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When maximum likelihood estimation is infeasible, one often turns to score matching, contrastive divergence, or minimum probability flow to obtain tractable parameter estimates. We provide a unifying perspective of these techniques as…

With larger data at their disposal, scientists are emboldened to tackle complex questions that require sophisticated statistical models. It is not unusual for the latter to have likelihood functions that elude analytical formulations. Even…

Unconstrained optimization problems are typically solved using iterative methods, which often depend on line search techniques to determine optimal step lengths in each iteration. This paper introduces a novel line search approach.…

We address the numerical solution of infinite-dimensional inverse problems in the framework of Bayesian inference. In the Part I companion to this paper (arXiv.org:1308.1313), we considered the linearized infinite-dimensional inverse…

In applications of imprecise probability, analysts must compute lower (or upper) expectations, defined as the infimum of an expectation over a set of parameter values. Monte Carlo methods consistently approximate expectations at fixed…

Inference for mechanistic models is challenging because of nonlinear interactions between model parameters and a lack of identifiability. Here we focus on a specific class of mechanistic models, which we term stable differential equations.…

Bayesian statistical inverse problems are often solved with Markov chain Monte Carlo (MCMC)-type schemes. When the problems are governed by large-scale discrete nonlinear partial differential equations (PDEs), they are computationally…

State estimation in robotic systems presents significant challenges, particularly due to the prevalence of multimodal posterior distributions in real-world scenarios. One effective strategy for handling such complexity is to compute maximum…

This paper studies the solvability, existence of unique solution, closed-form solution and numerical solution of matrix equation $X=Af(X) B+C$ with $f(X) =X^{\mathrm{T}},$ $f(X) =\bar{X}$ and $f(X) =X^{\mathrm{H}},$ where $X$ is the…

Standard Monte Carlo computation is widely known to exhibit a canonical square-root convergence speed in terms of sample size. Two recent techniques, one based on control variate and one on importance sampling, both derived from an…

Many problems of practical interest rely on Continuous-time Markov chains~(CTMCs) defined over combinatorial state spaces, rendering the computation of transition probabilities, and hence probabilistic inference, difficult or impossible…

This work introduces two Monte Carlo (MC)-based sampling methods, known as line sampling and subset simulation, to improve the performance of standard MC analyses in the context of asteroid impact risk assessment. Both techniques sample the…

We consider geothermal inverse problems and uncertainty quantification from a Bayesian perspective. Our main goal is to make standard, `out-of-the-box' Markov chain Monte Carlo (MCMC) sampling more feasible for complex simulation models by…

Modern imaging methods rely strongly on Bayesian inference techniques to solve challenging imaging problems. Currently, the predominant Bayesian computation approach is convex optimisation, which scales very efficiently to high dimensional…

As modern neural networks get more complex, specifying a model with high predictive performance and sound uncertainty quantification becomes a more challenging task. Despite some promising theoretical results on the true posterior…

Structural equation models are commonly used to capture the relationship between sets of observed and unobservable variables. Traditionally these models are fitted using frequentist approaches but recently researchers and practitioners have…

Stochastic reaction network models are often used to explain and predict the dynamics of gene regulation in single cells. These models usually involve several parameters, such as the kinetic rates of chemical reactions, that are not…

Almost all fields of science rely upon statistical inference to estimate unknown parameters in theoretical and computational models. While the performance of modern computer hardware continues to grow, the computational requirements for the…

Bayesian analysis is widely used in science and engineering for real-time forecasting, decision making, and to help unravel the processes that explain the observed data. These data are some deterministic and/or stochastic transformations of…

Through the Bayesian lens of data assimilation, uncertainty on model parameters is traditionally quantified through the posterior covariance matrix. However, in modern settings involving high-dimensional and computationally expensive…