In this course, we will present scalable Bayesian models and related Markov chain Monte Carlo based methods that can provide fast analysis of big spatial and spatio-temporal data using modest computing resources. We will begin with an introduction on point-referenced spatial data accompanied by an overview of statistical methods used to analyze them. We will briefly cover exploratory data analysis techniques like variogram fitting, basics of geo -statistical approaches like kriging and Gaussian Processes, and fundamentals of Bayesian hierarchical geospatial models. We will then highlight some of the computational issues experienced by Gaussian Process models when used to model large spatial data. In this context, we will present new scalable Bayesian models that can deliver fully model based inference for massive spatial data and demostrate how to analyze large datasets using these models in R.

• Introduction to Point-referenced Spatial Data (8:30 AM – 10:15 AM)

• Introduction to Geostatistics

  (3x2 slides)

• Code
• Simulated Dataset (Dataset 1)
• WEF Data
• WEF data prediction locations

• Bayesian Conjugate Linear Regression

  (3x2 slides)

• Spatial mapping and spBayes/R

• BREAK: 10:15AM-10:30AM

• High-dimensional Bayesian Geostatistics (10:30AM-12:30PM)

• Low-rank models and the Predictive Process

  (3x2 slides)

• Sparsity composite likelihoods and the Nearest Neighbor Gaussian Process (NNGP)

  (3x2 slides)

• Spatiotemporal NNGP

  (3x2 slides)

• LUNCH: 12:30PM-2:00PM

• Spatial Analysis in R using Predictive Processes and NNGPs (2:00PM-3:15PM)

• Advanced computing environments

  (3x2 slides)

• spBayes demo for Predictive Process

• spNNGP Intro and Demo

• BREAK: 3:15PM-3:30PM

• Practical Computational Considerations (3:30PM-5:00PM)

• Implementing NNGP in R/JAGS/Stan

• Conjugate Bayesian Models for Massive Data

  (3x2 slides)

• Hierarchical Modeling for Large Univariate Areal Data

  (3x2 slides)

• DAGAR model MCMC code