Accuracy of full lensed P(D) modeling relative to the tail statistic

Determine whether a forward model of the full lensed P(D), evaluated over the entire distribution and using the externally supplied magnification profile together with the count model, is more accurate than the generalized-Pareto tail-shape statistic alone, while quantifying the trade-off between increased sensitivity and exposure to calibration, cluster-dust, and clustered-CIB systematics.

Background

The paper argues that the dominant lensing response in the lensed P(D) is broadening of the confusion core and modulation of the exceedance rate, whereas the tail-shape response Δξ is much smaller. Consequently, a full forward model of the lensed P(D) over the whole distribution could be substantially more sensitive than the tail statistic alone.

However, exploiting the blended core would sacrifice the tail method’s invariance to absolute calibration and would make the analysis vulnerable to cluster dust and clustered-CIB biases. The authors therefore leave unresolved whether the increased sensitivity of full-distribution modeling is accompanied by improved accuracy, making a quantitative assessment of this sensitivity–accuracy trade-off an explicit open problem.