Title: Posterior contraction and credible sets for filaments of regression functions
Authors: Wei Li - Syracuse University (United States) [presenting]
Subhashis Ghosal - North Carolina State University (United States)
Abstract: A filament consists of local maximizers of a smooth function when moving in a certain direction. Filamentary structures are important features of the shape of objects and considered as a useful lower dimensional characterization of multivariate data. There have been some recent theoretical studies of filaments in the nonparametric kernel density estimation context. We shall discuss a Bayesian approach to the filament estimation in regression context and present some results on posterior contraction rates obtained using a finite random B-splines series. Compared with the kernel-estimation method, the bias can be better controlled using the series method when the function is smoother, which allows obtaining better rates. In addition, we discuss a way to construct a credible set with sufficient frequentist coverage for the filaments and demonstrate the proposed method in simulations and one application to earthquake data.