Related papers: Generalized Bayesian Multidimensional Scaling and …

The widespread use of Markov Chain Monte Carlo (MCMC) methods for high-dimensional applications has motivated research into the scalability of these algorithms with respect to the dimension of the problem. Despite this, numerous problems…

Markov chain Monte Carlo (MCMC) algorithms are generally regarded as the gold standard technique for Bayesian inference. They are theoretically well-understood and conceptually simple to apply in practice. The drawback of MCMC is that in…

Bayesian inverse problems highly rely on efficient and effective inference methods for uncertainty quantification (UQ). Infinite-dimensional MCMC algorithms, directly defined on function spaces, are robust under refinement of physical…

Markov chain Monte Carlo (MCMC) algorithms are ubiquitous in Bayesian computations. However, they need to access the full data set in order to evaluate the posterior density at every step of the algorithm. This results in a great…

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…

Annealed Sequential Monte Carlo (ASMC) samplers are special cases of SMC samplers where the sequence of distributions can be embedded in a smooth path of distributions. Using this underlying path and a performance model based on the…

The FBMS R package facilitates Bayesian model selection and model averaging in complex regression settings by employing a variety of Monte Carlo model exploration methods. At its core, the package implements an efficient Mode Jumping Markov…

Gaussian random fields play an important role in many areas of science and engineering. In practice, they are often simulated by sampling from a high-dimensional multivariate normal distribution, which arises from the discretisation of a…

Bayesian inference provides a methodology for parameter estimation and uncertainty quantification in machine learning and deep learning methods. Variational inference and Markov Chain Monte-Carlo (MCMC) sampling methods are used to…

Multidimensional scaling (MDS) is a family of methods that embed a given set of points into a simple, usually flat, domain. The points are assumed to be sampled from some metric space, and the mapping attempts to preserve the distances…

In the last few decades, Markov chain Monte Carlo (MCMC) methods have been widely applied to Bayesian updating of structural dynamic models in the field of structural health monitoring. Recently, several MCMC algorithms have been developed…

Variable selection is a key issue when analyzing high-dimensional data. The explosion of data with large sample sizes and dimensionality brings new challenges to this problem in both inference accuracy and computational complexity. To…

In Bayesian statistics, many problems can be expressed as the evaluation of the expectation of a quantity of interest with respect to the posterior distribution. Standard Monte Carlo method is often not applicable because the encountered…

Numerous engineering problems of interest to the industry are often characterized by expensive black-box objective experiments or computer simulations. Obtaining insight into the problem or performing subsequent optimizations requires…

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…

Sampling from the full posterior distribution of high-dimensional non-linear, non-Gaussian latent dynamical models presents significant computational challenges. While Particle Gibbs (also known as conditional sequential Monte Carlo) is…

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 the context of Bayesian inversion for scientific and engineering modeling, Markov chain Monte Carlo sampling strategies are the benchmark due to their flexibility and robustness in dealing with arbitrary posterior probability density…

Due to the escalating growth of big data sets in recent years, new Bayesian Markov chain Monte Carlo (MCMC) parallel computing methods have been developed. These methods partition large data sets by observations into subsets. However, for…

Bayesian inference promises to ground and improve the performance of deep neural networks. It promises to be robust to overfitting, to simplify the training procedure and the space of hyperparameters, and to provide a calibrated measure of…