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The estimation of unknown values of parameters (or hidden variables, control variables) that characterise a physical system often relies on the comparison of measured data with synthetic data produced by some numerical simulator of the…
We use rescaled Gaussian processes as prior models for functional parameters in nonparametric statistical models. We show how the rate of contraction of the posterior distributions depends on the scaling factor. In particular, we exhibit…
In Bayesian inverse problems, the posterior distribution is used to quantify uncertainty about the reconstructed solution. In practice, Markov chain Monte Carlo algorithms often are used to draw samples from the posterior distribution.…
Increasingly complex datasets pose a number of challenges for Bayesian inference. Conventional posterior sampling based on Markov chain Monte Carlo can be too computationally intensive, is serial in nature and mixes poorly between posterior…
We provide a survey of nonstationary surrogate models which utilize Gaussian processes (GPs) or variations thereof, including nonstationary kernel adaptations, partition and local GPs, and spatial warpings through deep Gaussian processes.…
We use Bayesian model selection paradigms, such as group least absolute shrinkage and selection operator priors, to facilitate generalized additive model selection. Our approach allows for the effects of continuous predictors to be…
Gibbs sampling is a widely popular Markov chain Monte Carlo algorithm that can be used to analyze intractable posterior distributions associated with Bayesian hierarchical models. There are two standard versions of the Gibbs sampler: The…
Gaussian process regression is a popular Bayesian framework for surrogate modeling of expensive data sources. As part of a broader effort in scientific machine learning, many recent works have incorporated physical constraints or other a…
Bayesian model selection enables comparison and ranking of conceptual subsurface models described by spatial prior models, according to the support provided by available geophysical data. Deep generative neural networks can efficiently…
Doubly intractable distributions arise in many settings, for example in Markov models for point processes and exponential random graph models for networks. Bayesian inference for these models is challenging because they involve intractable…
While Bayesian inference provides a principled framework for reasoning under uncertainty, its widespread adoption is limited by the intractability of exact posterior computation, necessitating the use of approximate inference. However,…
We consider Bayesian inference when only a limited number of noisy log-likelihood evaluations can be obtained. This occurs for example when complex simulator-based statistical models are fitted to data, and synthetic likelihood (SL) method…
Gaussian processes retain the linear model either as a special case, or in the limit. We show how this relationship can be exploited when the data are at least partially linear. However from the perspective of the Bayesian posterior, the…
This paper presents a probabilistic surrogate model for the accelerated design of electric vehicle battery enclosures with a focus on crash performance. The study integrates high-throughput finite element simulations and Gaussian Process…
Many processes in chemistry and physics take place on timescales that cannot be explored using standard molecular dynamics simulations. This renders the use of enhanced sampling mandatory. Here we introduce an enhanced sampling method that…
Accurate tuning of hyperparameters is crucial to ensure that models can generalise effectively across different settings. In this paper, we present theoretical guarantees for hyperparameter selection using variational Bayes in the…
Sensor-based sorting systems enable the physical separation of a material stream into two fractions. The sorting decision is based on the image data evaluation of the sensors used and is carried out using actuators. Various process…
We introduce a scalable approach to Gaussian process inference that combines spatio-temporal filtering with natural gradient variational inference, resulting in a non-conjugate GP method for multivariate data that scales linearly with…
We introduce a Bayesian framework for inference with a supervised version of the Gaussian process latent variable model. The framework overcomes the high correlations between latent variables and hyperparameters by using an unbiased pseudo…
Recently surrogate functions based on the tail inequalities were developed to evaluate the chance constraints in the context of evolutionary computation and several Pareto optimization algorithms using these surrogates were successfully…