Abstract
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 coincide unless the data covariance is exactly known. For sampled data covariances with Gaussiandistributed data and parameters, the parameter covariance matrix estimated from the width of the likelihood has a Wishart distribution, from which we derive the mean and covariance. This mean is biased and we propose an unbiased estimator of the parameter covariance matrix. Comparing our analytic results to a numerical Wishart sampler of the data covariance matrix we find excellent agreement. An accurate ansatz for the mean parameter covariance for the peak scatter estimator is found, and we fit its covariance to our numerical analysis. The mean is again biased and we propose an unbiased estimator for the peak parameter covariance. For sampled data covariances, the width estimator is more accurate than the peak scatter estimator. We investigate modelling the data covariance, or equivalently data compression, and show that the peak scatter estimator is less sensitive to biases in the model data covariance matrix than the width estimator, but requires independent realizations of the data to reduce the statistical error. If the model bias on the peak estimator is sufficiently low, this is promising, otherwise the sampled width estimator is preferable.
Original language  English 

Pages (fromto)  27282738 
Number of pages  11 
Journal  Monthly Notices of the Royal Astronomical Society 
Volume  442 
Issue number  3 
DOIs  
Publication status  Published  11 Aug 2014 
Keywords
 methods: data analysis
 methods: statistical
 cosmological parameters
 largescale structure of Universe
 POWER SPECTRUM COVARIANCE
 COSMIC SHEAR
 MATRIX
 INFORMATION
 STATISTICS
 PHYSICS
 SAMPLES
 IMPACT
 MATTER
 MODEL
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Andy Taylor
 School of Physics and Astronomy  Personal Chair in Astrophysics
Person: Academic: Research Active