Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userThe effect on cosmological parameter estimation of a parameter dependent covariance matrix
66
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Cosmological large-scale structure analyses based on two-point correlation functions often assume a Gaussian likelihood function with a fixed covariance matrix. We study the impact on cosmological parameter estimation of ignoring the parameter dependence of this covariance matrix, focusing on the particular case of joint weak-lensing and galaxy clustering analyses. Using a Fisher matrix formalism (calibrated against exact likelihood evaluation in particular simple cases), we quantify the effect of using a parameter dependent covariance matrix on both the bias and variance of the parameters. We confirm that the approximation of a parameter-independent covariance matrix is exceptionally good in all realistic scenarios. The information content in the covariance matrix (in comparison with the two point functions themselves) does not change with the fractional sky coverage. Therefore the increase in information due to the parameter dependent covariance matrix becomes negligible as the number of modes increases. Even for surveys covering less than $1%$ of the sky, this effect only causes a bias of up to ${cal O}(10%)$ of the statistical uncertainties, with a misestimation of the parameter uncertainties at the same level or lower. The effect will only be smaller with future large-area surveys. Thus for most analyses the effect of a parameter-dependent covariance matrix can be ignored both in terms of the accuracy and precision of the recovered cosmological constraints.
rate research
Read More
Cosmological parameter estimation is entering a new era. Large collaborations need to coordinate high-stakes analyses using multiple methods; furthermore such analyses have grown in complexity due to sophisticated models of cosmology and systematic uncertainties. In this paper we argue that modularity is the key to addressing these challenges: calculations should be broken up into interchangeable modular units with inputs and outputs clearly defined. We present a new framework for cosmological parameter estimation, CosmoSIS, designed to connect together, share, and advance development of inference tools across the community. We describe the modules already available in CosmoSIS, including CAMB, Planck, cosmic shear calculations, and a suite of samplers. We illustrate it using demonstration code that you can run out-of-the-box with the installer available at http://bitbucket.org/joezuntz/cosmosis
Fisher Information Matrix methods are commonly used in cosmology to estimate the accuracy that cosmological parameters can be measured with a given experiment, and to optimise the design of experiments. However, the standard approach usually assumes both data and parameter estimates are Gaussian-distributed. Further, for survey forecasts and optimisation it is usually assumed the power-spectra covariance matrix is diagonal in Fourier-space. But in the low-redshift Universe, non-linear mode-coupling will tend to correlate small-scale power, moving information from lower to higher-order moments of the field. This movement of information will change the predictions of cosmological parameter accuracy. In this paper we quantify this loss of information by comparing naive Gaussian Fisher matrix forecasts with a Maximum Likelihood parameter estimation analysis of a suite of mock weak lensing catalogues derived from N-body simulations, based on the SUNGLASS pipeline, for a 2-D and tomographic shear analysis of a Euclid-like survey. In both cases we find that the 68% confidence area of the Omega_m-sigma_8 plane increases by a factor 5. However, the marginal errors increase by just 20 to 40%. We propose a new method to model the effects of nonlinear shear-power mode-coupling in the Fisher Matrix by approximating the shear-power distribution as a multivariate Gaussian with a covariance matrix derived from the mock weak lensing survey. We find that this approximation can reproduce the 68% confidence regions of the full Maximum Likelihood analysis in the Omega_m-sigma_8 plane to high accuracy for both 2-D and tomographic weak lensing surveys. Finally, we perform a multi-parameter analysis of Omega_m, sigma_8, h, n_s, w_0 and w_a to compare the Gaussian and non-linear mode-coupled Fisher matrix contours. (Abridged)
In a Gaussian graphical model, the conditional independence between two variables are characterized by the corresponding zero entries in the inverse covariance matrix. Maximum likelihood method using the smoothly clipped absolute deviation (SCAD) penalty (Fan and Li, 2001) and the adaptive LASSO penalty (Zou, 2006) have been proposed in literature. In this article, we establish the result that using Bayesian information criterion (BIC) to select the tuning parameter in penalized likelihood estimation with both types of penalties can lead to consistent graphical model selection. We compare the empirical performance of BIC with cross validation method and demonstrate the advantageous performance of BIC criterion for tuning parameter selection through simulation studies.
The ability to obtain reliable point estimates of model parameters is of crucial importance in many fields of physics. This is often a difficult task given that the observed data can have a very high number of dimensions. In order to address this problem, we propose a novel approach to construct parameter estimators with a quantifiable bias using an order expansion of highly compressed deep summary statistics of the observed data. These summary statistics are learned automatically using an information maximising loss. Given an observation, we further show how one can use the constructed estimators to obtain approximate Bayes computation (ABC) posterior estimates and their corresponding uncertainties that can be used for parameter inference using Gaussian process regression even if the likelihood is not tractable. We validate our method with an application to the problem of cosmological parameter inference of weak lensing mass maps. We show in that case that the constructed estimators are unbiased and have an almost optimal variance, while the posterior distribution obtained with the Gaussian process regression is close to the true posterior and performs better or equally well than comparable methods.
We perform a model independent reconstruction of the cosmic expansion rate based on type Ia supernova data. Using the Union 2.1 data set, we show that the Hubble parameter behaviour allowed by the data without making any hypothesis about cosmological model or underlying gravity theory is consistent with a flat LCDM universe having H_0 = 70.43 +- 0.33 and Omega_m=0.297 +- 0.020, weakly dependent on the choice of initial scatter matrix. This is in closer agreement with the recently released Planck results (H_0 = 67.3 +- 1.2, Omega_m = 0.314 +- 0.020) than other standard analyses based on type Ia supernova data. We argue this might be an indication that, in order to tackle subtle deviations from the standard cosmological model present in type Ia supernova data, it is mandatory to go beyond parametrized approaches.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
