams & Notz, The Design and Analysis of Computer Experiments
Reed & Simon, Functional Analysis, Volume I
Meyn & Tweedie, Markov Chains and Stochastic Stability
Michael Stein, Interpolation of Spatial Data


I. Brownian Bridge and Related Topics ProblemsDue
Jan 09 Intro: Probability distributions & Function spaces
Jan 14-16 Motivation: Donsker & Kolmogorov-Smirnov
Jan 21-23 Dirichlet Sobolev spaces & Brownian Bridge hw1 Feb 18
Jan 28-30 Free Sobolev & O-U, Karhunen-Loève
Feb 04-06 No class (SAMSI Workshop: Topological Analysis)
Feb 11 Reflection and Maxima of the Brownian Bridge
Feb 13 No class--- Snow Day. Homework postponed.
II. Gaussian Processes and Computer Emulation
Feb 18-20 Isotropic Covariance Functions & Gaussian Procs
Feb 25-27 Sacks/Welch/Mitchell & Kennedy/O'Hagan & c.
Mar 04-06 Prediction & Inference for GPs (PCA notes)
--- Spring Break (Mar 09-16) ---
Mar 18 Multiple Regression, GPs, and PCA
Mar 20 Case Study: Heavy Ion Collisions (Chris C-S)
III. Exotic Time Series
Mar 25-27 Examples: Gaussian AR(p) & Linear B/D PPs hw2 Apr 10
Apr 01-03 No class (SIAM/ASA Conference in Savannah)
Apr 08-10 Six different AR(1)-like Gamma Processes notes1 notes2
Apr 15 Integer-valued AR(1)-like Processes or α-Stables hw3 Apr 24

Spring 2014 Edition

This year STA 961 will focus primarily on some basics and on two special topics: Familiarity with a wide range of probability distributions (at the level of STA 230 or, better, STA 831) and the multivariate normal distribution (at the level of STA 210 or, better, STA 721) are assumed. Measure-theoretic probability (e.g. STA 711) is helpful but not required. There will be negligible overlap with topics covered in the Spring 2012 course STA 357 (Topics in Stochastic Processes) or STA 942 (Time Series & Forecasting).

STA 961 Course Description

STA 961: Statistical Stochastic Processes

Topics in the theory and modelling aspects of Stochastic Processes central to Bayesian statistical analysis. Topics vary from year to year but may include some of: