March 2010
This article considers a broad class of kernel mixture density models on compact metric spaces and manifolds. Following a Bayesian approach with a nonparametric prior on the location mixing distribution and bandwidth, sufficient conditions are obtained on the kernel, prior and the underlying space for strong posterior consistency at any positive continuous density, thereby extending the results of Bhattacharya and Dunson (2010). The prior is also allowed to depend on the sample size n and sufficient conditions are obtained for weak and strong consistency. These conditions are verified on the hypersphere using a von Mises-Fisher kernel and on the planar shape space using complex Watson kernels.
Keywords: Nonparametric Bayes, Density Estimation, Posterior consistency, Sample dependent prior, Riemannian manifold, Hypersphere, Planar shape space
The manuscript is available here in PDF format.