Reliable empirical quantification of atomic hydrogen (H) density in the Martian thermosphere and lower exosphere is needed for advancing understanding of current atmospheric processes such as thermal escape and their implications for past planetary evolution. In this presentation, we use observations of H emission at Lyman-alpha (121.6 nm) acquired across the Martian limb by the UV spectrograph (IUVS) onboard MAVEN to infer the solar cycle climatology of H density in this region. The emission is created by resonant scattering of solar Lyman-alpha photons, and we use sophisticated radiative transfer models to derive the associated H density distributions on the dayside of Mars during several MAVEN orbit periapsis intervals. Our analysis is based on a technique we first developed for terrestrial H density estimation from limb scanning data, an approach which yields Martian exospheric density estimates that are independent of IUVS sensitivity calibration and incident solar flux. The results provide unprecedented quantification of hydrogen density and thermal H escape in the Martian exosphere throughout the solar cycle. In addition, we use measured solar flux data to provide novel constraints on the IUVS absolute sensitivity that are independent of those derived from stellar calibration. We will also present a comparative analysis of RT model formulation, input specification, and assumptions on the derived density estimates.