Estimation and Inference in Changepoint Models

Abstract

This thesis is motivated by statistical challenges that arise in the analysis of calcium imaging data, a new technology in neuroscience that makes it possible to record from huge numbers of neurons at single-neuron resolution. We consider the problem of estimating a neuron’s spike times from calcium imaging data. A simple and natural model suggests a non-convex optimization problem for this task. We show that by recasting the non-convex problem as a changepoint detection problem, we can efficiently solve it for the global optimum using a clever dynamic programming strategy. Furthermore, we introduce a new framework to quantify the uncertainty associated with a set of estimated changepoints in a change-in-mean model. In particular, we propose a new framework to test the null hypothesis that there is no change in mean around an estimated changepoint. This framework can be efficiently carried out in the case of changepoints estimated by binary segmentation and its variants, l0 segmentation, or the fused lasso, and is valid in finite samples. Our setup allows us to condition on much less information than existing approaches, thereby yielding higher powered tests. These ideas can be generalized to the spike estimation problem.