Related papers: On estimating cosmology-dependent covariance matri…

A grand challenge of the 21st century cosmology is to accurately estimate the cosmological parameters of our Universe. A major approach to estimating the cosmological parameters is to use the large-scale matter distribution of the Universe.…

Based on a generalized cosine measure between two symmetric matrices, we propose a general framework for one-sample and two-sample tests of covariance and correlation matrices. We also develop a set of associated permutation algorithms for…

We obtain a sharp convergence rate for banded covariance matrix estimates of stationary processes. A precise order of magnitude is derived for spectral radius of sample covariance matrices. We also consider a thresholded covariance matrix…

Cosmological studies of large-scale structure have relied on two-point statistics, not fully exploiting the rich structure of the cosmic web. In this paper we show how to capture some of this cosmic web information by using the minimum…

We consider the problem of learning error covariance matrices for robotic state estimation. The convergence of a state estimator to the correct belief over the robot state is dependent on the proper tuning of noise models. During inference,…

Accurate covariance matrices for two-point functions are critical for inferring cosmological parameters in likelihood analyses of large-scale structure surveys. Among various approaches to obtaining the covariance, analytic computation is…

We present a comparative study of the accuracy and precision of correlation function methods and full-field inference in cosmological data analysis. To do so, we examine a Bayesian hierarchical model that predicts log-normal fields and…

Modern sky surveys are returning precision measurements of cosmological statistics such as weak lensing shear correlations, the distribution of galaxies, and cluster abundance. To fully exploit these observations, theorists must provide…

Maximising the information that can be extracted from weak lensing measurements is a key goal for upcoming surveys such as LSST and Euclid. This is typically achieved through statistics that are complementary to the cosmic shear two-point…

Mark-point dependence plays a critical role in research problems that can be fitted into the general framework of marked point processes. In this work, we focus on adjusting for mark-point dependence when estimating the mean and covariance…

A crucial assumption to reduce computational complexity in spatial-temporal data analysis is separability, which factors the covariance structure into a purely spatial and a purely temporal component. In this paper, we develop statistical…

The major sources of abundant data are constantly expanding with the available data collection methodologies in various applications - medical, insurance, scientific, bio-informatics and business. These data sets may be distributed…

Accurate theoretical prediction for halo mass function across a broad cosmological space is crucial for the forthcoming China Space Station Telescope (CSST) observations, which will capture cosmological information from multiple probes,…

We introduce statistical techniques required to handle complex computer models with potential applications to astronomy. Computer experiments play a critical role in almost all fields of scientific research and engineering. These computer…

Analyzing the covariance structure of data is a fundamental task of statistics. While this task is simple for low-dimensional observations, it becomes challenging for more intricate objects, such as multivariate functions. Here, the…

This paper considers the problem of estimating a change point in the covariance matrix in a sequence of high-dimensional vectors, where the dimension is substantially larger than the sample size. A two-stage approach is proposed to…

We consider the problem of estimating a high-dimensional covariance matrix from a small number of observations when covariates on pairs of variables are available and the variables can have spatial structure. This is motivated by the…

Constraints on cosmological parameters are often distilled from sky surveys by fitting templates to summary statistics of the data that are motivated by a fiducial cosmological model. However, recent work has shown how to estimate the…

Physical processes rarely occur in isolation, rather they influence and interact with one another. Thus, there is great benefit in modeling potential dependence between both spatial locations and different processes. It is the interaction…

We study the mean number counts and two-point correlation functions, along with their covariance matrices, of cosmological surveys such as for clusters. In particular, we consider correlation functions averaged over finite redshift…