Cosmological Systematics Beyond Nuisance Parameters : Form Filling Functions

TL;DR

This paper introduces a functional form filling method to better account for unknown cosmological systematics, avoiding biases from nuisance parameter marginalization, and demonstrates its application to cosmic shear measurements.

Contribution

It proposes a novel functional form filling approach for systematic errors, providing a more robust alternative to nuisance parameter marginalization in cosmology.

Findings

Parameter errors are sensitive to the choice of functions in marginalization.

Functional form filling is basis-independent and more comprehensive.

A shear calibration bias of |m(z)|< 0.001(1+z)^0.7 is needed for unbiased cosmology.

Abstract

In the absence of any compelling physical model, cosmological systematics are often misrepresented as statistical effects and the approach of marginalising over extra nuisance systematic parameters is used to gauge the effect of the systematic. In this article we argue that such an approach is risky at best since the key choice of function can have a large effect on the resultant cosmological errors. As an alternative we present a functional form filling technique in which an unknown, residual, systematic is treated as such. Since the underlying function is unknown we evaluate the effect of every functional form allowed by the information available (either a hard boundary or some data). Using a simple toy model we introduce the formalism of functional form filling. We show that parameter errors can be dramatically affected by the choice of function in the case of marginalising over a systematic, but that in contrast the functional form filling approach is independent of the choice of basis set. We then apply the technique to cosmic shear shape measurement systematics and show that a shear calibration bias of |m(z)|< 0.001(1+z)^0.7 is required for a future all-sky photometric survey to yield unbiased cosmological parameter constraints to percent accuracy. A module associated with the work in this paper is available through the open source iCosmo code available at http://www.icosmo.org .