Optimal dataset combining in f_nl constraints from large scale structure in an idealised case

TL;DR

This paper derives optimal weighting schemes for tracers of large-scale structure to maximize constraints on the non-Gaussianity parameter f_NL, revealing that simple division into two samples is often near-optimal.

Contribution

It provides an analytic framework for optimal weighting of tracers to improve f_NL constraints, including simple weighting functions that recover maximal information.

Findings

Optimal weighting schemes enhance f_NL constraints.

Simple division into two samples is nearly optimal under certain conditions.

Weighted sampling approaches outperform naive methods in constraining non-Gaussianity.

Abstract

We consider the problem of optimal weighting of tracers of structure for the purpose of constraining the non-Gaussianity parameter f_NL. We work within the Fisher matrix formalism expanded around fiducial model with f_NL=0 and make several simplifying assumptions. By slicing a general sample into infinitely many samples with different biases, we derive the analytic expression for the relevant Fisher matrix element. We next consider weighting schemes that construct two effective samples from a single sample of tracers with a continuously varying bias. We show that a particularly simple ansatz for weighting functions can recover all information about f_NL in the initial sample that is recoverable using a given bias observable and that simple division into two equal samples is considerably suboptimal when sampling of modes is good, but only marginally suboptimal in the limit where Poisson errors dominate.