Galaxy formation is one of the most intractable phenomena in astrophysics due to the enormous complexity and diversity in the assembly histories of individual galaxies. Modern galaxy surveys provide a unique avenue to understanding galaxy formation physics in a statistical context, through various large-scale structure measurements and the weak gravitational lensing of large numbers of galaxies. I will introduce a new probabilistic framework, called the "iHOD" model, which enables strong constraints on the stellar-to-halo mass relation and the underlying driver for the quenching of star formation in galaxies probed by the Sloan Digital Sky Survey. I will also highlight the advantages of the iHOD model by comparing it with traditional HOD and SHAM methods, as well as an age-matching model in which galaxy quenching depends on halo age at fixed stellar mass. Lastly I will discuss the prospect of extending the iHOD framework to constrain the curious effect of "galaxy assembly bias" using marked statistics.