Related papers: Cosmic Statistics of Statistics
Applying random matrix theory to quantum transport in chaotic cavities, we develop a novel approach to computation of the moments of the conductance and shot-noise (including their joint moments) of arbitrary order and at any number of open…
The last few years have seen a surge in excitement about measurements of statistics of the primordial fluctuations beyond the power spectrum. New ideas for precision tests of Gaussianity and statistical isotropy in the data are developing…
The general idea of determining cosmological parameters with gravitational lensing statistics is outlined, and then recent work---with an emphasis on applicability to all cosmological models, observational bias, better statistics and…
We develop a general method to "self-calibrate" observations of galaxy clustering with respect to systematics associated with photometric calibration errors. We first point out the danger posed by the multiplicative effect of calibration…
Upcoming and ongoing large area weak lensing surveys will also discover large samples of galaxy clusters. Accurate and precise masses of galaxy clusters are of major importance for cosmology, for example, in establishing well calibrated…
Many recent studies have demonstrated that scaling arguments, such as the so-called hierarchical {\em ansatz}, are extremely useful in understanding the statistical properties of weak gravitational lensing. This is especially true on small…
A fundamental assumption in cosmology is that of statistical isotropy - that the universe, on average, looks the same in every direction in the sky. Statistical isotropy has recently been tested stringently using Cosmic Microwave Background…
In this introductory talk we will establish connections between the statistical analysis of galaxy clustering in cosmology and recent work in mainstream spatial statistics. The lecture will review the methods of spatial statistics used by…
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…
We give an expository review of applications of computational algebraic statistics to design and analysis of fractional factorial experiments based on our recent works. For the purpose of design, the techniques of Gr\"obner bases and…
A new method for the statistical analysis of 3D point processes, based on the family of Minkowski functionals, is explained and applied to modelled galaxy distributions generated by a toy-model and cosmological simulations of the…
We demonstrate that accurate and precise cosmological information can be extracted from the cell count analysis of the 3D spatial clustering of galaxies once the second-order ratio between one- and two-point moments of the smoothed galaxy…
A factor copula model is proposed in which factors are either simulable or estimable from exogenous information. Point estimation and inference are based on a simulated methods of moments (SMM) approach with non-overlapping simulation…
Several cosmological measurements have attained significant levels of maturity and accuracy over the last decade. Continuing this trend, future observations promise measurements of the statistics of the cosmic mass distribution at an…
The estimation of cosmological parameters from a given data set requires a construction of a likelihood function which, in general, has a complicated functional form. We adopt a Gaussian copula and constructed a copula likelihood function…
In the second paper of this series we extend our Bayesian reanalysis of the evidence for a cosmic variation of the fine structure constant to the semi-parametric modelling regime. By adopting a mixture of Dirichlet processes prior for the…
The fully general calculation of the cosmic error on N-point correlation functions and related quantities is presented. More precisely, the variance caused by the finite volume, discreteness, and edge effects is determined for {\em any}…
Galaxy cluster counts have historically been important for the measurement of cosmological parameters and upcoming surveys will greatly reduce the statistical errors. To exploit the potential of current and future cluster surveys,…
We developed a modification to the calculation of the two-point correlation function commonly used in the analysis of large scale structure in cosmology. An estimator of the two-point correlation function is constructed by contrasting the…
In these notes we describe heuristics to predict computational-to-statistical gaps in certain statistical problems. These are regimes in which the underlying statistical problem is information-theoretically possible although no efficient…