Related papers: How to use KL-divergence to construct conjugate pr…
The prediction of the variance-covariance matrix of the multivariate normal distribution is important in the multivariate analysis. We investigated Bayesian predictive distributions for Wishart distributions under the Kullback-Leibler…
The power spectrum of weak lensing fluctuations has a non-Gaussian distribution due to its quadratic nature. On small scales the Central Limit Theorem acts to Gaussianize this distribution but non-Gaussianity in the signal due to…
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…
The Wishart distribution and its generalizations are among the most prominent probability distributions in multivariate statistical analysis, arising naturally in applied research and as a basis for theoretical models. In this paper, we…
In probabilstic supervised learning of an input-output relationship - as a sample function of a Gaussian Process (GP) - priors are typically specified for the hyperparameters of the kernel that parametrises the covariance function of the…
Gaussian covariance graph models encode marginal independence among the components of a multivariate random vector by means of a graph $G$. These models are distinctly different from the traditional concentration graph models (often also…
The noncentral Wishart distribution has become more mainstream in statistics as the prevalence of applications involving sample covariances with underlying multivariate Gaussian populations as dramatically increased since the advent of…
In a traditional Gaussian graphical model, data homogeneity is routinely assumed with no extra variables affecting the conditional independence. In modern genomic datasets, there is an abundance of auxiliary information, which often gets…
The normal-inverse-Wishart (NIW) distribution is commonly used as a prior distribution for the mean and covariance parameters of a multivariate normal distribution. The family of NIW distributions is also a minimal exponential family. In…
Random quantum states are useful in various areas of quantum information science. Distributions of random quantum states using Gaussian distributions have been used in various scenarios in quantum information science. One of this is the…
The G-Wishart distribution is an essential component for the Bayesian analysis of Gaussian graphical models as the conjugate prior for the precision matrix. Evaluating the marginal likelihood of such models usually requires computing…
We consider the shape of the likelihood and posterior surfaces to be used when fitting cosmological models to CMB temperature and polarisation power spectra measured from experiments. In the limit of an all-sky survey with Gaussian…
The scaled complex Wishart distribution is a widely used model for multilook full polarimetric SAR data whose adequacy has been attested in the literature. Classification, segmentation, and image analysis techniques which depend on this…
Statistical modelling of covariate distributions allows to generate virtual populations or to impute missing values in a covariate dataset. Covariate distributions typically have non-Gaussian margins and show nonlinear correlation…
We discuss Bayesian inference for a known-mean Gaussian model with a compound symmetric variance-covariance matrix. Since the space of such matrices is a linear subspace of that of positive definite matrices, we utilize the methods of…
Gaussian graphical models have received considerable attention during the past four decades from the statistical and machine learning communities. In Bayesian treatments of this model, the G-Wishart distribution serves as the conjugate…
Marginal likelihood, also known as model evidence, is a fundamental quantity in Bayesian statistics. It is used for model selection using Bayes factors or for empirical Bayes tuning of prior hyper-parameters. Yet, the calculation of…
The Wishart probability distribution on symmetricmatrices has been initially defined by mean of the multivariateGaussian distribution as an of the chi-square distribution. A moregeneral definition is given using results for harmonic…
In Gaussian graphical models, the zero entries in the precision matrix determine the dependence structure, so estimating that sparse precision matrix and, thereby, learning this underlying structure, is an important and challenging problem.…
Standard present day large-scale structure (LSS) analyses make a major assumption in their Bayesian parameter inference --- that the likelihood has a Gaussian form. For summary statistics currently used in LSS, this assumption, even if the…