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Computer simulations have become an important tool across the biomedical sciences and beyond. For many important problems several different models or hypotheses exist and choosing which one best describes reality or observed data is not…
Closed-form, interpretable mathematical models have been instrumental for advancing our understanding of the world; with the data revolution, we may now be in a position to uncover new such models for many systems from physics to the social…
In this paper we present a novel inference methodology to perform Bayesian inference for spatiotemporal Cox processes where the intensity function depends on a multivariate Gaussian process. Dynamic Gaussian processes are introduced to…
Undirected graphical models are widely used in statistics, physics and machine vision. However Bayesian parameter estimation for undirected models is extremely challenging, since evaluation of the posterior typically involves the…
A Gaussian Cox process is a popular model for point process data, in which the intensity function is a transformation of a Gaussian process. Posterior inference of this intensity function involves an intractable integral (i.e., the…
We describe a Bayesian approach to estimating luminosity functions. We derive the likelihood function and posterior probability distribution for the luminosity function, given the observed data, and we compare the Bayesian approach with…
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…
Making good predictions of a physical system using a computer code requires the inputs to be carefully specified. Some of these inputs called control variables have to reproduce physical conditions whereas other inputs, called parameters,…
Posterior distributions often feature intractable normalizing constants, called marginal likelihoods or evidence, that are useful for model comparison via Bayes factors. This has motivated a number of methods for estimating ratios of…
Bayesian optimization through Gaussian process regression is an effective method of optimizing an unknown function for which every measurement is expensive. It approximates the objective function and then recommends a new measurement point…
A Gaussian process has been one of the important approaches for emulating computer simulations. However, the stationarity assumption for a Gaussian process and the intractability for large-scale dataset limit its availability in practice.…
The dynamic emulation of non-linear deterministic computer codes where the output is a time series, possibly multivariate, is examined. Such computer models simulate the evolution of some real-world phenomenon over time, for example models…
Real-world autonomous systems operate under uncertainty about both their pose and dynamics. Autonomous control systems must simultaneously perform estimation and control tasks to maintain robustness to changing dynamics or modeling errors.…
Markov Chain Monte Carlo (MCMC) methods have become a cornerstone of many modern scientific analyses by providing a straightforward approach to numerically estimate uncertainties in the parameters of a model using a sequence of random…
Boson sampling is a promising candidate for quantum supremacy. It requires to sample from a complicated distribution, and is trusted to be intractable on classical computers. Among the various classical sampling methods, the Markov chain…
Consider a real-valued function that can only be observed with stochastic noise at a finite set of design points within a Euclidean space. We wish to determine whether there exists a convex function that goes through the true function…
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…
Hidden Markov models can describe time series arising in various fields of science, by treating the data as noisy measurements of an arbitrarily complex Markov process. Sequential Monte Carlo (SMC) methods have become standard tools to…
In this article, an overview of Bayesian methods for sequential simulation from posterior distributions of nonlinear and non-Gaussian dynamic systems is presented. The focus is mainly laid on sequential Monte Carlo methods, which are based…
Bayesian methods for learning Gaussian graphical models offer a principled framework for quantifying model uncertainty and incorporating prior knowledge. However, their scalability is constrained by the computational cost of jointly…