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This paper introduces Bayesian frameworks for tackling various aspects of multi-criteria decision-making (MCDM) problems, leveraging a probabilistic interpretation of MCDM methods and challenges. By harnessing the flexibility of Bayesian…

Employing Bayesian inference to calibrate constitutive model parameters has grown substantially in recent years. Among the available techniques, Markov Chain Monte Carlo (MCMC) sampling remains one of the most widely used approaches for…

Deep learning tools have gained tremendous attention in applied machine learning. However such tools for regression and classification do not capture model uncertainty. In comparison, Bayesian models offer a mathematically grounded…

One of the major challenges in the Bayesian solution of inverse problems governed by partial differential equations (PDEs) is the computational cost of repeatedly evaluating numerical PDE models, as required by Markov chain Monte Carlo…

Bayesian Neural Networks (BNNs) offer robust uncertainty quantification in model predictions, but training them presents a significant computational challenge. This is mainly due to the problem of sampling multimodal posterior distributions…

Bayesian hierarchical modeling is a popular approach to capturing unobserved heterogeneity across individual units. However, standard estimation methods such as Markov chain Monte Carlo (MCMC) can be impracticable for modeling outcomes from…

The Bayesian Context Trees (BCT) framework is a recently introduced, general collection of statistical and algorithmic tools for modelling, analysis and inference with discrete-valued time series. The foundation of this development is built…

Deep neural networks (NNs) are known for their high-prediction performances. However, NNs are prone to yield unreliable predictions when encountering completely new situations without indicating their uncertainty. Bayesian variants of NNs…

Bayesian phylogenetic inference is currently done via Markov chain Monte Carlo (MCMC) with simple proposal mechanisms. This hinders exploration efficiency and often requires long runs to deliver accurate posterior estimates. In this paper,…

Advances in digital sensors, digital data storage and communications have resulted in systems being capable of accumulating large collections of data. In the light of dealing with the challenges that massive data present, this work proposes…

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…

Bayesian methods have been very successful in quantifying uncertainty in physics-based problems in parameter estimation and prediction. In these cases, physical measurements y are modeled as the best fit of a physics-based model…

The deployment of deep neural networks in safety-critical systems necessitates reliable and efficient uncertainty quantification (UQ). A practical and widespread strategy for UQ is repurposing stochastic regularizers as scalable approximate…

Model comparison for the purposes of selection, averaging and validation is a problem found throughout statistics. Within the Bayesian paradigm, these problems all require the calculation of the posterior probabilities of models within a…

Inverse problems involving partial differential equations (PDEs) are widely used in science and engineering. Although such problems are generally ill-posed, different regularisation approaches have been developed to ameliorate this problem.…

The goal of this paper is to compare several widely used Bayesian model selection methods in practical model selection problems, highlight their differences and give recommendations about the preferred approaches. We focus on the variable…

Species distribution models (SDMs), which aim to predict species occurrence based on environmental variables, are widely used to monitor and respond to biodiversity change. Recent deep learning advances for SDMs have been shown to perform…

Bayesian model selection provides a powerful framework for objectively comparing models directly from observed data, without reference to ground truth data. However, Bayesian model selection requires the computation of the marginal…

Approximate Bayesian computation (ABC) methods are standard tools for inferring parameters of complex models when the likelihood function is analytically intractable. A popular approach to improving the poor acceptance rate of the basic…

Bayesian models are a powerful tool for studying complex data, allowing the analyst to encode rich hierarchical dependencies and leverage prior information. Most importantly, they facilitate a complete characterization of uncertainty…