STA961: Statistical Stochastic Processes

Prof:Robert L. Wolpert OH: Mon 2:00-3:00pm, 211c Old Chem
TA:Xi Chen  OH: Wed 1:30-2:30pm, 211a Old Chem
Class: Tue/Thu 11:45a-1:00p, Old Chem 123
Opt'l:Rasmussen & Williams, Gaussian Processes for Machine Learning Free on-line version
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      14 Intro: Probability distributions & Function spaces
Jan 19-21 Brownian Motion construction Einstein 1905 in English or original German
Jan 26-28 No class (Volcano workshop at Kilauea)
Feb 02-04 Stochastic Integration & Diffusions
Feb 09-11 Dirichlet Sobolev spaces & Brownian Bridge hw1Feb 25
II. Gaussian Processes and Computer Emulation
Feb 16-18 Isotropic Covariance Functions & Gaussian Procs
Feb 23-25 Sacks/Welch/Mitchell & Kennedy/O'Hagan & c.
Mar 01-03 Guest Lecture by Mengyang Gu, plus ARMA hw2 Mar 22
III. ID Dist'ns & Lévy Processes
Mar 08-10 ID & Lévy
--- Spring Recess (Mar 12-20) ---
Mar 22-24 LARK Models and Lévy Random Fields
Mar 29-31 Spatial Extremes & Smith Models
Apr 05-07 No class (SIAM/ASA Conference in Lausanne)
IV. Exotic Time Series
Apr 12-14 Non-Gauss. ID AR(1)-like Procs: Ga, Po, NB hw3 Apr 19
Birth & Death, NB Inference
Apr 19 Non-Gauss. Non-Stat. Irreg. Observed Procs

Spring 2016 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: