Related papers: On the half-Cauchy prior for a global scale parame…
This is a follow-up paper of Polson and Scott (2012, Bayesian Analysis), which claimed that the half-Cauchy prior is a sensible default prior for a scale parameter in hierarchical models. For estimation of a normal mean vector under the…
While the importance of prior selection is well understood, establishing guidelines for selecting priors in hierarchical models has remained an active, and sometimes contentious, area of Bayesian methodology research. Choices of…
This is a follow-up paper of Polson and Scott (2012, Bayesian Analysis), which claimed that the half-Cauchy prior is a sensible default prior for a scale parameter in hierarchical models. For estimation of a p-variate normal mean under the…
Bayesian hierarchical models are commonly employed for inference in count datasets, as they account for multiple levels of variation by incorporating prior distributions for parameters at different levels. Examples include Beta-Binomial,…
In recent years, a rich variety of shrinkage priors have been proposed that have great promise in addressing massive regression problems. In general, these new priors can be expressed as scale mixtures of normals, but have more complex…
The use of Cauchy Markov random field priors in statistical inverse problems can potentially lead to posterior distributions which are non-Gaussian, high-dimensional, multimodal and heavy-tailed. In order to use such priors successfully,…
We propose a new prior distribution for classical (nonhierarchical) logistic regression models, constructed by first scaling all nonbinary variables to have mean 0 and standard deviation 0.5, and then placing independent Student-$t$ prior…
We consider a class of non-conjugate priors as a mixing family of distributions for a parameter (e.g., Poisson or gamma rate, inverse scale or precision of an inverse-gamma, inverse variance of a normal distribution) of an exponential…
We consider nonparametric Bayesian estimation inference using a rescaled smooth Gaussian field as a prior for a multidimensional function. The rescaling is achieved using a Gamma variable and the procedure can be viewed as choosing an…
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…
The Bayesian formulation of inverse problems is attractive for three primary reasons: it provides a clear modelling framework; means for uncertainty quantification; and it allows for principled learning of hyperparameters. The posterior…
Bayesian inversion generates a posterior distribution of model parameters from an observation equation and prior information both weighted by hyperparameters. The prior is also introduced for the hyperparameters in fully Bayesian inversions…
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.…
The multivariate normal linear model is one of the most widely employed models for statistical inference in applied research. Special cases include (multivariate) t testing, (M)AN(C)OVA, (multivariate) multiple regression, and repeated…
Scale-mixture shrinkage priors have recently been shown to possess robust empirical performance and excellent theoretical properties such as model selection consistency and (near) minimax posterior contraction rates. In this paper, the…
The sparse structure of the solution for an inverse problem can be modelled using different sparsity enforcing priors when the Bayesian approach is considered. Analytical expression for the unknowns of the model can be obtained by building…
In this paper we propose an objective Bayesian estimation approach for the parameters of the generalized gamma distribution. Various reference priors are obtained, but showing that they lead to improper posterior distributions. We overcome…
Gaussian variational approximations are widely used for summarizing posterior distributions in Bayesian models, especially in high-dimensional settings. However, a drawback of such approximations is the inability to capture skewness or more…
This paper introduces a novel Bayesian approach for variable selection in high-dimensional and potentially sparse regression settings. Our method replaces the indicator variables in the traditional spike and slab prior with continuous,…
Counterfactual explanations utilize feature perturbations to analyze the outcome of an original decision and recommend an actionable recourse. We argue that it is beneficial to provide several alternative explanations rather than a single…