Adaptive Convergence Rates of a Dirichlet Process Mixture of Multivariate Normals

2011/11/17 by Surya T. Tokdar, Tokdar, Surya T.
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #FOS: Mathematics #Functional Equations Stability Results #Mathematical Dynamics and Fractals #Methodology (stat.ME) #Statistics Theory (math.ST) #math.ST #stat.ME #stat.TH

paper · pdf · doi:10.48550/arxiv.1111.4148

12 pages

arxiv created 2011/11/17 · openalex publication_date 2011/11/17 · arxiv updated 2011/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is shown that a simple Dirichlet process mixture of multivariate normals offers Bayesian density estimation with adaptive posterior convergence rates. Toward this, a novel sieve for non-parametric mixture densities is explored, and its rate adaptability to various smoothness classes of densities in arbitrary dimension is demonstrated. This sieve construction is expected to offer a substantial technical advancement in studying Bayesian non-parametric mixture models based on stick-breaking priors.

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