Neuroscience has recently proven to be a rich source of interesting statistical problems. This talk will address three such problems (with relative emphasis depending on audience interest):
1) Nonparametric estimation of information-theoretic quantities (especially the Shannon entropy and mutual information) from sparsely-sampled data.
2) Optimal, adaptive experimental design (how do we select stimuli online to learn the most about the brain in the least amount of time).
3) Minimax theory for estimating sparsely-sampled discrete distributions under Kullback-Leibler loss.
Brief biography