Systematic and Statistical Uncertainties in Cepheid PL Relations: Incorporating a Cross-Filter Random-Phase Mitigation Approach

The Period-Luminosity (PL) relation of Cepheid variable stars is a fundamental tool for measuring extragalactic distances and constraining the Hubble constant (H0). Achieving high precision in PL based distances requires careful consideration of both systematic and statistical uncertainties. We review the main sources of these uncertainties in PL relations, highlighting the increasing impact of random-phase errors in single-epoch observations from limited temporal coverage, such as those obtained with the James Webb Space Telescope (JWST). We discuss mitigation strategies for systematic errors, including photo metric calibration offsets, metallicity effects, blending, and parallax biases, and quantify key contributors to statistical errors, such as photometric noise, intrinsic scatter, and phase-sampling limitations. Special attention is given to a recently proposed cross-filter random-phase correction method (Abdollahi et al., 2025), which recovers mean magnitudes from single-epoch data by exploiting correlations between PL residuals in different bands. This technique reduces the dispersion in the infrared PL relation by 28%, equivalent to an order-of-magnitude increase in effective temporal sampling, demonstrating an efficient path to improving Cepheid-based distance measurements and the precision of H0.