Related papers: Bayesian inference for a covariance matrix

A major problem in numerical weather prediction (NWP) is the estimation of high-dimensional covariance matrices from a small number of samples. Maximum likelihood estimators cannot provide reliable estimates when the overall dimension is…

We introduce a novel Bayesian approach for both covariate selection and sparse precision matrix estimation in the context of high-dimensional Gaussian graphical models involving multiple responses. Our approach provides a sparse estimation…

Many modern experiments, such as microarray gene expression and genome-wide association studies, present the problem of estimating a large number of parallel effects. Bayesian inference is a popular approach for analyzing such data by…

We consider joint inversion for two or more unknown parameters from observational data in the Bayesian framework. Standard approaches often either treat the parameters as independent or impose structural similarity through regularisation…

The Inverse-Wishart (IW) distribution is a standard and popular choice of priors for covariance matrices and has attractive properties such as conditional conjugacy. However, the IW family of priors has crucial drawbacks, including the lack…

In the presence of modeling errors, the mainstream Bayesian methods seldom give a realistic account of uncertainties as they commonly underestimate the inherent variability of parameters. This problem is not due to any misconception in the…

Bayesian inverse problems use observed data to update a prior probability distribution for an unknown state or parameter of a scientific system to a posterior distribution conditioned on the data. In many applications, the unknown parameter…

Objective probabilistic forecasts of future climate that include parameter uncertainty can be made by using the Bayesian prediction integral with the prior set to Jeffreys' Prior. The calculations involved in determining the prior can then…

Bayesian model comparison is often based on the posterior distribution over the set of compared models. This distribution is often observed to concentrate on a single model even when other measures of model fit or forecasting ability…

Estimation of the mean vector and covariance matrix is of central importance in the analysis of multivariate data. In the framework of generalized linear models, usually the variances are certain functions of the means with the normal…

We present a Bayesian perspective on quantifying the uncertainty of graph signals estimated or reconstructed from imperfect observations. We show that many conventional methods of graph signal estimation, reconstruction and imputation, can…

In multivariate time series, the estimation of the covariance matrix of the observation innovations plays an important role in forecasting as it enables the computation of the standardized forecast error vectors as well as it enables the…

In Bayesian nonparametric models, Gaussian processes provide a popular prior choice for regression function estimation. Existing literature on the theoretical investigation of the resulting posterior distribution almost exclusively assume a…

For a Bayesian, real-time forecasting with the posterior predictive distribution can be challenging for a variety of time series models. First, estimating the parameters of a time series model can be difficult with sample-based approaches…

We consider estimation of the covariance matrix of a multivariate random vector under the constraint that certain covariances are zero. We first present an algorithm, which we call Iterative Conditional Fitting, for computing the maximum…

We consider the classical problem of estimating the covariance matrix of a subgaussian distribution from i.i.d. samples in the novel context of coarse quantization, i.e., instead of having full knowledge of the samples, they are quantized…

In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when…

Hierarchical Bayesian methods enable information sharing across multiple related regression problems. While standard practice is to model regression parameters (effects) as (1) exchangeable across datasets and (2) correlated to differing…

Bayesian inference can quantify uncertainty in the predictions of neural networks using posterior distributions for model parameters and network output. By looking at these posterior distributions, one can separate the origin of uncertainty…

Datasets are rarely a realistic approximation of the target population. Say, prevalence is misrepresented, image quality is above clinical standards, etc. This mismatch is known as sampling bias. Sampling biases are a major hindrance for…