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Hierarchical random effects models using Markov chain Monte Carlo: Analysis of spatio-temporal data.

Course description

The one-day short course will explore recent advancements in hierarchical random effects models using Markov chain Monte Carlo methods with application and examples for statistical ecology. The focus is on linear and generalized linear modeling frameworks that accommodate spatial and temporal associations. Lecture and exercises offer an applied perspective on model specification, identifiability of parameters, and computational considerations for Bayesian inference from posterior distributions. The lectures will begin with a basic introduction to Bayesian hierarchical linear models and proceed to address several common challenges in environmental data, including missing data and when the number of observations is too large to efficiently fit the desired hierarchical random effects models. The exercises blend modeling, computing, and data analysis including a hands-on introduction to spBayes package in the R statistical environment. Special attention is given to exploration and visualization of spatial-temporal data and the practical and accessible implementation of spatial-temporal models. Material is also made available for self-guided review of Bayesian basics and computing, see self study modules at the bottom of this page.

Pre-course material

I encourage participants to bring a laptop and follow along with the illustrative R sessions. However, this level of participation is purely optional. For those who are not familiar with R, please review "An Introduction to R" (PDF, HTML). This introductory tutorial is ideal for beginners. It contains a description of data types, commands, and basic statistical analysis. Another excellent tutorial, with more of a forestry emphasis, was written by Andrew Robinson and is available here. The latest release of R is necessary for those who choose to participate in the computing sessions. Also, the latest releases of the various R packages used in the illustrative sessions are necessary. The majority of these packages can be installed all at once using the Spatial CRAN Task View.

  • Linux users -- some packages used in the sessions require lower-level c/c++ libraries. Here is a brief howto on installing these supporting libraries.

  • Windows users -- should be able to install the necessary packages by running the Packages.R script within R.

  • Mac users -- should be able to install all of the binary packages from CRAN, except for rgdal. Instructions for installing rgdal are given on the package's CRAN page here.

  • We will be using spBayes_0.3-8 in all of the exercises. Some details about spBayes models and computing can be found here.

Please note that handouts of slides and annotated R sessions will not be provided. Rather, if desired, you can print them out beforehand and bring them along. Slide handouts can be downloaded at once here or by topic below. The R code with and without annotation and supporting data files (in compressed form) are also provided below. Feel free to download these material prior to the course. Alternatively, memory sticks with this material will be passed around at the beginning at the workshop.

Course materials

We will not have time to cover all material. Some slides and exercises will change between now and the beginning of the course.

Module-1

Motivating hierarchical random effects models using spatial data analysis

Geostatistics and exploratory data analysis (handout)

R session on spatial data exploration and graphics

Annotated, code, and session data as tar.gz or zip archive.

Hierarchical models for spatial data

Spatial point-referenced models (handout)

R and Bugs session on univariate Gaussian spatial models

• Univariate spatial via spLM annotated, code, and session data as tar.gz or zip archive.

• Univariate spatial via rjags annotated, R code, and JAGS code and session data as tar.gz or zip archive.

• Adaptive MCMC example annotated, code, and session data as tar.gz or zip archive.

Module-2

Models for non-Gaussian spatial data

Generalized linear spatial models and illustration (handout)

R session on generalized linear spatial models

Annotated, code, and session data as tar.gz or zip archive.

Module-3

Computing environment and R/C/C++ API

Computing notes (handout)

• API examples as tar.gz or zip

Module-4

Recap and additional thoughts (handout)

Lunch

Module-5

Hierarchical random effects models—the rest of the story (handout)

Module-6

Models for multivariate spatial data

Multivariate spatial models and illustration (handout)

R session on multivariate Gaussian spatial models

Annotated, code, and session data as tar.gz or zip archive.

Multivariate misalignment.

Module-7

Models for large spatial datasets

Spatial predictive process models and illustration (handout)

R session on predictive process models

• Multivariate Gaussian with predictive process annotated, code, and session data as tar.gz or zip archive.

Module-8

Models for space time data

Dynamic models for space-time data (handout)

Spatial-temporal case study

R session on univariate spatio-temporal models

Annotated, code, and session data as tar.gz or zip archive.

Self study

Principles of Bayesian inference

Basic principles (handout)

Bayesian linear regression (handout)

Model comparison (handout)

Computing

• Exploring the influence of priors norm-priors.R

• MCMC chains and convergence binorm-nh.R

• JAGS in R via rjags package annotated, R code, JAGS code, and session data as tar.gz or zip archive.

Course authors

Dr. Andrew Finley, Department of Forestry, Geography, and Statistics & Probability, Michigan State University.

Dr. Alan Gelfand, Department of Statistical Science, Duke University.

Dr. Sudipto Banerjee, Department of Biostatistics, University of California, Los Angeles.