GFDI Student Seminar: Dr. James B. Elsner
A Tutorial on Bayesian Models in R
Dr. James B. Elsner
Abstract: We start with a standard language for describing and coding regression models. A language used in all statistical journals and general Bayesian and non-Bayesian models. Increasingly, scientists are using this language to describe their methods. Learning the language is an investment.
In the abstract the grammar is built in five steps.
- First we recognize a set of measurements that we hope to predict or learn about, the “outcome” (response, dependent, variate) variable or variables.
- Next for each outcome variable, we choose a likelihood distribution that defines the plausibility of individual observations of the variable. In linear regression this likelihood is always Gaussian.
- Then we recognize a set of other measurements that we hope to use to predict or learn about the outcome. Call these “predictors” (explanatory or independent variables, covariates).
- We relate the exact shape of the likelihood distribution to the predictor variables (e.g., location and variance and other aspects of its shape). In choosing a way to relate the predictors to the outcomes, we are forced to name and define all of the parameters of the model.
- Finally, we choose priors for all the model parameters. These priors define the initial information state of the model before seeing the data.
With the new Stan engine for sampling and some new R packages for making use of it, interest in Bayesian models will continue to grow.