GEOMAX: beyond linear compression for 3pt galaxy clustering statistics. (arXiv:1912.01011v1 [astro-ph.CO])

<a href="http://arxiv.org/find/astro-ph/1/au:+Gualdi_D/0/1/0/all/0/1">Davide Gualdi</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Gil_Marin_H/0/1/0/all/0/1">Héctor Gil-Marín</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Manera_M/0/1/0/all/0/1">Marc Manera</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Joachimi_B/0/1/0/all/0/1">Benjamin Joachimi</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Lahav_O/0/1/0/all/0/1">Ofer Lahav</a>

We present the GEOMAX algorithm and its Python implementation for a two-step

compression of bispectrum measurements. The first step groups bispectra by the

geometric properties of their arguments; the second step then maximises the

Fisher information with respect to a chosen set of model parameters in each

group. The algorithm only requires the derivatives of the data vector with

respect to the parameters and a small number of mock data, producing an

effective, non-linear compression. By applying GEOMAX to bispectrum monopole

measurements from BOSS DR12 CMASS redshift-space galaxy clustering data, we

reduce the $68%$ credible intervals for the inferred parameters

$left(b_1,b_2,f,sigma_8right)$ by $left(50.4%,56.1%,33.2%,38.3%right)$

with respect to standard MCMC on the full data vector. We run the analysis and

comparison between compression methods over one hundred galaxy mocks to test

the statistical significance of the improvements. On average GEOMAX performs

$sim15%$ better than geometrical or maximal linear compression alone and is

consistent with being lossless. Given its flexibility, the GEOMAX approach has

the potential to optimally exploit three-point statistics of various

cosmological probes like weak lensing or line-intensity maps from current and

future cosmological data-sets such as DESI, Euclid, PFS and SKA.

We present the GEOMAX algorithm and its Python implementation for a two-step

compression of bispectrum measurements. The first step groups bispectra by the

geometric properties of their arguments; the second step then maximises the

Fisher information with respect to a chosen set of model parameters in each

group. The algorithm only requires the derivatives of the data vector with

respect to the parameters and a small number of mock data, producing an

effective, non-linear compression. By applying GEOMAX to bispectrum monopole

measurements from BOSS DR12 CMASS redshift-space galaxy clustering data, we

reduce the $68%$ credible intervals for the inferred parameters

$left(b_1,b_2,f,sigma_8right)$ by $left(50.4%,56.1%,33.2%,38.3%right)$

with respect to standard MCMC on the full data vector. We run the analysis and

comparison between compression methods over one hundred galaxy mocks to test

the statistical significance of the improvements. On average GEOMAX performs

$sim15%$ better than geometrical or maximal linear compression alone and is

consistent with being lossless. Given its flexibility, the GEOMAX approach has

the potential to optimally exploit three-point statistics of various

cosmological probes like weak lensing or line-intensity maps from current and

future cosmological data-sets such as DESI, Euclid, PFS and SKA.

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