# 7 September 8

## 7.1 Announcements

• 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

## 7.2 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

## 7.3 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
• Live demonstration
• 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)