Hierarchical models in ecology

• one-parameter models
  • simulation
    • what simulation is and why we do it
    • simulation in R
    • simulation in Stan -- first intro to Stan syntax
  • model fit to simulated data
    • simple example: number of birds we see in a day
    • recovering a parameter
    • bayesplot
    • tidybayes
    • possible exercise: effect of sample size
    • making predictions -- for new observers
    • real data application: mite abundance (ONE species)
• hierarchical models
  • learning the prior from the data -- one way to think about hyperpriors
  • random-intercept model for our bird example -- differing birding skill among participants
  • simulate data and fit
  • real data application: random intercept model for ONE mite species (no predictors)
  • making predictions -- hierarchical models and "focus".
  • regularization and sample size -- simulated differences
  • random intercepts have information: intercepts correlate with plot variables (water)
  • When not to do a hierachical model: negative binomial distribution
• Univariate regression (one slope)
  • What poisson regression looks like
  • Intro to matrix multiplication in linear models
  • fitting in Stan
  • Predictions -- plotting in tidybayes
  • Comparison with intercept-only model: random effect is "smaller"
• Other models: Binomial GLM
  • redo the workflow from above:
  • prior simulations (narrow on the logit scale)
  • parameter recovery
  • fit to real data
  • plotting
• Multiple regression
  • form of the model (math)
  • code for the model (using matrix multiplication)
  • Causal inference with DAGs

• simple linear regression
  • data simulation
  • parameter recovery
• simple logistic regression (1 species)
  • link functions
  • posterior predictive checks
• multiple species logistic regression
  • parameter distributions
  • "secret weapon"
  • log likelihood / IC
• multiple species