Related papers: The EFT Likelihood for Large-Scale Structure
Analysing non-Gaussian spatial-temporal data requires introducing spatial as well as temporal dependence in generalised linear models through the link function of an exponential family distribution. Unlike in Gaussian likelihoods, inference…
In variational inference, the benefits of Bayesian models rely on accurately capturing the true posterior distribution. We propose using neural samplers that specify implicit distributions, which are well-suited for approximating complex…
Tracer-kinetic analysis of dynamic contrast-enhanced magnetic resonance imaging data is commonly performed with the well-known Tofts model and nonlinear least squares (NLLS) regression. This approach yields point estimates of model…
Bayesian experimental design involves the optimal allocation of resources in an experiment, with the aim of optimising cost and performance. For implicit models, where the likelihood is intractable but sampling from the model is possible,…
Bayesian models quantify uncertainty and facilitate optimal decision-making in downstream applications. For most models, however, practitioners are forced to use approximate inference techniques that lead to sub-optimal decisions due to…
We review the effective field theory (EFT) approach to gravitational dynamics. We focus on extended objects in long-wavelength backgrounds and gravitational wave emission from spinning binary systems. We conclude with an introduction to EFT…
In recent years there has been a flurry of works on learning Bayesian networks from data. One of the hard problems in this area is how to effectively learn the structure of a belief network from incomplete data- that is, in the presence of…
We revisit the stochastic, or noise, contributions to the galaxy density field within the effective field theory (EFT) of large-scale structure. Starting from the general, all-order expression of the EFT partition function, we elucidate how…
Bayesian Neural Networks provide a principled framework for uncertainty quantification by modeling the posterior distribution of network parameters. However, exact posterior inference is computationally intractable, and widely used…
In Bayesian optimization, accounting for the importance of the output relative to the input is a crucial yet challenging exercise, as it can considerably improve the final result but often involves inaccurate and cumbersome entropy…
In spatial statistics, it is often assumed that the spatial field of interest is stationary and its covariance has a simple parametric form, but these assumptions are not appropriate in many applications. Given replicate observations of a…
The dark matter halos that host galaxies and clusters form out of initial high-density patches, providing a biased tracer of the linear matter density field. In the simplest local bias approximation, the halo field is treated as a…
This work addresses the problem of high-dimensional classification by exploring the generalized Bayesian logistic regression method under a sparsity-inducing prior distribution. The method involves utilizing a fractional power of the…
We present a survey of some of our recent results on Bayesian nonparametric inference for a multitude of stochastic processes. The common feature is that the prior distribution in the cases considered is on suitable sets of piecewise…
Bayesian statistics is concerned with conducting posterior inference for the unknown quantities in a given statistical model. Conventional Bayesian inference requires the specification of a probabilistic model for the observed data, and the…
We consider the use of randomised forward models and log-likelihoods within the Bayesian approach to inverse problems. Such random approximations to the exact forward model or log-likelihood arise naturally when a computationally expensive…
Generalised Bayesian inference updates prior beliefs using a loss function, rather than a likelihood, and can therefore be used to confer robustness against possible mis-specification of the likelihood. Here we consider generalised Bayesian…
We study a nonparametric Bayesian approach to linear inverse problems under discrete observations. We use the discrete Fourier transform to convert our model into a truncated Gaussian sequence model, that is closely related to the classical…
We formulate natural gradient variational inference (VI), expectation propagation (EP), and posterior linearisation (PL) as extensions of Newton's method for optimising the parameters of a Bayesian posterior distribution. This viewpoint…
Iterative methods for fitting a Gaussian Random Field (GRF) model via maximum likelihood (ML) estimation requires solving a nonconvex optimization problem. The problem is aggravated for anisotropic GRFs where the number of covariance…