The figure below shows an example of the problem of regions. A bivariate normal vector having an unknown expectation vector and identity covariance matrix has been observed to fall into the region "R_quad", rather than the regions "R_con" or "R_lin". How confident should we be that the expectation vector itself lies in R_quad? A bootstrap methodology is proposed for answering this question, in a way that combines frequentist and Bayesian measures of confidence. The figure relates to the choice of the degree of a polynomial regression. Other examples will include assigning confidence to the branches of an observed phylogenetic tree, and saying how confident we can be that a density function is bimodal given that its kernel estimate appears that way.

This is a joint work with Robert Tibshirani.

Back to Workshop Schedule