Related papers: Applications of Bayesian model selection to cosmol…

Background: Many mathematical models have now been employed across every area of systems biology. These models increasingly involve large numbers of unknown parameters, have complex structure which can result in substantial evaluation time…

In the problem of selecting variables in a multivariate linear regression model, we derive new Bayesian information criteria based on a prior mixing a smooth distribution and a delta distribution. Each of them can be interpreted as a fusion…

Theories can be represented as statistical models for empirical testing. There is a vast literature on model selection and multimodel inference that focuses on how to assess which statistical model, and therefore which theory, best fits the…

When combining data sets to perform parameter inference, the results will be unreliable if there are unknown systematics in data or models. Here we introduce a flexible methodology, BACCUS: BAyesian Conservative Constraints and Unknown…

The estimation of unknown values of parameters (or hidden variables, control variables) that characterise a physical system often relies on the comparison of measured data with synthetic data produced by some numerical simulator of the…

We apply two Bayesian hierarchical inference schemes to infer shear power spectra, shear maps and cosmological parameters from the CFHTLenS weak lensing survey - the first application of this method to data. In the first approach, we sample…

We present a Bayesian analysis of large-scale structure and cosmic microwave background data to constrain the form of the primordial power spectrum. We have extended the usual presumption of a scale invariant spectrum to include: (i) a…

Bayesian (Probabilistic) Machine Learning is used to probe the opacity of the Universe. It relies on a generative process where the model is the key object to generate the data involving the unknown parameters of the model, our prior…

This is an introduction to Bayesian inference with a focus on hierarchical models and hyper-parameters. We write primarily for an audience of Bayesian novices, but we hope to provide useful insights for seasoned veterans as well. Examples…

Consider the setting where there are B>1 candidate statistical models, and one is interested in model selection. Two common approaches to solve this problem are to select a single model or to combine the candidate models through model…

We provide a flexible framework for selecting among a class of additive partial linear models that allows both linear and nonlinear additive components. In practice, it is challenging to determine which additive components should be…

This paper presents an efficient Bayesian framework for solving nonlinear, high-dimensional model calibration problems. It is based on a Variational Bayesian formulation that aims at approximating the exact posterior by means of solving an…

The choice of tuning parameters in Bayesian variable selection is a critical problem in modern statistics. In particular, for Bayesian linear regression with non-local priors, the scale parameter in the non-local prior density is an…

The next generation of weak lensing probes can place strong constraints on cosmological parameters by measuring the mass distribution and geometry of the low redshift universe. We show that a future all-sky tomographic cosmic shear survey…

What do the data, as distinguished from cosmological models, tell us about cosmological parameters that determined the model of the universe? In this paper, we address this question in the context of the WMAP angular power spectra for the…

Approximate Bayesian computation (ABC) have become a essential tool for the analysis of complex stochastic models. Earlier, Grelaud et al. (2009) advocated the use of ABC for Bayesian model choice in the specific case of Gibbs random…

We present a novel approach to derive constraints on neutrino masses from cosmological data, while taking into account our ignorance of the neutrino mass ordering. We derive constraints from a combination of current and future cosmological…

Learning of a smooth but nonparametric probability density can be regularized using methods of Quantum Field Theory. We implement a field theoretic prior numerically, test its efficacy, and show that the data and the phase space factors…

In many hypothesis testing applications, we have mixed priors, with well-motivated informative priors for some parameters but not for others. The Bayesian methodology uses the Bayes factor and is helpful for the informative priors, as it…

Modern imaging techniques heavily rely on Bayesian statistical models to address difficult image reconstruction and restoration tasks. This paper addresses the objective evaluation of such models in settings where ground truth is…