Project #2 With Richard Lockhart

Bayesian evaluation and interpretation of LASSO model fits

The LASSO method of fitting linear models uses a so-called penalty. The penalty may be thought of as a prior distribution for the unknown regression coefficients. For a single fixed choice of the parameter in that prior distribution, the posterior mode is then the usual LASSO estimate. It has the appealing property that many of the estimated slopes will be exactly zero if the penalty parameter has been picked correctly.

In this project we will investigate this Bayesian interpretation. The USRA student will:

1. Conduct a literature review finding papers that consider the penalty as a prior in a fully Bayesian analysis.
2. Develop R code to treat the penalty as a prior and do Bayesian analysis on this basis.
3. Investigate the use of a hyperprior on the penalty parameter by repeating 1) with a variety of hyperpriors.
4. Investigate methods proposed by the supervisor for doing "calibrated" Bayesian inference -- adjusting priors or loss functions to produce Bayesian procedures with specified coverage or Type I error rates.