Related papers: Gaussianisation for fast and accurate inference fr…
In this paper, we propose an efficient pseudo-marginal Markov chain Monte Carlo (MCMC) sampling approach to draw samples from posterior shape distributions for image segmentation. The computation time of the proposed approach is independent…
Gaussian processes (GPs) are Bayesian nonparametric generative models that provide interpretability of hyperparameters, admit closed-form expressions for training and inference, and are able to accurately represent uncertainty. To model…
We explore a systematic approach to the analysis of primordial non-Gaussianity using fluctuations in temperature and polarization of the Cosmic Microwave Background (CMB). Following Munshi & Heavens (2009), we define a set of power-spectra…
We describe a new numerical algorithm to obtain high-resolution simulated maps of the Cosmic Microwave Background (CMB), for a broad class of non-Gaussian models. The kind of non-Gaussianity we account for is based on the simple idea that…
We consider the problem of estimating the uncertainty in statistical inverse problems using Bayesian inference. When the probability density of the noise and the prior are Gaussian, the solution of such a statistical inverse problem is also…
One of the main unsolved problems of cosmology is how to maximize the extraction of information from nonlinear data. If the data are nonlinear the usual approach is to employ a sequence of statistics (N-point statistics, counting statistics…
We propose a general framework using spike-and-slab prior distributions to aid with the development of high-dimensional Bayesian inference. Our framework allows inference with a general quasi-likelihood function. We show that highly…
We present a novel Bayesian method for the joint reconstruction of cosmological matter density fields, peculiar velocities and power-spectra in the quasi-nonlinear regime. We study its applicability to the Ly-alpha forest based on multiple…
Minimization of a stochastic cost function is commonly used for approximate sampling in high-dimensional Bayesian inverse problems with Gaussian prior distributions and multimodal posterior distributions. The density of the samples…
While the probability density function (PDF) of the cosmic microwave background (CMB) convergence field approximately follows a Gaussian distribution, primordial non-Gaussianities and small contributions from structures at low redshifts…
Markov Chain Monte Carlo (MCMC) methods have revolutionised Bayesian data analysis over the years by making the direct computation of posterior probability densities feasible on modern workstations. However, the calculation of the prior…
In (Hansen et al. 2002) we presented a new approach for measuring non-Gaussianity of the Cosmic Microwave Background (CMB) anisotropy pattern, based on the multivariate empirical distribution function of the spherical harmonics a_lm of a…
Likelihood fitting to two-point clustering statistics made from galaxy surveys usually assumes a multivariate normal distribution for the measurements, with justification based on the central limit theorem given the large number of…
In statistical applications, it is common to encounter parameters supported on a varying or unknown dimensional space. Examples include the fused lasso regression, the matrix recovery under an unknown low rank, etc. Despite the ease of…
In Bayesian nonparametric models, Gaussian processes provide a popular prior choice for regression function estimation. Existing literature on the theoretical investigation of the resulting posterior distribution almost exclusively assume a…
A method is presented for performing joint analyses of cosmological datasets, in which the weight assigned to each dataset is determined directly by it own statistical properties. The weights are considered in a Bayesian context as a set of…
Several strategies have been developed recently to ensure valid inference after model selection; some of these are easy to compute, while others fare better in terms of inferential power. In this paper, we consider a selective inference…
The Planck satellite, along with several ground based telescopes, have mapped the cosmic microwave background (CMB) at sufficient resolution and signal-to-noise so as to allow a detection of the subtle distortions due to the gravitational…
The joint retrieval of surface reflectances and atmospheric parameters in VSWIR imaging spectroscopy is a computationally challenging high-dimensional problem. Using NASA's Surface Biology and Geology mission as the motivational context,…
Fields in cosmology, such as the matter distribution, are observed by experiments up to experimental noise. The first step in cosmological data analysis is usually to de-noise the observed field using an analytic or simulation driven prior.…