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Modern scientific cosmology pushes the boundaries of knowledge and the knowable. This is prompting questions on the nature of scientific knowledge. A central issue is what defines a 'good' model. When addressing global properties of the…
Cosmological probes pose an inverse problem where the measurement result is obtained through observations, and the objective is to infer values of model parameters which characterize the underlying physical system -- our Universe. Modern…
In cosmology, we would like to explain our observations and predict future observations from theories of the entire universe. Such cosmological theories make ontological assumptions of what entities exist and what their properties and…
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…
In this paper we consider the estimation of unknown parameters in Bayesian inverse problems. In most cases of practical interest, there are several barriers to performing such estimation, This includes a numerical approximation of a…
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…
We study empirical and hierarchical Bayes approaches to the problem of estimating an infinite-dimensional parameter in mildly ill-posed inverse problems. We consider a class of prior distributions indexed by a hyperparameter that quantifies…
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…
Using observation data to estimate unknown parameters in computational models is broadly important. This task is often challenging because solutions are non-unique due to the complexity of the model and limited observation data. However,…
Model inadequacy and measurement uncertainty are two of the most confounding aspects of inference and prediction in quantitative sciences. The process of scientific inference (the inverse problem) and prediction (the forward problem)…
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…
One of the challenges in testing gravity with cosmology is the vast freedom opened when extending General Relativity. For linear perturbations, one solution consists in using the Effective Field Theory of Dark Energy (EFT of DE). Even then,…
By way of a complete integration of the Friedmann equations, in terms of observables, it is shown that for the cosmological constant $\Lambda > 0$ there exist non-flat FLRW models for which the total density parameter $\Omega$ remains $\sim…
The interpretation of cosmological observables requires the use of increasingly sophisticated theoretical models. Since these models are becoming computationally very expensive and display non-trivial uncertainties, the use of standard…
Bayesian model selection is a tool to decide whether the introduction of a new parameter is warranted by data. I argue that the usual sampling statistic significance tests for a null hypothesis can be misleading, since they do not take into…
Astronomical measurements of the Omegas for mass density, cosmological constant lambda and curvature k are shown to be sufficient to produce a unique and detailed cosmological model describing dark energy influences based on the Friedman…
Although the broad outlines of the appropriate pipeline for cosmological likelihood analysis with CMB data has been known for several years, only recently have we had to contend with the full, large-scale, computationally challenging…
We present general, analytic methods for Cosmological likelihood analysis and solve the "many-parameters" problem in Cosmology. Maxima are found by Newton's Method, while marginalization over nuisance parameters, and parameter errors and…
We constrain the basic comological parameters using the first observations by the Very Small Array (VSA) in its extended configuration, together with existing cosmic microwave background data and other cosmological observations. We estimate…
We review observational tests for the homogeneity of the Universe on large scales. Redshift and peculiar velocity surveys, radio sources, the X-Ray Background, the Lyman-$\alpha$ forest and the Cosmic Microwave Background are used to set…