Bayesian Test and Selection for Bandwidth of High-dimensional Banded Precision Matrices

by   Kyoungjae Lee, et al.

Assuming a banded structure is one of the common practice in the estimation of high-dimensional precision matrix. In this case, estimating the bandwidth of the precision matrix is a crucial initial step for subsequent analysis. Although there exist some consistent frequentist tests for the bandwidth parameter, bandwidth selection consistency for precision matrices has not been established in a Bayesian framework. In this paper, we propose a prior distribution tailored to the bandwidth estimation of high-dimensional precision matrices. The banded structure is imposed via the Cholesky factor from the modified Cholesky decomposition. We establish the strong model selection consistency for the bandwidth as well as the consistency of the Bayes factor. The convergence rates for Bayes factors under both the null and alternative hypotheses are derived which yield similar order of rates. As a by-product, we also proposed an estimation procedure for the Cholesky factors yielding an almost optimal order of convergence rates. Two-sample bandwidth test is also considered, and it turns out that our method is able to consistently detect the equality of bandwidths between two precision matrices. The simulation study confirms that our method in general outperforms or is comparable to the existing frequentist and Bayesian methods.


page 1

page 2

page 3

page 4


Minimax Posterior Convergence Rates and Model Selection Consistency in High-dimensional DAG Models based on Sparse Cholesky Factors

In this paper, we study the high-dimensional sparse directed acyclic gra...

Bayesian inference for high-dimensional decomposable graphs

In this paper, we consider high-dimensional Gaussian graphical models wh...

Maximum Pairwise Bayes Factors for Covariance Structure Testing

Hypothesis testing of structure in covariance matrices is of significant...

Scalable Bayesian high-dimensional local dependence learning

In this work, we propose a scalable Bayesian procedure for learning the ...

Use of Cross-validation Bayes Factors to Test Equality of Two Densities

We propose a non-parametric, two-sample Bayesian test for checking wheth...

Fast and Adaptive Sparse Precision Matrix Estimation in High Dimensions

This paper proposes a new method for estimating sparse precision matrice...

Direct estimation of differential Granger causality between two high-dimensional time series

Differential Granger causality, that is understanding how Granger causal...

Please sign up or login with your details

Forgot password? Click here to reset