Joint measurements of ground deformation and micro-gravity changes are an indispensable component for any volcano monitoring strategy. A number of analytical mathematical models are available in the literature that can be used to fit geodetic data and infer source location, depth and density. Bootstrap statistical methods allow estimations of the range of the inferred parameters. Although analytical models often assume that the crust is elastic, homogenous and isotropic, they can take into account different source geometries, the influence of topography, and gravity background noise. The careful use of analytical models, together with high quality data sets, can produce valuable insights into the nature of the deformation/gravity source. Here we present a review of various modeling methods, and use the historical unrest at Long Valley caldera (California) from 1982 to 1999 to illustrate the practical application of analytical modeling and bootstrap to constrain the source of unrest. A key question is whether the unrest at Long Valley since the late 1970s can be explained without calling upon an intrusion of magma. The answer, apparently, is no. Our modeling indicates that the inflation source is a slightly tilted prolate ellipsoid (dip angle between 91° and 105°) at a depth of 6.5 to 7.9 km beneath the caldera resurgent dome with an aspect ratio between 0.44 and 0.60, a volume change from 0.161 to 0.173 km³ and a density of 1241 to 2093 kg/m³. The larger uncertainty of the density estimate reflects the higher noise of gravity measurements. These results are consistent with the intrusion of silicic magma with a significant amount of volatiles beneath the caldera resurgent dome.