- 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)
- simulation
- 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