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The efficiency of Markov Chain Monte Carlo (MCMC) depends on how the underlying geometry of the problem is taken into account. For distributions with strongly varying curvature, Riemannian metrics help in efficient exploration of the target…

We consider the problem of estimating rare event probabilities, focusing on systems whose evolution is governed by differential equations with uncertain input parameters. If the system dynamics is expensive to compute, standard sampling…

Probabilistic inference in graphical models is the task of computing marginal and conditional densities of interest from a factorized representation of a joint probability distribution. Inference algorithms such as variable elimination and…

In this note, we define a Gaussian probability distribution over matrices. We prove some useful properties of this distribution, namely, the fact that marginalization, conditioning, and affine transformations preserve the matrix Gaussian…

This paper proposed a new probability distribution named as inverse xgamma distribution (IXGD). Different mathematical and statistical properties,viz., reliability characteristics, moments, inverse moments, stochastic ordering and order…

Monte Carlo methods are essential tools for Bayesian inference. Gibbs sampling is a well-known Markov chain Monte Carlo (MCMC) algorithm, extensively used in signal processing, machine learning, and statistics, employed to draw samples from…

Bayesian modelling and computational inference by Markov chain Monte Carlo (MCMC) is a principled framework for large-scale uncertainty quantification, though is limited in practice by computational cost when implemented in the simplest…

A new class of survival frailty models based on the Generalized Inverse-Gaussian (GIG) distributions is proposed. We show that the GIG frailty models are flexible and mathematically convenient like the popular gamma frailty model.…

In this article, a generalized inverse xgamma distribution (GIXGD) has been introduced as the generalized version of the inverse xgamma distribution. The proposed model exhibits the pattern of non-monotone hazard rate and belongs to family…

Non-Gaussian mixture models are gaining increasing attention for mixture model-based clustering particularly when dealing with data that exhibit features such as skewness and heavy tails. Here, such a mixture distribution is presented,…

The inverse Gaussian distribution (IGD) is a well known and often used probability distribution for which fully reliable numerical algorithms have not been available. Our aim in this article is to develop software for this distribution for…

By formulating the inverse problem of partial differential equations (PDEs) as a statistical inference problem, the Bayesian approach provides a general framework for quantifying uncertainties. In the inverse problem of PDEs, parameters are…

In applications of Gaussian processes where quantification of uncertainty is a strict requirement, it is necessary to accurately characterize the posterior distribution over Gaussian process covariance parameters. Normally, this is done by…

Markov Chain Monte Carlo (MCMC) sampling from a posterior distribution corresponding to a massive data set can be computationally prohibitive since producing one sample requires a number of operations that is linear in the data size. In…

Discrete data are abundant and often arise as counts or rounded data. These data commonly exhibit complex distributional features such as zero-inflation, over-/under-dispersion, boundedness, and heaping, which render many parametric models…

We consider posterior sampling in the very common Bayesian hierarchical model in which observed data depends on high-dimensional latent variables that, in turn, depend on relatively few hyperparameters. When the full conditional over the…

Markov Chain Monte Carlo (MCMC) methods have a drawback when working with a target distribution or likelihood function that is computationally expensive to evaluate, specially when working with big data. This paper focuses on…

We introduce a Markov Chain Monte Carlo (MCMC) method that is designed to sample from target distributions with irregular geometry using an adaptive scheme. In cases where targets exhibit non-Gaussian behaviour, we propose that adaption…

Sparsity has become a key concept for solving of high-dimensional inverse problems using variational regularization techniques. Recently, using similar sparsity-constraints in the Bayesian framework for inverse problems by encoding them in…

Gaussian graphical models are useful tools for conditional independence structure inference of multivariate random variables. Unfortunately, Bayesian inference of latent graph structures is challenging due to exponential growth of…