9 September 15

9.1 Announcements

  • Go over assignment #2
    • Oppportunity to redo the assignment #2
    • Why you may want to come to office hours
    • Common issues
  • New resource

9.2 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)

9.3 Gaussian process

  • See bottom of pg. 139 in Wikle et al. (2019)
  • A Gaussian process is a probability distribution over functions
    • If the function is observed at a finite number of points or “locations,” then the vector of values follows a multivariate normal distribution.

9.3.1 Multivariate normal distribution