Calendar and Notes | AMS245, Spring 19, Section 01

This is a tentative syllabus for the Spatial Statistics course. For some topics there will be notes and slides prepared by me. The references consider the sections in the textbooks that are more likely to contain relevant material. BCG refers to Banerjee, Carlin and Gelfand, DR refers to Diggle and Ribeiro, and SG to Schabenberger and Gotway. This table may change substantially during the quarter. The level of proofreading of the notes provided here is not as high as you'd expect from a book. Moreover they are meant to be complemented by my comments and examples during lectures.

TOPIC	References
Introduction	BCG 1; DR 1; SG 1
Fundamentals of Gaussian Processes
Some course notes Basic Definitions Smoothness of random fields Spectra of random fields Spectral representations of random fields	BCG 2-3; DR 3.1-3.7; SG 2.1-2.5; 4.7
Inference for Gaussian Processes
Variogram estimation Maximum likelihood estimation Spatial Prediction Bayesian Inference (1), (2) Process Convolutions Predictive Processes	BCG 6.1-6.2; DR 5.1-5.5; 6.1-6.7; 7.2; SG 4.1-4.5 Lemos and Sansó (2012) doi:10.1016/j.stamet.2011.02.001 Annalisa 1 Banerjee 2017 doi:10.1214/17-BA1056R
Markov Randon Fields
Gaussian Markov Random Fields Non-Gaussian MRF	BCG 4; 6.4-6.6 Higdon (2007) A Primer on Space-Time Modeling From a Bayesian Perspective Rue and Held (2005) Gaussian Markov Random Fields Lindgren and Rue (2011)
Multivariate Gaussian Processes
Multivariate GP	BCG 9
Space-Time Processes
Space-time GP (1) (2)