The emergence of large data sets in environmental science has changed statistical analysis: more focus on data wrangling and algorithmic approaches, especially Bayes. Bayesian analysis departs from alternative methods in its application of probability to all aspects of model fitting with side benefits of simplifying interpretation. The elements of a Bayesian analysis include distributions for prior, likelihood, and posterior. Hierarchical models emerge naturally in the Bayesian framework as a means for analyzing high-dimensional problems without requiring a change in approach. Graphs help to organize hierarchical modeling. Basic concepts are introduced using regression.

Logistics

From last time

Discussion reading: select two papers and come prepared to discuss them. Post questions for discussion on sakai resources/groupDocs.

Today’s plan

  1. Breakout: Discussion of papers, approx 20 min

  2. Foundation materials in Unit 1 and R

    • Regression example
    • Least squares versus maximum likelihood versus Bayes
    • Model graphs
    • Vectors and matrices (indexing, algebra, identity, inverse, vectorization)

For next time

post problems in Intro to R to Sakai, one set per group

Recall objectives:

  1. Recognize and generate notation for a simple model
  2. Identify the basic elements of a Bayesian model and its probability interpretation
  3. Identify the deterministic vs stochastic variables in a model
  4. Interpret a hierarchical model
    • construct a simple graphical model
    • assemble parameters, process, and data as a hierarchy
    • describe a regression model with notation and graph
  5. Articulate advantages and disadvantages of observational and experimental evidence
  6. Define Simpson’s Paradox and identify when it could be operating
  7. Identify key advantages and limitations of artificial intelligence