相关论文: Modeling the uncertainty on the covariance matrix …

Forecast reconciliation of multivariate time series is the process of mapping a set of incoherent forecasts into coherent forecasts to satisfy a given set of linear constraints. Commonly used projection matrix based approaches for point…

Covariance matrix estimation arises in multivariate problems including multivariate normal sampling models and regression models where random effects are jointly modeled, e.g. random-intercept, random-slope models. A Bayesian analysis of…

Covariance estimation and selection for multivariate datasets in a high-dimensional regime is a fundamental problem in modern statistics. Gaussian graphical models are a popular class of models used for this purpose. Current Bayesian…

This paper focuses on Bayesian shrinkage for covariance matrix estimation. We examine posterior properties and frequentist risks of Bayesian estimators based on new hierarchical inverse-Wishart priors. More precisely, we give the existence…

Time series often appear in an additive hierarchical structure. In such cases, time series on higher levels are the sums of their subordinate time series. This hierarchical structure places a natural constraint on forecasts. However,…

Forecast reconciliation is a post-forecasting process that involves transforming a set of incoherent forecasts into coherent forecasts which satisfy a given set of linear constraints for a multivariate time series. In this paper we extend…

We propose to estimate the weight matrix used for forecast reconciliation as parameters in a general linear model in order to quantify its uncertainty. This implies that forecast reconciliation can be formulated as an orthogonal projection…

The inverse covariance matrix provides considerable insight for understanding statistical models in the multivariate setting. In particular, when the distribution over variables is assumed to be multivariate normal, the sparsity pattern in…

Accurate and precise covariance matrices will be important in enabling planned cosmological surveys to detect new physics. Standard methods imply either the need for many N-body simulations in order to obtain an accurate estimate, or a…

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…

Point forecast reconciliation of collection of time series with linear aggregation constraints has evolved substantially over the last decade. A few commonly used methods are GLS (generalized least squares), OLS (ordinary least squares),…

We present a novel approach for reconciling hierarchical forecasts, based on Bayes rule. We define a prior distribution for the bottom time series of the hierarchy, based on the bottom base forecasts. Then we update their distribution via…

We propose a novel framework for joint magnetic resonance image reconstruction and uncertainty quantification using under-sampled k-space measurements. The problem is formulated as a Bayesian linear inverse problem, where prior…

In this paper, we address the fusion problem in wireless sensor networks, where the cross-correlation between the estimates is unknown. To solve the problem within the Bayesian framework, we assume that the covariance matrix has a prior…

It has been proposed that complex populations, such as those that arise in genomics studies, may exhibit dependencies among observations as well as among variables. This gives rise to the challenging problem of analyzing unreplicated…

Reconciliation enforces coherence between hierarchical forecasts, in order to satisfy a set of linear constraints. While most works focus on the reconciliation of the point forecasts, we consider probabilistic reconciliation and we analyze…

A Bayesian approach is used to estimate the covariance matrix of Gaussian data. Ideas from Gaussian graphical models and model selection are used to construct a prior for the covariance matrix that is a mixture over all decomposable graphs.…

We derive a maximum a posteriori estimator for the linear observation model, where the signal and noise covariance matrices are both uncertain. The uncertainties are treated probabilistically by modeling the covariance matrices with prior…

We present a Bayesian model for area-level count data that uses Gaussian random effects with a novel type of G-Wishart prior on the inverse variance--covariance matrix. Specifically, we introduce a new distribution called the truncated…

Forecast reconciliation is an important research topic. Yet, there is currently neither formal framework nor practical method for the probabilistic reconciliation of count time series. In this paper we propose a definition of coherency and…