Arsia Mons - the southernmost of the Tharsis shield volcanoes - has the largest diameter single summit caldera on Mars indicating the presence of a single large magma chamber underneath. The subsidence at the summit, caused by emptying of this large chamber, followed by rift-fed volcanism on the caldera floor not observed in the other Tharsis shields point to longer duration activity and higher degree of structural evolution for Arsia Mons when compared to the other Tharsis Montes (Ascraeus Mons and Pavonis Mons). At the summit, possible ash deposits near the caldera rim, <10 km away from ~130 Myr young lava flows on the caldera floor, have been identified. The eruption history of Arsia Mons is not well-known, especially the question of whether the shield volcano underwent periods of explosive style of eruption in between prolonged effusive activity. In this study, we use orbital sounding radar data from SHAllow RADar (SHARAD) to investigate the volcanic stratigraphy within the caldera. SHARAD has been used extensively in assessing the near-subsurface geology on Mars, including volcanic provinces like Elysium and Tharsis where SHARAD has been successful in detecting buried lava flows. Using a similar approach, we use SHARAD backscatter measurements from the subsurface to map dielectric horizons. These dielectric boundaries are caused by an abrupt change in the density of the subsurface unit, thereby allowing us to delineate different lithologies. We find groups of reflectors at two locations within the caldera - west and south - with different radar backscatter characteristics. Using these distinct properties as input, we perform inverse modeling of the one-dimensional signal propagation equations to obtain the dielectric permittivity and loss tangent of the subsurface layers. We use a Markov Chain Monte Carlo approach to determine the probability distribution of these two variables that could give rise to the observed SHARAD data. The results show spatially diverse dielectric structures likely caused by spatial and temporal differences in the style of volcanism. We argue that explosive basaltic eruptions in the caldera, followed by mostly effusive post-caldera volcanism, could explain the unusual distribution of dielectric properties of the reflectors close to the caldera wall. We also examine possible causes for the uneven spatial distribution of layered radar interfaces by incorporating analysis of thermal inertia observations. This provides further insight into preferential detection of subsurface reflectors by SHARAD in volcanic units.