Polka-dotted Stars: a Hierarchical Model for Mapping Stellar Surfaces Using Occultation Light Curves and the Case of TOI-3884

We present StarryStarryProcess, a novel hierarchical Bayesian framework for mapping stellar surfaces using exoplanet transit light curves. While previous methods relied solely on stellar rotational light curves -- which contain limited information about spot properties -- our approach leverages planetary transits as probes of stellar surfaces. When a planet crosses a spot during transit, it creates a distinctive change in the light curve that directly reveals spot properties. Our model integrates planetary transit modeling with stellar variability analysis by combining the spherical harmonic surface map representation from starry, the probabilistic approach to spot properties of StarryProcess, and a comprehensive transit model that accounts for spot-crossing events during transits. We demonstrate through synthetic data experiments that our model successfully recovers spot distributions, stellar orientation, and spot physical properties. We extend the framework to handle evolving stellar surfaces through time-dependent modeling. Applying our method to TESS observations of TOI-3884, we find evidence for high-latitude spot concentrations and significant spin-orbit misalignment. The transit-based approach overcomes fundamental limitations of previous models by providing constraints on spot properties that would remain hidden in the null space of rotational light curves alone. This methodology enables more accurate exoplanet characterization by disentangling stellar activity due to starspots from planetary signals while simultaneously providing insights into stellar magnetic activity patterns. The whole paper is reproducible, and can be found by clicking the GitHub icon.