Related papers: Partition function approach to non-Gaussian likeli…

Monte-Carlo techniques are standard numerical tools for exploring non-Gaussian and multivariate likelihoods. Many variants of the original Metropolis-Hastings algorithm have been proposed to increase the sampling efficiency. Motivated by…

Motivated by constraints on the dark energy equation of state from supernova-data, we propose a formalism for the Bayesian inference of functions: Starting at a functional variant of the Kullback-Leibler divergence we construct a functional…

Subject of this paper is the simplification of Markov chain Monte Carlo sampling as used in Bayesian statistical inference by means of normalising flows, a machine learning method which is able to construct an invertible and differentiable…

Non-Gaussian distributions in cosmology are commonly evaluated with Monte Carlo Markov-chain methods, as the Fisher-matrix formalism is restricted to the Gaussian case. The Metropolis-Hastings algorithm will provide samples from the…

We generalize the maximum likelihood method to non-Gaussian distribution functions by means of the multivariate Edgeworth expansion. We stress the potential interest of this technique in all those cosmological problems in which the…

We present a method to transform multivariate unimodal non-Gaussian posterior probability densities into approximately Gaussian ones via non-linear mappings, such as Box--Cox transformations and generalisations thereof. This permits an…

A Bayesian approach to the classification problem is proposed in which random partitions play a central role. It is argued that the partitioning approach has the capacity to take advantage of a variety of large-scale spatial structures, if…

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…

A standard method to obtain information on a quantum state is to measure marginal distributions along many different axes in phase space, which forms a basis of quantum state tomography. We theoretically propose and experimentally…

We present a framework to compute non-Gaussian likelihoods for two-point correlation functions. The non-Gaussianity is most pronounced on large scales that will be well-measured by stage-IV weak-lensing surveys. We show how such a…

We propose a new method, called MonteCarlo Posterior Fit, to boost the MonteCarlo sampling of likelihood (posterior) functions. The idea is to approximate the posterior function by an analytical multidimensional non-Gaussian fit. The many…

This paper proposes a non-Gaussian Markov field with a special feature: an explicit partition function. To the best of our knowledge, this is an original contribution. Moreover, the explicit expression of the partition function enables the…

Recently, a class of stochastic processes known as piecewise deterministic Markov processes has been used to define continuous-time Markov chain Monte Carlo algorithms with a number of attractive properties, including compatibility with…

The main challenges that arise when adopting Gaussian Process priors in probabilistic modeling are how to carry out exact Bayesian inference and how to account for uncertainty on model parameters when making model-based predictions on…

We establish a systematic framework of unbiased quantum sampling and estimation protocols for the classical Gibbs expectation. This framework generalizes existing approaches to the partition function estimation and has broader applications…

Statistical inference more often than not involves models which are non-linear in the parameters thus leading to non-Gaussian posteriors. Many computational and analytical tools exist that can deal with non-Gaussian distributions, and…

We study the significance of non-Gaussianity in the likelihood of weak lensing shear two-point correlation functions, detecting significantly non-zero skewness and kurtosis in one-dimensional marginal distributions of shear two-point…

Structure formation in our Universe creates non-Gaussian random fields that will soon be observed over almost the entire sky by the Euclid satellite, the Vera-Rubin observatory, and the Square Kilometre Array. An unsolved problem is how to…

We consider the problem of approximating partition functions for Ising models. We make use of recent tools in combinatorial optimization: the Sherali-Adams and Lasserre convex programming hierarchies, in combination with variational methods…

Gaussian processes (GPs) are frequently used in machine learning and statistics to construct powerful models. However, when employing GPs in practice, important considerations must be made, regarding the high computational burden,…