English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Non-linear gravitational collapse introduces non-Gaussian statistics into thematter fields of the late Universe. As the large-scale structure is the targetof current and future observational campaigns, one would ideally like to havethe full probability density function of these non-Gaussian fields. The onlyviable way we see to achieve this analytically, at least approximately and inthe near future, is via the Edgeworth expansion. We hence rederive thisexpansion for Fourier modes of non-Gaussian fields and then continue by puttingit into a wider statistical context than previously done. We show that in itsoriginal form, the Edgeworth expansion only works if the non-Gaussian signal isaveraged away. This is counterproductive, since we target theparameter-dependent non-Gaussianities as a signal of interest. We hence alterthe analysis at the decisive step and now provide a roadmap towards acontrolled and unadulterated analysis of non-Gaussianities in structureformation (with the Edgeworth expansion). Our central result is that, althoughthe Edgeworth expansion has pathological properties, these can be predicted andavoided in a careful manner. We also show that, despite the non-Gaussianitycoupling all modes, the Edgeworth series may be applied to any desired subsetof modes, since this is equivalent (to the level of the approximation) tomarginalising over the exlcuded modes. In this first paper of a series, werestrict ourselves to the sampling properties of the Edgeworth expansion,i.e.~how faithfully it reproduces the distribution of non-Gaussian data. Afollow-up paper will detail its Bayesian use, when parameters are to beinferred.

On the use of the Edgeworth expansion in cosmology I: how to foresee and evade its pitfalls