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A convex pseudolikelihood framework for high dimensional partial correlation estimation with convergence guarantees
This work proposes a new pseudolikelihood‐based graphical model selection method that aims to overcome some of the shortcomings of current methods, but at the same time retain all their respective strengths, and introduces a novel framework that leads to a convex formulation of the partial covariance regression graph problem, resulting in an objective function comprised of quadratic forms.
Gibbs sampling, exponential families and orthogonal polynomials
We give families of examples where sharp rates of convergence to stationarity of the widely used Gibbs sampler are available. The examples involve standard exponential families and their conjugate…
Posterior graph selection and estimation consistency for high-dimensional Bayesian DAG models
This paper considers a flexible and general class of these 'DAG-Wishart' priors with multiple shape parameters, and establishes strong graph selection consistency and posterior convergence rates for estimation when the number of variables p is allowed to grow at an appropriate sub-exponential rate with the sample size n.
RATES OF CONVERGENCE OF SOME MULTIVARIATE MARKOV CHAINS WITH POLYNOMIAL EIGENFUNCTIONS
We provide a sharp nonasymptotic analysis of the rates of convergence for some standard multivariate Markov chains using spectral techniques. All chains under consideration have multivariate…
Wishart distributions for decomposable covariance graph models
This paper constructs on the cone P G a family of Wishart distributions which serve a similar purpose in the covariance graph setting as those constructed by Letac and Massam and proves convergence of this block Gibbs sampler and establishes hyper-Markov properties for this class of priors.
A spectral analytic comparison of trace-class data augmentation algorithms and their sandwich variants
A substantial refinement of this operator norm inequality is developed, and under regularity conditions implying that $K$ is a trace-class operator, it is shown that it is also a positive, trace- class operator, and that the spectrum of $K^*$ dominates that of$K$ in the sense that the ordered elements of the former are all less than or equal to the corresponding element of the latter.
Geometric ergodicity of the Bayesian lasso
In this paper, the Markov chain underlying the Bayesian lasso algorithm is shown to be geometrically ergodic, for arbitrary values of the sample size n and the number of variables p.
High dimensional posterior convergence rates for decomposable graphical models
A convex framework for high-dimensional sparse Cholesky based covariance estimation
A new penalized likelihood method for sparse estimation of the inverse covariance Cholesky parameter is proposed that aims to overcome some of the shortcomings of current methods, but retains their respective strengths.
High-Dimensional Posterior Consistency in Bayesian Vector Autoregressive Models
- Satyajit Ghosh, K. Khare, G. Michailidis
- Computer ScienceJournal of the American Statistical Association
- 7 August 2018
A VAR model with two prior choices for the autoregressive coefficient matrix is considered: a nonhierarchical matrix-normal prior and a hierarchical prior, which corresponds to an arbitrary scale mixture of normals, which establishes posterior consistency for both these priors under standard regularity assumptions.