Impact of Observational Systematics on Cosmological Parameter Inference
For a given survey, the galaxy window function, $W_g$, encodes what weight a particular pixel should be given when calculating galaxy angular clustering. Most surveys account for the window function by estimating it from observational systematics such as imaging depth, galactic extinctio, etc., and then divide out $W_g$ from the data to get a uniform galaxy overdensity map.
However, this procedure of dividing the observed galaxy map by $W_g$ can bias the overdensity map, $\delta_g$. We propose a better estimator for the $\delta_g$. We also show that using only the best fit window function does not treat the multiplicative and additive biases properly, and can bias cosmological inference. We propose an alternative probablistic scheme to deal with the window function in the cosmological inference step that debiases these effects.