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Dirichlet–Laplace Priors for Optimal Shrinkage
- A. Bhattacharya, D. Pati, N. Pillai, D. Dunson
- MathematicsJournal of the American Statistical Association
- 21 January 2014
This article proposes a new class of Dirichlet–Laplace priors, which possess optimal posterior concentration and lead to efficient posterior computation.
Posterior consistency in conditional distribution estimation
Posterior contraction in sparse Bayesian factor models for massive covariance matrices
One of the major contributions is to develop a new class of continuous shrinkage priors and provide insights into their concentration around sparse vectors in inferring high-dimensional covariance matrices where the dimension can be larger than the sample size.
Bayesian fractional posteriors
We consider the fractional posterior distribution that is obtained by updating a prior distribution via Bayes theorem with a fractional likelihood function, a usual likelihood function raised to a…
Bayesian geostatistical modelling with informative sampling locations.
A Bayesian approach is proposed, which models the locations using a log Gaussian Cox process, while modelling the outcomes conditionally on the locations as Gaussian with a Gaussian process spatial random effect and adjustment for the location intensity process.
On Statistical Optimality of Variational Bayes
General conditions for obtaining optimal risk bounds for point estimates acquired from mean-field variational Bayesian inference are provided and a general recipe for verification of the conditions is outlined which is broadly applicable to existing Bayesian models with or without latent variables.
Frequentist coverage and sup-norm convergence rate in Gaussian process regression
The theory and results show that inference based on GP regression tends to be conservative; when the prior is under-smoothed, the resulting credible intervals and bands have minimax-optimal sizes, with their frequentist coverage converging to a non-degenerate value between their nominal level and one.
Bayesian model selection consistency and oracle inequality with intractable marginal likelihood
In this article, we investigate large sample properties of model selection procedures in a general Bayesian framework when a closed form expression of the marginal likelihood function is not…
Probabilistic Community Detection With Unknown Number of Communities
- J. Geng, A. Bhattacharya, D. Pati
- Computer ScienceJournal of the American Statistical Association
- 25 February 2016
A coherent probabilistic framework for simultaneous estimation of the number of communities and the community structure is proposed, adapting recently developed Bayesian nonparametric techniques to network models and developed concentration properties of nonlinear functions of Bernoulli random variables.
It is demonstrated that most used shrinkage priors, including the Bayesian Lasso, are suboptimal in high-dimensional set tings, and a new class of Dirichlet Laplace (DL) priors are proposed, which are optimal and lead to effici nt posterior computation exploiting results from normalized random measure theory.