Related papers: Cosmological parameter inference with Bayesian sta…

We investigate the potential of using cosmic voids as a probe to constrain cosmological parameters through the gravitational lensing effect of the cosmic microwave background (CMB) and make predictions for the next generation surveys. By…

Markov chain Monte Carlo (MCMC) algorithms are generally regarded as the gold standard technique for Bayesian inference. They are theoretically well-understood and conceptually simple to apply in practice. The drawback of MCMC is that in…

In the following article we provide an exposition of exact computational methods to perform parameter inference from partially observed network models. In particular, we consider the duplication attachment (DA) model which has a likelihood…

Bayesian inference for Markov processes has become increasingly relevant in recent years. Problems of this type often have intractable likelihoods and prior knowledge about model rate parameters is often poor. Markov Chain Monte Carlo…

Extracting accurate cosmological information from galaxy-galaxy and galaxy-matter correlation functions on non-linear scales ($\lesssim 10 h^{-1} \mathrm{Mpc}$) requires cosmological simulations. Additionally, one has to marginalise over…

We consider conditional tests for non-negative discrete exponential families. We develop two Markov Chain Monte Carlo (MCMC) algorithms which allow us to sample from the conditional space and to perform approximated tests. The first…

We present a new blind formulation of the Cosmic Microwave Background (CMB) inference problem. The approach relies on a phenomenological model of the multi-frequency microwave sky without the need for physical models of the individual…

Based on the cosmological principle only, the method of describing the evolution of the Universe, called cosmography, is in fact a kinematics of cosmological expansion. The effectiveness of cosmography lies in the fact that it allows, based…

The Hamiltonian Monte Carlo (HMC) algorithm is a powerful Markov Chain Monte Carlo (MCMC) method that uses Hamiltonian dynamics to generate samples from a target distribution. To fully exploit its potential, we must understand how…

Bayesian learning in undirected graphical models|computing posterior distributions over parameters and predictive quantities is exceptionally difficult. We conjecture that for general undirected models, there are no tractable MCMC (Markov…

To conduct Bayesian inference with large data sets, it is often convenient or necessary to distribute the data across multiple machines. We consider a likelihood function expressed as a product of terms, each associated with a subset of the…

The good agreement between large-scale observations and the predictions of the now-standard $\Lambda$CDM theory gives us hope that this will become a lasting foundation for cosmology. After briefly reviewing the current status of the key…

We discuss a method of calculating the key cosmological parameters on the basis of a selected scale factor by using exact solutions of the background equations. We specify the formulas for calculating the power spectrum, the spectral…

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…

I present CMBAnalysis, a state-of-the-art Python framework designed for high-precision analysis of Cosmic Microwave Background (CMB) radiation data. This comprehensive package implements parallel Markov Chain Monte Carlo (MCMC) techniques…

Current analysis of astronomical data are confronted with the daunting task of modeling the awkward features of astronomical data, among which heteroscedastic (point-dependent) errors, intrinsic scatter, non-ignorable data collection…

This book aims to provide a graduate-level introduction to advanced topics in Markov chain Monte Carlo (MCMC) algorithms, as applied broadly in the Bayesian computational context. Most, if not all of these topics (stochastic gradient MCMC,…

We present a sequential Monte Carlo sampler algorithm for the Bayesian analysis of generalised linear mixed models (GLMMs). These models support a variety of interesting regression-type analyses, but performing inference is often extremely…

We present a Bayesian methodology for infinite as well as finite dimensional parameter identification for partial differential equation models. The Bayesian framework provides a rigorous mathematical framework for incorporating prior…

While Bayesian model selection is a useful tool to discriminate between competing cosmological models, it only gives a relative rather than an absolute measure of how good a model is. Bayesian doubt introduces an unknown benchmark model…