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.
Optimal tuning of the hybrid Monte Carlo algorithm
- A. Beskos, N. Pillai, G. Roberts, J. M. Sanz-Serna, A. Stuart
- Computer Science
- 25 January 2010
It is proved that, to obtain an O(1) acceptance probability as the dimension d of the state space tends to, the leapfrog step-size h should be scaled as h=l ×d−1/ 4, which means that in high dimensions, HMC requires O(d1/ 4 ) steps to traverse the statespace.
Universality of covariance matrices
In this paper we prove the universality of covariance matrices of the form $H_{N\times N}={X}^{\dagger}X$ where $X$ is an ${M\times N}$ rectangular matrix with independent real valued entries…
Bayesian density regression
- D. Dunson, N. Pillai, Juhyun Park
- Computer Science
- 1 April 2007
The paper considers Bayesian methods for density regression, allowing a random probability distribution to change flexibly with multiple predictors, and proposes a kernel‐based weighting scheme that incorporates weights that are dependent on the distance between subjects’ predictor values.
Lack of confidence in approximate Bayesian computation model choice
- C. Robert, J. Cornuet, J. Marin, N. Pillai
- Computer ScienceProceedings of the National Academy of Sciences
- 29 August 2011
It is concluded that additional empirical verifications of the performances of the ABC procedure as those available in DIY-ABC are necessary to conduct model choice, because the algorithm involves an unknown loss of information induced by the use of insufficient summary statistics.
Causal inference from 2K factorial designs by using potential outcomes
- Tirthankar Dasgupta, N. Pillai, D. Rubin
- Mathematics, Economics
- 1 September 2015
A framework for causal inference from two‐level factorial designs is proposed, which uses potential outcomes to define causal effects. The paper explores the effect of non‐additivity of unit level…
Posterior contraction in sparse Bayesian factor models for massive covariance matrices
- D. Pati, A. Bhattacharya, N. Pillai, D. Dunson
- Computer Science
- 16 June 2012
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.
Accelerating Asymptotically Exact MCMC for Computationally Intensive Models via Local Approximations
- Patrick R. Conrad, Y. Marzouk, N. Pillai, Aaron Smith
- Computer Science, Mathematics
- 7 February 2014
The ergodicity of the approximate Markov chain is proved, showing that it samples asymptotically from the exact posterior distribution of interest, and variations of the algorithm that employ either local polynomial approximations or local Gaussian process regressors are described.
Relevant statistics for Bayesian model choice
- J. Marin, N. Pillai, C. Robert, J. Rousseau
- Computer Science
- 21 October 2011
This work derives necessary and sufficient conditions on summary statistics for the corresponding Bayes factor to be convergent, namely to select the true model asymptotically under the two models.
Regularity of laws and ergodicity of hypoelliptic SDEs driven by rough paths
- Martin Hairer, N. Pillai
- Mathematics
- 27 April 2011
We consider differential equations driven by rough paths and study the regularity of the laws and their long time behavior. In particular, we focus on the case when the driving noise is a rough path…
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