Online Program

Estimating a Mixing Distribution on the Sphere Using Predictive Recursion (309875)

Keywords: Directional data, EM algorithm, marginal likelihood, mixture model, von Mises–Fisher distribution

Mixture models are commonly used when data show signs of heterogeneity and, often, it is important to estimate the distribution of the latent variable responsible for that heterogeneity. This is a common problem for data taking values in an Euclidean space, but the work on mixing distribution estimation based on directional data taking values on the unit sphere is limited. In this presentation I will talk about using the predictive recursion (PR) algorithm to solve for a mixture on a sphere. Unlike likelihood-based methods which only support finite mixing distribution estimates, PR can estimate a smooth mixing density, it gives an asymptotically consistent estimate and is computationally efficient. The presentation will also cover two real data examples where this PR-based methodology can be employed, namely goodness-of-fit testing and for clustering surface normals (three-dimensional unit vectors) to reconstruct images.