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Markov Chain Monte Carlo (MCMC) is a well-established family of algorithms primarily used in Bayesian statistics to sample from a target distribution when direct sampling is challenging. Existing work on Bayesian decision trees uses MCMC.…

Quantifying uncertainty and updating reliability are essential for ensuring the safety and performance of engineering systems. This study develops a hierarchical Bayesian modeling (HBM) framework to quantify uncertainty and update…

We deal with Bayesian inference for Beta autoregressive processes. We restrict our attention to the class of conditionally linear processes. These processes are particularly suitable for forecasting purposes, but are difficult to estimate…

A simple and efficient adaptive Markov Chain Monte Carlo (MCMC) method, called the Metropolized Adaptive Subspace (MAdaSub) algorithm, is proposed for sampling from high-dimensional posterior model distributions in Bayesian variable…

Recent papers in the field of Finite Element Model (FEM) updating have highlighted the benefits of Bayesian techniques. The Bayesian approaches are designed to deal with the uncertainties associated with complex systems, which is the main…

Over decades, Markov chain Monte Carlo (MCMC) methods have been widely studied, with a typical application being the quantification of posterior uncertainties in Bayesian system identification of structural dynamic models. To address the…

The Bayesian inversion method demonstrates significant potential for solving inverse problems, enabling both point estimation and uncertainty quantification (UQ). However, Bayesian maximum a posteriori (MAP) estimation may become unstable…

In this paper we address the problem of Monte Carlo approximation of posterior probability distributions in stochastic kinetic models (SKMs). SKMs are multivariate Markov jump processes that model the interactions among species in…

The Bayesian paradigm is becoming an increasingly popular framework for estimation and uncertainty quantification of unknown parameters in geo-physical inversion problems. Badlands is a basin and landscape evolution forward model for…

Although large language models (LLMs) are becoming increasingly capable of solving challenging real-world tasks, accurately quantifying their uncertainty remains a critical open problem--one that limits their applicability in high-stakes…

Sequential Monte Carlo (SMC) algorithms represent a suite of robust computational methodologies utilized for state estimation and parameter inference within dynamical systems, particularly in real-time or online environments where data…

Markov Chain Monte Carlo (MCMC) algorithms are commonly used for their versatility in sampling from complicated probability distributions. However, as the dimension of the distribution gets larger, the computational costs for a satisfactory…

The Metropolis-Hastings (MH) algorithm is one of the most widely used Markov Chain Monte Carlo schemes for generating samples from Bayesian posterior distributions. The algorithm is asymptotically exact, flexible and easy to implement.…

Dynamic Bayesian predictive synthesis is a formal approach to coherently synthesizing multiple predictive distributions into a single distribution. In sequential analysis, the computation of the synthesized predictive distribution has…

Stochastic approximation Monte Carlo (SAMC) has recently been proposed by Liang, Liu and Carroll [J. Amer. Statist. Assoc. 102 (2007) 305--320] as a general simulation and optimization algorithm. In this paper, we propose to improve its…

Recently there have been exciting developments in Monte Carlo methods, with the development of new MCMC and sequential Monte Carlo (SMC) algorithms which are based on continuous-time, rather than discrete-time, Markov processes. This has…

Bayesian methods hold significant promise for improving the uncertainty quantification ability and robustness of deep neural network models. Recent research has seen the investigation of a number of approximate Bayesian inference methods…

Bayesian max-margin models have shown superiority in various practical applications, such as text categorization, collaborative prediction, social network link prediction and crowdsourcing, and they conjoin the flexibility of Bayesian…

Many applications in signal processing require the estimation of some parameters of interest given a set of observed data. More specifically, Bayesian inference needs the computation of {\it a-posteriori} estimators which are often…

We propose two new Bayesian smoothing methods for general state-space models with unknown parameters. The first approach is based on the particle learning and smoothing algorithm, but with an adjustment in the backward resampling weights.…