13 September 28

13.1 Announcements

  • Teaching assessment and assignment 3 due today
    • Questions?
    • We will go over assignment 3 in-class on Thursday
  • Review of Bayesian kriging example from last lecture

13.2 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)

13.2.1 Generalized additive models

  • Most of what I present can be found in Wikle et al. (2019; pgs. 165-170 and 189-191) and Wood (2017)
  • Use the hierarchical modeling framework to describe generalized additive models
    • Demonstrate on ipad
  • Fit generalized additive model model to precipitation and demonstrate how to answer the problems in assignment #2
  • Summary of generalized additive models
    • Positives and negatives to using this approach to solve problems in assignment #2.

13.2.2 Summary of precipitation example

  • I demonstrated Bayesian kriging and generalized additive models to solve all problems in assignment #2
    • Both approaches required some flavor of Bayesian inference
    • Overall there were fairly major difference in the inference obtained from the two approaches
    • Generally speaking spatial data sets are very small, but spatio-temporal data sets are much larger