Related papers: Multivariate sensitivity analysis for a large-scal…

This article presents an approach to Bayesian semiparametric inference for Gaussian multivariate response regression. We are motivated by various small and medium dimensional problems from the physical and social sciences. The statistical…

The cumulative shrinkage process is an increasing shrinkage prior that can be employed within models in which additional terms are supposed to play a progressively negligible role. A natural application is to Gaussian factor models, where…

Multiple imputation has become one of the standard methods in drawing inferences in many incomplete data applications. Applications of multiple imputation in relatively more complex settings, such as high-dimensional clustered data, require…

Adaptive learning is necessary for non-stationary environments where the learning machine needs to forget past data distribution. Efficient algorithms require a compact model update to not grow in computational burden with the incoming data…

Gaussian graphical models are used for determining conditional relationships between variables. This is accomplished by identifying off-diagonal elements in the inverse-covariance matrix that are non-zero. When the ratio of variables (p) to…

Experimental calibration of dynamic thermal models is required for model predictive control and characterization of building energy performance. In these applications, the uncertainty assessment of the parameter estimates is decisive; this…

Standard Gaussian Process (GP) regression, a powerful machine learning tool, is computationally expensive when it is applied to large datasets, and potentially inaccurate when data points are sparsely distributed in a high-dimensional…

Information theory is an excellent framework for analyzing Earth system data because it allows us to characterize uncertainty and redundancy, and is universally interpretable. However, accurately estimating information content is…

We introduce efficient Markov chain Monte Carlo methods for inference and model determination in multivariate and matrix-variate Gaussian graphical models. Our framework is based on the G-Wishart prior for the precision matrix associated…

The multivariate regression model basically offers the analysis of a single dataset with multiple responses. However, such a single-dataset analysis often leads to unsatisfactory results. Integrative analysis is an effective method to pool…

We explore various Bayesian approaches to estimate partial Gaussian graphical models. Our hierarchical structures enable to deal with single-output as well as multiple-output linear regressions, in small or high dimension, enforcing either…

We discuss efficient Bayesian estimation of dynamic covariance matrices in multivariate time series through a factor stochastic volatility model. In particular, we propose two interweaving strategies (Yu and Meng, Journal of Computational…

Graphical models describe associations between variables through the notion of conditional independence. Gaussian graphical models are a widely used class of such models where the relationships are formalized by non-null entries of the…

Modeling correlation (and covariance) matrices can be challenging due to the positive-definiteness constraint and potential high-dimensionality. Our approach is to decompose the covariance matrix into the correlation and variance matrices…

Nonlinear regression is a useful statistical tool, relating observed data and a nonlinear function of unknown parameters. When the parameter-dependent nonlinear function is computationally intensive, a straightforward regression analysis by…

This paper investigates the high-dimensional linear regression with highly correlated covariates. In this setup, the traditional sparsity assumption on the regression coefficients often fails to hold, and consequently many model selection…

Gaussian processes (GPs) are a powerful tool for probabilistic inference over functions. They have been applied to both regression and non-linear dimensionality reduction, and offer desirable properties such as uncertainty estimates,…

The recent availability of huge, many-dimensional data sets, like those arising from genome-wide association studies (GWAS), provides many opportunities for strengthening causal inference. One popular approach is to utilize these…

In high-dimensional Bayesian statistics, various methods have been developed, including prior distributions that induce parameter sparsity to handle many parameters. Yet, these approaches often overlook the rich spectral structure of the…

Approximate Bayesian inference methods that scale to very large datasets are crucial in leveraging probabilistic models for real-world time series. Sparse Markovian Gaussian processes combine the use of inducing variables with efficient…