Estimating a mixing distribution on the sphere using predictive recursion

by   Vaidehi Dixit, et al.

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 a Euclidean space, but the work on mixing distribution estimation based on directional data taking values on the unit sphere is limited. In this paper, we propose using the predictive recursion (PR) algorithm to solve for a mixture on a sphere. One key feature of PR is its computational efficiency. Moreover, compared to likelihood-based methods that only support finite mixing distribution estimates, PR is able to estimate a smooth mixing density. PR's asymptotic consistency in spherical mixture models is established, and simulation results showcase its benefits compared to existing likelihood-based methods. We also show two real-data examples to illustrate how PR can be used for goodness-of-fit testing and clustering.



There are no comments yet.


page 15

page 18

page 21


Revisiting consistency of a recursive estimator of mixing distributions

Estimation of the mixing distribution under a general mixture model is a...

Fast nonparametric near-maximum likelihood estimation of a mixing density

Mixture models are regularly used in density estimation applications, bu...

Mixture models for spherical data with applications to protein bioinformatics

Finite mixture models are fitted to spherical data. Kent distributions a...

Blindness of score-based methods to isolated components and mixing proportions

A large family of score-based methods are developed recently to solve un...

Censored pairwise likelihood-based tests for mixing coefficient of spatial max-mixture models

Max-mixture processes are defined as Z = max(aX, (1 -- a)Y) with X an as...

Data Harmonization Via Regularized Nonparametric Mixing Distribution Estimation

Data harmonization is the process by which an equivalence is developed b...

Representational Rényi heterogeneity

A discrete system's heterogeneity is measured by the Rényi heterogeneity...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.