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Activity Number:
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225
- Recent Advances in Bayesian Methods for Complex Data Structures
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Type:
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Invited
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Date/Time:
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Wednesday, August 11, 2021 : 10:00 AM to 11:50 AM
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Sponsor:
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Section on Bayesian Statistical Science
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Abstract #316865
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Title:
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Optimal Bayesian Estimation of Gaussian Mixtures with Growing Number of Components
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Author(s):
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Lizhen Lin* and Ilsang Ohn
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Companies:
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The University of Notre Dame and The University of Notre Dame
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Keywords:
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Finite mixture model ;
Mixing distribution estimation;
Dirichlet process mixture;
Growing number of components;
Minimax estimation;
Posterior consistency on the number of components
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Abstract:
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This talk focuses on Bayesian estimation of finite mixture models in a general setup where the number of components is unknown and allowed to grow with the sample size. An assumption on growing number of components is a natural one as the degree of heterogeneity present in the sample can grow and new component can arise as sample size increases, allowing full flexibility in modeling the complexity of data. This however will lead to a high-dimensional model which poses great challenges for estimation. We novelly employ the idea of data dependent prior in a Bayesian model and establish a number of important theoretical results including minimax optimal estimation of mixing distribution and posterior consistency on the number of components. In addition, we consider Dirichlet process (DP) mixture prior for estimating the finite mixture models and provide theoretical guarantees in a general setup. In particular, we provide a solution for adopting the number of a cluster in a DP mixture model as an estimate of the number of estimate of the number of components in a finite mixture model with growing number of components.
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Authors who are presenting talks have a * after their name.
