September 28
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
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)
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
- 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.
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