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This paper introduces a new neural network based prior for real valued functions on $\mathbb R^d$ which, by construction, is more easily and cheaply scaled up in the domain dimension $d$ compared to the usual Karhunen-Lo\`eve function space…
We introduce priors and algorithms to perform Bayesian inference in Gaussian models defined by acyclic directed mixed graphs. Such a class of graphs, composed of directed and bi-directed edges, is a representation of conditional…
Forecasting on sparse multivariate time series (MTS) aims to model the predictors of future values of time series given their incomplete past, which is important for many emerging applications. However, most existing methods process MTS's…
Deep learning models, such as convolutional neural networks, have long been applied to image and multi-media tasks, particularly those with structured data. More recently, there has been more attention to unstructured data that can be…
In this work, we propose a Bayesian type sparse deep learning algorithm. The algorithm utilizes a set of spike-and-slab priors for the parameters in the deep neural network. The hierarchical Bayesian mixture will be trained using an…
We consider priors for several nonparametric Bayesian models which use finite random series with a random number of terms. The prior is constructed through distributions on the number of basis functions and the associated coefficients. We…
The multivariate generalized Gaussian distribution (MGGD), also known as the multivariate exponential power (MEP) distribution, is widely used in signal and image processing. However, estimating MGGD parameters, which is required in…
Dirichlet process mixtures are particularly sensitive to the value of the precision parameter controlling the behavior of the latent partition. Randomization of the precision through a prior distribution is a common solution, which leads to…
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…
Bayesian models have become very popular over the last years in several fields such as signal processing, statistics, and machine learning. Bayesian inference requires the approximation of complicated integrals involving posterior…
Multinomial probit (mnp) models are fundamental and widely-applied regression models for categorical data. Fasano and Durante (2022) proved that the class of unified skew-normal distributions is conjugate to several mnp sampling models.…
Varying coefficient models (VCMs) are widely used for estimating nonlinear regression functions for functional data. Their Bayesian variants using Gaussian process priors on the functional coefficients, however, have received limited…
In this paper we propose to numerically assess the performance of standard Gaussian approximations to probe the posterior distribution that arises from Bayesian data assimilation in petroleum reservoirs. In particular we assess the…
Learning in deep models using Bayesian methods has generated significant attention recently. This is largely because of the feasibility of modern Bayesian methods to yield scalable learning and inference, while maintaining a measure of…
Bayesian computation of high dimensional linear regression models with a popular Gaussian scale mixture prior distribution using Markov Chain Monte Carlo (MCMC) or its variants can be extremely slow or completely prohibitive due to the…
The Bayesian elastic net regression model is characterized by the regression coefficient prior distribution, the negative log density of which corresponds to the elastic net penalty function. While Markov chain Monte Carlo (MCMC) methods…
Many probabilistic models introduce strong dependencies between variables using a latent multivariate Gaussian distribution or a Gaussian process. We present a new Markov chain Monte Carlo algorithm for performing inference in models with…
Variational inference has recently emerged as a popular alternative to the classical Markov chain Monte Carlo (MCMC) in large-scale Bayesian inference. The core idea is to trade statistical accuracy for computational efficiency. In this…
While the Matrix Generalized Inverse Gaussian ($\mathcal{MGIG}$) distribution arises naturally in some settings as a distribution over symmetric positive semi-definite matrices, certain key properties of the distribution and effective ways…
In parameter estimation problems one computes a posterior distribution over uncertain parameters defined jointly by a prior distribution, a model, and noisy data. Markov Chain Monte Carlo (MCMC) is often used for the numerical solution of…