A PRticle filter algorithm for nonparametric estimation of multivariate mixing distributions

• Published in: Statistics and computing Vol. 33; no. 4
• Main Authors: Dixit, Vaidehi, Martin, Ryan
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.08.2023; Springer Nature B.V
• Subjects: Algorithms; Approximation; Artificial Intelligence; Computer Science; Data analysis; Empirical analysis; Iterative methods; Nonparametric statistics; Original Paper; Probability and Statistics in Computer Science; Quadratures; Statistical Theory and Methods; Statistics and Computing/Statistics Programs; Mixture model; Marked point process; Monte Carlo; Predictive recursion; Importance sampling
• ISSN: 0960-3174; 1573-1375
• DOI: 10.1007/s11222-023-10242-2

Predictive recursion (PR) is a fast, recursive algorithm that gives a smooth estimate of the mixing distribution under the general mixture model. However, the PR algorithm requires evaluation of a normalizing constant at each iteration. When the support of the mixing distribution is of relatively low dimension, this is not a problem since quadrature methods can be used and are very efficient. But when the support is of higher dimension, quadrature methods are inefficient and there is no obvious Monte Carlo-based alternative. In this paper, we propose a new strategy, which we refer to as PRticle filter , wherein we augment the basic PR algorithm with a filtering mechanism that adaptively reweights an initial set of particles along the updating sequence which are used to obtain Monte Carlo approximations of the normalizing constants. Convergence properties of the PRticle filter approximation are established and its empirical accuracy is demonstrated with simulation studies and a marked spatial point process data analysis.