Related papers: Copula Cosmology: Constructing a Likelihood Functi…
The two-point correlation function of the galaxy distribution is a key cosmological observable that allows us to constrain the dynamical and geometrical state of our Universe. To measure the correlation function we need to know both the…
A functional risk curve gives the probability of an undesirable event as a function of the value of a critical parameter of a considered physical system. In several applicative situations, this curve is built using phenomenological…
Copula models have become one of the most widely used tools in the applied modelling of multivariate data. Similarly, Bayesian methods are increasingly used to obtain efficient likelihood-based inference. However, to date, there has been…
In this paper, we propose simple estimation methods dedicated to a semiparametric family of bivariate copulas. These copulas can be simply estimated through the estimation of their univariate generating function. We take profit of this…
A useful method for representing Bayesian classifiers is through \emph{discriminant functions}. Here, using copula functions, we propose a new model for discriminants. This model provides a rich and generalized class of decision boundaries.…
Cosmological weak lensing by the large scale structure of the Universe, cosmic shear, is coming of age as a powerful probe of the parameters describing the cosmological model and matter power spectrum. It complements CMB studies, by…
The probability density function of a probability distribution is a fundamental concept in probability theory and a key ingredient in various widely used machine learning methods. However, the necessary framework for compiling probabilistic…
We describe an approximate statistical model for the sample variance distribution of the non-linear matter power spectrum that can be calibrated from limited numbers of simulations. Our model retains the common assumption of a multivariate…
We consider the shape of the posterior distribution to be used when fitting cosmological models to power spectra measured from galaxy surveys. At very large scales, Gaussian posterior distributions in the power do not approximate the…
We assume that we have multiple ordinal time series and we would like to specify their joint distribution. In general it is difficult to create multivariate distribution that can be easily used to jointly model ordinal variables and the…
We infer gravitational lensing shear and convergence fields from galaxy ellipticity catalogs under a spatial process prior for the lensing potential. We demonstrate the performance of our algorithm with simulated Gaussian-distributed…
A composite likelihood is an inference function derived by multiplying a set of likelihood components. This approach provides a flexible framework for drawing inference when the likelihood function of a statistical model is computationally…
In this article, a copula-based method for mixed regression models is proposed, where the conditional distribution of the response variable, given covariates, is modelled by a parametric family of continuous or discrete distributions, and…
Meta-elliptical copulas are often proposed to model dependence between the components of a random vector. They are specified by a correlation matrix and a map $g$, called density generator. While the latter correlation matrix can easily be…
We develop a general variational inference method that preserves dependency among the latent variables. Our method uses copulas to augment the families of distributions used in mean-field and structured approximations. Copulas model the…
We investigate whether a Gaussian likelihood is sufficient to obtain accurate parameter constraints from a Euclid-like combined tomographic power spectrum analysis of weak lensing, galaxy clustering and their cross-correlation. Testing its…
Nonparanormal models describe the joint distribution of multivariate responses via latent Gaussian, and thus parametric, copulae while allowing flexible nonparametric marginals. Some aspects of such distributions, for example conditional…
We re-examine a genuine power of weak lensing bispectrum tomography for constraining cosmological parameters, when combined with the power spectrum tomography, based on the Fisher information matrix formalism. To account for the full…
Non-Gaussian likelihoods, ubiquitous throughout cosmology, are a direct consequence of nonlinearities in the physical model. Their treatment requires Monte-Carlo Markov-chain or more advanced sampling methods for the determination of…
We present a modular, extensible likelihood framework for spectroscopic inference based on synthetic model spectra. The subtraction of an imperfect model from a continuously sampled spectrum introduces covariance between adjacent datapoints…