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Recent advancements in Markov chain Monte Carlo (MCMC) sampling and surrogate modelling have significantly enhanced the feasibility of Bayesian analysis across engineering fields. However, the selection and integration of surrogate models…

The multilevel Monte Carlo (MLMC) method has proven to be an effective variance-reduction statistical method for Uncertainty quantification in PDE models. It combines approximations at different levels of accuracy using a hierarchy of…

Quantifying the uncertainty in model parameters and output is a critical component in model-driven decision support systems for groundwater management. This paper presents a novel algorithmic approach which fuses Markov Chain Monte Carlo…

Autoencoders gained popularity in the deep learning revolution given their ability to compress data and provide dimensionality reduction. Although prominent deep learning methods have been used to enhance autoencoders, the need to provide…

Deep learning has been shown to be highly effective for automatic modulation classification (AMC), which is a pivotal technology for next-generation cognitive communications. Yet, existing deep learning methods for AMC often lack robust…

Constructing unbiased estimators from Markov chain Monte Carlo (MCMC) outputs is a difficult problem that has recently received a lot of attention in the statistics and machine learning communities. However, the current unbiased MCMC…

Models of stochastic processes are widely used in almost all fields of science. Theory validation, parameter estimation, and prediction all require model calibration and statistical inference using data. However, data are almost always…

Bayesian inference for Markov processes has become increasingly relevant in recent years. Problems of this type often have intractable likelihoods and prior knowledge about model rate parameters is often poor. Markov Chain Monte Carlo…

Bayesian model comparison (BMC) offers a principled approach for assessing the relative merits of competing computational models and propagating uncertainty into model selection decisions. However, BMC is often intractable for the popular…

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…

Sequential Monte Carlo (SMC) methods offer a principled approach to Bayesian uncertainty quantification but are traditionally limited by the need for full-batch gradient evaluations. We introduce a scalable variant by incorporating…

Markov Chain Monte Carlo (MCMC) methods often take many iterations to converge for highly correlated or high-dimensional target density functions. Methods such as Hamiltonian Monte Carlo (HMC) or No-U-Turn Sampling (NUTS) use the…

We consider the problem of estimating expectations with respect to a target distribution with an unknown normalizing constant, and where even the unnormalized target needs to be approximated at finite resolution. This setting is ubiquitous…

While multilevel Monte Carlo (MLMC) methods for the numerical approximation of partial differential equations with random coefficients enjoy great popularity, combinations with spatial adaptivity seem to be rare. We present an adaptive MLMC…

Multi-fidelity machine learning methods address the accuracy-efficiency trade-off by integrating scarce, resource-intensive high-fidelity data with abundant but less accurate low-fidelity data. We propose a practical multi-fidelity strategy…

Bayesian inference often faces a trade-off between computational speed and sampling accuracy. We propose an adaptive workflow that integrates rapid amortized inference with gold-standard MCMC techniques to achieve a favorable combination of…

Bayesian inference with Markov Chain Monte Carlo (MCMC) is challenging when the likelihood function is irregular and expensive to compute. We explore several sampling algorithms that make use of subset evaluations to reduce computational…

As the size of engineered systems grows, problems in reliability theory can become computationally challenging, often due to the combinatorial growth in the cut sets. In this paper we demonstrate how Multilevel Monte Carlo (MLMC) - 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…

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…