Related papers: On combining estimated and analytic covariance mat…
We investigate whether a Gaussian likelihood, as routinely assumed in the analysis of cosmological data, is supported by simulated survey data. We define test statistics, based on a novel method that first destroys Gaussian correlations in…
When inferring unknown parameters or comparing different models, data must be compared to underlying theory. Even if a model has no closed-form solution to derive summary statistics, it is often still possible to simulate mock data in order…
When inferring parameters from a Gaussian-distributed data set by computing a likelihood, a covariance matrix is needed that describes the data errors and their correlations. If the covariance matrix is not known a priori, it may be…
We investigate the Student-t process as an alternative to the Gaussian process as a nonparametric prior over functions. We derive closed form expressions for the marginal likelihood and predictive distribution of a Student-t process, by…
We investigate the bias and error in estimates of the cosmological parameter covariance matrix, due to sampling or modelling the data covariance matrix, for likelihood width and peak scatter estimators. We show that these estimators do not…
It is well-known that the posterior density of linear inverse problems with Gaussian prior and Gaussian likelihood is also Gaussian, hence completely described by its covariance and expectation. Sampling from a Gaussian posterior may be…
Likelihood fitting to two-point clustering statistics made from galaxy surveys usually assumes a multivariate normal distribution for the measurements, with justification based on the central limit theorem given the large number of…
A new robust stochastic volatility (SV) model having Student-t marginals is proposed. Our process is defined through a linear normal regression model driven by a latent gamma process that controls temporal dependence. This gamma process is…
Accurate and precise covariance matrices will be important in enabling planned cosmological surveys to detect new physics. Standard methods imply either the need for many N-body simulations in order to obtain an accurate estimate, or a…
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…
The random matrix theory method of planar Gaussian diagrammatic expansion is applied to find the mean spectral density of the Hermitian equal-time and non-Hermitian time-lagged cross-covariance estimators, firstly in the form of master…
An accurate covariance matrix is essential for obtaining reliable cosmological results when using a Gaussian likelihood. In this paper we study the covariance of pseudo-$C_\ell$ estimates of tomographic cosmic shear power spectra. Using two…
We present methods to rigorously extract parameter combinations that are constrained by data from posterior distributions. The standard approach uses linear methods that apply to Gaussian distributions. We show the limitations of the linear…
The Poisson model is frequently employed to describe count data, but in a Bayesian context it leads to an analytically intractable posterior probability distribution. In this work, we analyze a variational Gaussian approximation to the…
We propose and analyze a new estimator of the covariance matrix that admits strong theoretical guarantees under weak assumptions on the underlying distribution, such as existence of moments of only low order. While estimation of covariance…
Estimation of the mean vector and covariance matrix is of central importance in the analysis of multivariate data. In the framework of generalized linear models, usually the variances are certain functions of the means with the normal…
Gaussian process regression is a powerful Bayesian nonlinear regression method. Recent research has enabled the capture of many types of observations using non-Gaussian likelihoods. To deal with various tasks in spatial modeling, we benefit…
This paper considers the Laplace method to derive approximate inference for the Gaussian process (GP) regression in the location and scale parameters of the Student-t probabilistic model. This allows both mean and variance of the data to…
Observational astrophysics consists of making inferences about the Universe by comparing data and models. The credible intervals placed on model parameters are often as important as the maximum a posteriori probability values, as the…
Context. Whenever correlation functions are used for inference about cosmological parameters in the context of a Bayesian analysis, the likelihood function of correlation functions needs to be known. Usually, it is approximated as a…