# September 8

## Announcements

- Reading assignment
- Please talk to me or send a proposal for applied problems we can work on in class
- Phase II and problem based learning!

- Student presentations

## Review

- What we have covered so far
- Review of matrix algebra and distribution theory
- Philosophy of statistical modeling
- Hierarchical modeling framework
- Technical note 1.1 on pg. 13 of Wikle et al. (2019)

- Building our first statistical model!
- Whooping crane data example
- The model building process:
- 1). Choose appropriate PDFs or PMFs for the data, process, and parameter models
- 2). Choose appropriate mathematical models for the “parameters” or moments of the PDFs/PMFs from step 1.

- 3). Choose an algorithm fit the statistical model to the data
- 4). Make statistical inference (e.g., calculate derived quantities and summarize the posterior distribution)

- What are most important skills you need for the model building process

- What is next
- Intro to spatial statistics
- Motivated by data from assignment 2
- This will rely heavily on chs 3 and 4 and lightly on ch 2 of Wikle et al. (2019)

- First spatio-temporal example
- Feel free to suggest ideas/data sets

## Extreme precipitation in Kansas

- During the next few lectures, I will demonstrate multiple ways that I would go about meeting the goals in assignment #2
- My process
- Determine the goals of the study
- Exploratory data analysis
- The model building process
- 1). Choose appropriate PDFs or PMFs for the data, process, and parameter models
- 2). Choose appropriate mathematical models for the “parameters” or moments of the PDFs/PMFs from step 1.

- 3). Choose an algorithm fit the statistical model to the data
- 4). Make statistical inference (e.g., calculate derived quantities and summarize the posterior distribution)

- Model checking, improvements, validation, and selection (Ch. 6)

- 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)