Optimal weighting in fNL constraints from large scale structure in an idealised case

We consider the problem of optimal weighting of tracers of structure for the purpose of constraining the non-Gaussianity parameter fNL. We work within the Fisher matrix formalism expanded around fiducial model with fNL = 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 fNL 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.