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Register a new userNon-Gaussian error bars in galaxy surveys -- II
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Added by
Joachim Harnois-Deraps
Publication date
2012
fields
Physics
and research's language is
English
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(Abridged) Estimating the uncertainty on the matter power spectrum internally (i.e. directly from the data) is made challenging by the simple fact that galaxy surveys offer at most a few independent samples. In addition, surveys have non-trivial geometries, which make the interpretation of the observations even trickier, but the uncertainty can nevertheless be worked out within the Gaussian approximation. With the recent realization that Gaussian treatments of the power spectrum lead to biased error bars about the dilation of the baryonic acoustic oscillation scale, efforts are being directed towards developing non-Gaussian analyses, mainly from N-body simulations so far. Unfortunately, there is currently no way to tell how the non-Gaussian features observed in the simulations compare to those of the real Universe, and it is generally hard to tell at what level of accuracy the N-body simulations can model complicated non-linear effects such as mode coupling and galaxy bias. We propose in this paper a novel method that aims at measuring non-Gaussian error bars on the matter power spectrum directly from galaxy survey data. We utilize known symmetries of the 4-point function, Wiener filtering and principal component analysis to estimate the full covariance matrix from only four independent fields with minimal prior assumptions. With the noise filtering techniques and only four fields, we are able to recover the Fisher information obtained from a large N=200 sample to within 20 per cent, for k < 1.0 h/Mpc. Finally, we provide a prescription to extract a noise-filtered, non-Gaussian, covariance matrix from a handful of fields in the presence of a survey selection function.
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Model uncertainty quantification is an essential component of effective data assimilation. Model errors associated with sub-grid scale processes are often represented through stochastic parameterizations of the unresolved process. Many existing Stochastic Parameterization schemes are only applicable when knowledge of the true sub-grid scale process or full observations of the coarse scale process are available, which is typically not the case in real applications. We present a methodology for estimating the statistics of sub-grid scale processes for the more realistic case that only partial observations of the coarse scale process are available. Model error realizations are estimated over a training period by minimizing their conditional sum of squared deviations given some informative covariates (e.g. state of the system), constrained by available observations and assuming that the observation errors are smaller than the model errors. From these realizations a conditional probability distribution of additive model errors given these covariates is obtained, allowing for complex non-Gaussian error structures. Random draws from this density are then used in actual ensemble data assimilation experiments. We demonstrate the efficacy of the approach through numerical experiments with the multi-scale Lorenz 96 system using both small and large time scale separations between slow (coarse scale) and fast (fine scale) variables. The resulting error estimates and forecasts obtained with this new method are superior to those from two existing methods.
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