10 Day 10 (February 19)

10.1 Announcements

  • Read Ch. 4 pgs 137-192

  • Questions/clarifications from journals

    • “I would like to know more about how everything we’ve been discussing ties into our final project. I’m a bit confused about what kind of analyses and models we are expected to learn and be able to apply at the end of the course.”
    • “My concern is that rejection sampling can be slow if the acceptance rate is low,”
    • “Related to that, my question is about what happens when the prior does not reflect reality.”
    • “I am confused about Monte Carlo methods. In the Bayesian approach we use Monte Carlo to find the value where the posterior distribution is centered. Is rejection sampling also a Monte Carlo method, or is it something different?”

10.2 Hierarchical models

10.3 Review and future direction

  • 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
        • Most important: Write out the goals of the analysis. Usually contains both prediction/forecasting and statistical inference.
        • Very important, but not most important: Write out the statistical model you want to use
        • Not very important: Using a statistical programming language to fit model to data and conduct analysis
  • What is next
    • Intro to spatial statistics
      • Motivated by activity 2 and KS rain example
      • This will rely heavily on chs 3 and 4 and lightly on ch 2 of Wikle et al. (2019)

10.4 Extreme precipitation in Kansas

  • Note, this is essentially the same as activity 2

  • On September 3, 2018 there was an extreme precipitation event that resulted in flooding in Manhattan, KS and the surrounding areas. If you would like to know more about this, check out this link and this video here and here.

  • My process

    • Determine the goals of the study
    • Data acquisition
    • 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)