TY - JOUR
AU1 - Bhattacharya, Abhishek
AU2 - Dunson, David B.
AB - Statistical analysis on landmark-based shape spaces has diverse applications in morphometrics, medical diagnostics, machine vision and other areas. These shape spaces are non-Euclidean quotient manifolds. To conduct nonparametric inferences, one may define notions of centre and spread on this manifold and work with their estimates. However, it is useful to consider full likelihood-based methods, which allow nonparametric estimation of the probability density. This article proposes a broad class of mixture models constructed using suitable kernels on a general compact metric space and then on the planar shape space in particular. Following a Bayesian approach with a nonparametric prior on the mixing distribution, conditions are obtained under which the KullbackLeibler property holds, implying large support and weak posterior consistency. Gibbs sampling methods are developed for posterior computation, and the methods are applied to problems in density estimation and classification with shape-based predictors. Simulation studies show improved estimation performance relative to existing approaches.
TI - Nonparametric Bayesian density estimation on manifolds with applications to planar shapes
JF - Biometrika
DO - 10.1093/biomet/asq044
DA - 2010-12-21
UR - https://www.deepdyve.com/lp/oxford-university-press/nonparametric-bayesian-density-estimation-on-manifolds-with-ZeSGQUVWHQ
SP - 851
EP - 865
VL - 97
IS - 4
DP - DeepDyve
ER -