Related papers: Design and Structure Dependent Priors for Scale Pa…
We propose an efficient way to sample from a class of structured multivariate Gaussian distributions which routinely arise as conditional posteriors of model parameters that are assigned a conditionally Gaussian prior. The proposed…
We consider the problem of learning the structure of a high dimensional precision matrix under sparsity assumptions. We propose to use a shrinkage prior, called the DL-graphical prior based on the Dirichlet-Laplace prior used for the…
Here, we investigate whether (and how) experimental design could aid in the estimation of the precision matrix in a Gaussian chain graph model, especially the interplay between the design, the effect of the experiment and prior knowledge…
Sample selection models are a widely used approach for correcting bias caused by data that are missing not at random. Their formulation requires specifying the variables that influence the outcome and those that drive the selection process.…
In Bayesian statistics, the choice of prior distribution is often debatable, especially if prior knowledge is limited or data are scarce. In imprecise probability, sets of priors are used to accurately model and reflect prior knowledge.…
Bayesian model selection with improper priors is not well-defined because of the dependence of the marginal likelihood on the arbitrary scaling constants of the within-model prior densities. We show how this problem can be evaded 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…
It has become increasingly common to collect high-dimensional binary response data; for example, with the emergence of new sampling techniques in ecology. In smaller dimensions, multivariate probit (MVP) models are routinely used for…
Bayesian computational strategies for inference can be inefficient in approximating the posterior distribution in models that exhibit some form of periodicity. This is because the probability mass of the marginal posterior distribution of…
For Bayesian D-optimal design, we define a singular prior distribution for the model parameters as a prior distribution such that the determinant of the Fisher information matrix has a prior geometric mean of zero for all designs. For such…
A statistical method for the elicitation of priors in Bayesian generalised linear models (GLMs) and extensions is proposed. Probabilistic predictions are elicited from the expert to parametrise a multivariate t prior distribution for the…
A scale mixture of normals is a distribution formed by mixing a collection of normal distributions with fixed mean but different variances. A generalized gamma scale mixture draws the variances from a generalized gamma distribution.…
We study high-dimensional Bayesian linear regression with a general beta prime distribution for the scale parameter. Under the assumption of sparsity, we show that appropriate selection of the hyperparameters in the beta prime prior leads…
Testing whether a probability distribution is compatible with a given Bayesian network is a fundamental task in the field of causal inference, where Bayesian networks model causal relations. Here we consider the class of causal structures…
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.…
A fundamental issue in causal inference for Big Observational Data is confounding due to covariate imbalances between treatment groups. This can be addressed by designing the data prior to analysis. Existing design methods, developed for…
The choice of the prior distribution is a key aspect of Bayesian analysis. For the spatial regression setting a subjective prior choice for the parameters may not be trivial, from this perspective, using the objective Bayesian analysis…
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…
We introduce a methodology for nonlinear inverse problems using a variational Bayesian approach where the unknown quantity is a spatial field. A structured Bayesian Gaussian process latent variable model is used both to construct a…
The Bradley-Terry model assigns probabilities for the outcome of paired comparison experiments based on strength parameters associated with the objects being compared. We consider different proposed choices of prior parameter distributions…