12 September 24

12.1 Announcements

• Added to Sept. 22 lecture notes: How do you find the full-conditional distributions for the Bayesian linear model?
  • \([\boldsymbol{\beta}|\sigma_{\varepsilon}^{2},\mathbf{y}]\)
  • \([\sigma_{\varepsilon}^{2}|\boldsymbol{\beta},\mathbf{y}]\)
• Please complete the teaching teaching assessment by next Tuesday.

12.2 Extreme precipitation in Kansas

• What we will need to learn
  • How to use R as a geographic information system
  • New general tools from statistics
    • Gaussian process
    • Metropolis and Metropolis–Hastings algorithms
    • Gibbs sampler
  • How to use the hierarchical modeling framework to describe kriging
    • Hierarchical Bayesian model vs. “empirical” hierarchical model
  • Specialized language used in spatial statistics (e.g., range, nugget, variogram)

12.2.1 Kriging

• Most of what I present can be found in Wikle et al. (2019; pgs. 137-164) and Hooten and Hefley (2019; 175-189)
• Classic reference is Cressie (1993; Ch. 3)
• Use the hierarchical modeling framework to describe kriging
  • Demonstrate on ipad
• Fit Bayesian kriging model to precipitation and demonstrate how to answer the problems in assignment #2
  • Semi-live example R code can be downloaded here
• Summary of kriging
  • Positives and negatives to using this approach to solve problems in assignment #2.