Statistical biases in parametrized searches for gravitational-wave polarizations

TL;DR

This paper examines how event selection biases in gravitational-wave data analysis can distort the measurement of scalar polarization modes, highlighting overestimation issues in certain models.

Contribution

It demonstrates the impact of prior-based event selection on scalar mode amplitude estimation in gravitational-wave polarization tests, revealing potential biases.

Findings

Scalar dipole amplitude overestimated when true value is nonzero

No false deviation detected when scalar mode is absent

Biases are significant in scalar dipole models, less so in quadrupole models

Abstract

In tests of gravity using gravitational waves (GWs), GW events analyzed are often selected based on specific criteria, particularly the signal-to-noise ratio. However, such event selection can introduce bias into parameter estimation unless the selection effect is appropriately taken into account in the analysis. In this paper, we investigate how event selection with certain prior information affects parameter inference within the scalar-tensor polarization framework, focusing on the measurement of the scalar mode amplitude parameters. We find that for the Tensor+Scalar(dipole) model, the amplitude of the scalar dipole radiation is overestimated when its true value is nonzero while there is no false deviation in the absence of the scalar mode. The same bias is expected to occur also for the Tensor+Scalar(quadrupole) model. However, the error typically exceeds the bias as the scalar quadrupole mode is difficult to be distinguished from the tensor mode.