A Malmquist-like bias in the inferred areas of diamond caustics and the resulting bias in inferred time delays for gravitationally lensed quasars.

Quadruply lensed quasars are visible only when the source quasar lies within the diamond caustic of the lensing galaxy. This condition creates a Malmquist-like selection effect in the population of observed quadruply lensed quasars, increasing the true caustic area. The inferred areas are therefore biased low by an amount proportional to the square of the uncertainty in the natural logarithm of the area, $\sigma_{\ln{A}}$. The inferred time delays, $\tau$, vary with the caustic area of the lensing galaxy as $\sqrt{A}$. As a consequence, model time delays are biased low, leading to underestimates of the Hubble constant. Classical Malmquist bias also plays a role, with inferred magnifications biased low. As magnification is strongly anti-correlated with the area of the caustic, this classical Malmquist bias has an effect opposite to, but smaller than, the effect of the area bias. The overall effect is estimated to be small (median bias of less than 1%), but has the potential to be larger. Current posterior plots do not include caustic area, which limits the capability to accurately estimate the bias. With anticipated increases in sample sizes (in particular with the completion of LSST), correction for these biases becomes increasingly important.