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National Ecological Observatory Network (NEON) Applied Bayesian Regression Workshop, March 7 - 8, 2013

Course description

The focus is on applied Bayesian regression models 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 lecture series begins with a basic introduction to Bayesian analysis and hierarchical linear and generalized linear models. More advanced topics will address common challenges in environmental data analysis including missing data and when the number of observations is too large to efficiently fit the desired hierarchical model. The exercises blend modeling, computing, and data analysis including a hands-on introduction to R, JAGS, and openBUGS. Special attention is given to exploration and visualization of spatial-temporal data and the practical and accessible implementation of spatial-temporal models.

Pre-course material

We 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. 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_0.3-5 in all of the exercises.

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.

Course Materials

Some slides will change between now and the beginning of the course. Also, we will likely not have time to cover all material.

Module-1

Principles of Bayesian inference

1: Basic principles (handout)

2: Bayesian linear regression (handout)

3: Model comparison (handout)

Computing

1: Exploring the influence of priors norm-priors.R

2: MCMC chains and convergence binorm-nh.R

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

Module-2

Introduction to spatial data and models

1: Basics of point-referenced (geostatistical) datasets (handout)

R session on spatial data exploration and graphics

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

Module-3

Hierarchical models for spatial data

1: Spatial point-referenced models (handout)

2: Spatial autoregressive models (handout)

Bugs and R session on univariate Gaussian spatial models

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

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

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

4: Illustration of areal model using Bugs code.

5: NEON Harvard forest data.

Module-4

Models for non-Gaussian spatial data

1: Generalized linear spatial models and illustration (handout)

R session on generalized linear spatial models

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

2: Illustration of binomial model with multiple trials at each location code.

Module-5

Models for multivariate spatial data

1: Multivariate spatial models and illustration (handout)

R session on multivariate Gaussian spatial models

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

Module-6

Models for space time data

1: Spatial-temporal models (handout)

2: Spatial-temporal case study

R session on univariate spatio-temporal models

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

Module-7

Models for large spatial datasets

1: Spatial predictive process models and illustration (handout)

R session on predictive process models

1: Univariate Gaussian with predictive process annotated, code, and session data as tar.gz or zip archive.

2: Univariate GLM with predictive process annotated, code, and session data as tar.gz or zip archive.

Module-8

Computing environment and R/C/C++ API

1: Computing notes (handout)

2: API examples as tar.gz or zip

Course instructors

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

Dr. Sudipto Banerjee, Division of Biostatistics, School of Public Health, University of Minnesota.

  Andrew O Finley