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A common problem in natural sciences is the comparison of competing models in the light of observed data. Bayesian model comparison provides a statistically sound framework for this comparison based on the evidence each model provides for…

We present dynesty, a public, open-source, Python package to estimate Bayesian posteriors and evidences (marginal likelihoods) using Dynamic Nested Sampling. By adaptively allocating samples based on posterior structure, Dynamic Nested…

In real-world Bayesian inference applications, prior assumptions regarding the parameters of interest may be unrepresentative of their actual values for a given dataset. In particular, if the likelihood is concentrated far out in the wings…

Denoising diffusion models have driven significant progress in the field of Bayesian inverse problems. Recent approaches use pre-trained diffusion models as priors to solve a wide range of such problems, only leveraging inference-time…

Quality by design in pharmaceutical manufacturing hinges on computational methods and tools that are capable of accurate quantitative prediction of the design space. This paper investigates Bayesian approaches to design space…

Predictive uncertainty quantification is crucial for reliable decision-making in various applied domains. Bayesian neural networks offer a powerful framework for this task. However, defining meaningful priors and ensuring computational…

We introduce a novel technique within the Nested Sampling framework to enhance efficiency of the computation of Bayesian evidence, a critical component in scientific data analysis. In higher dimensions, Nested Sampling relies on Markov…

Bayesian inference has theoretical attractions as a principled framework for reasoning about beliefs. However, the motivations of Bayesian inference which claim it to be the only 'rational' kind of reasoning do not apply in practice. They…

Compressive imaging aims to recover a latent image from under-sampled measurements, suffering from a serious ill-posed inverse problem. Recently, deep neural networks have been applied to this problem with superior results, owing to the…

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…

Deep Gaussian processes provide a flexible approach to probabilistic modelling of data using either supervised or unsupervised learning. For tractable inference approximations to the marginal likelihood of the model must be made. The…

Model-based approaches bear great promise for decision making of agents interacting with the physical world. In the context of spatial environments, different types of problems such as localisation, mapping, navigation or autonomous…

The recent literature on deep learning offers new tools to learn a rich probability distribution over high dimensional data such as images or sounds. In this work we investigate the possibility of learning the prior distribution over neural…

In this paper, we present a novel approach to accelerate the Bayesian inference process, focusing specifically on the nested sampling algorithms. Bayesian inference plays a crucial role in cosmological parameter estimation, providing a…

The data torrent unleashed by current and upcoming astronomical surveys demands scalable analysis methods. Many machine learning approaches scale well, but separating the instrument measurement from the physical effects of interest, dealing…

Prior information often takes the form of parameter constraints. Bayesian methods include such information through prior distributions having constrained support. By using posterior sampling algorithms, one can quantify uncertainty without…

Nested sampling is a powerful approach to Bayesian inference ultimately limited by the computationally demanding task of sampling from a heavily constrained probability distribution. An effective algorithm in its own right, Hamiltonian…

Bayesian inference for inverse problems hinges critically on the choice of priors. In the absence of specific prior information, population-level distributions can serve as effective priors for parameters of interest. With the advent of…

Pareto front learning is a technique that introduces preference vectors in a neural network to approximate the Pareto front. Previous Pareto front learning methods have demonstrated high performance in approximating simple Pareto fronts.…

There is significant interest in using modern neural networks for scientific applications due to their effectiveness in modeling highly complex, non-linear problems in a data-driven fashion. However, a common challenge is to verify the…