STA 961 Syllabus

STA961: Statistical Stochastic Processes

Prof:	Robert L. Wolpert	wolpert@stat.duke.edu	OH: Mon 2:00-3:00pm, 211c Old Chem
TA:	Xi Chen	xc54@duke.edu	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

Syllabus

Week Topic Homework

I. Brownian Bridge and Related Topics Problems Due

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 hw1 Feb 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

Week	Topic	Homework
	I. Brownian Bridge and Related Topics	Problems	Due
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	hw1	Feb 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:

Basics of Statical SPs: Donsker's Theorem and the Brownian Bridge; Karhunen-Loève; Likelihood Ratios in sequential procedures as martingales and random walks; some function space background (L₂ Sobolev theory, Hilbert & Banach spaces), probability distributions on function spaces.
Inference and prediction for Gaussian Processes and Random Fields, and in particular on building GP emulators for modeling complex computer output;
Exotic time series with Infinitely Divisible distributions including integer-valued autocorrelated AR(p)-like processes with Poisson or Negative Binomial marginals, useful for modeling autocorrelated count data, and positive-valued processes with Gamma or α-Stable marginals, useful for modeling correlated positive quantities or for use at intermediate stages of hierarchical models (e.g., for building more flexible Bayesian semi- or non-parametric models than is possible with Dirichlet processes).

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:

Convergence theory of Markov chains in general state spaces;
Convergence rates and mixing times for Markov chains;
Stochastic approximation and adaptive estimators;
Inference and prediction for Gaussian Processes and Random Fields;
Modeling and Inference with Continuous-time Jump Processes;
Theory, Application, and inference for Lévy Random Flights;
Inference for Diffusions;
Exotic time series with Infinitely Divisible distributions;
Functional Data Analysis.