We present a simple formalism to interpret the observations of two galaxy statistics, the UV luminosity function (LF) and two-point correlation functions for star-forming galaxies at z∼4, 5, and 6 in the context of Λ cold dark matter cosmology. Both statistics are the result of how star formation takes place in dark matter halos, and thus are used to constrain how UV light depends on halo properties, in particular halo mass. The two physical quantities we explore are the star formation duty cycle, and the range of UV luminosity that a halo of mass M can have (mean and variance). The former directly addresses the typical duration of star formation activity in halos, while the latter addresses the averaged star formation history and regularity of gas inflow into these systems. In the context of this formalism, we explore various physical models consistent with all the available observational data, and find the following: (1) the typical duration of star formation observed in the data is ≲0.4 Gyr (1σ); (2) the inferred scaling law between the observed LUV and halo mass M from the observed faint-end slope of the LFs is roughly linear out to M ≈ 1011.5–1012 h−1 M☉ at all redshifts probed in this work; and (3) the observed LUV for a fixed halo mass M decreases with time, implying that the star formation efficiency (after dust extinction) is higher at earlier times. We explore several different physical scenarios relating star formation to halo mass, but find that these scenarios are indistinguishable due to the limited range of halo mass probed by our data. In order to discriminate between different scenarios, we discuss the possibility of using the bright-faint galaxy cross-correlation functions and more robust determination of luminosity-dependent galaxy bias for future surveys.