Conditional distributions for the nested Dirichlet process via sequential imputation

TL;DR

This paper introduces a sequential imputation method for calculating posterior distributions in the nested Dirichlet process, enabling more feasible Bayesian nonparametric inference for complex, exchangeable data arrays.

Contribution

It proposes a novel sequential imputation approach to approximate posterior distributions in the nested Dirichlet process, overcoming computational challenges.

Findings

Efficient approximation of NDP posteriors using sequential imputation.

Improved computational feasibility for large exchangeable arrays.

Enhanced Bayesian inference capabilities for complex data structures.

Abstract

We consider an array of random variables, taking values in a complete and separable metric space, that exhibits a kind of symmetry which we call row exchangeability. Given such an array, a natural model for Bayesian nonparametric inference is the nested Dirichlet process (NDP). Exactly determining posterior distributions for the NDP is infeasible, since the computations involved grow exponentially with the sample size. In this paper, we present a new approach to determining these posterior distributions that involves the use of sequential