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The location, volume and physical states of magma reservoirs are primary controls on the eruptive behavior of volcanic systems. Fundamental to understanding and monitoring these systems is the ability to identify reservoir size and physical properties, in particular melt fraction which plays an important role in the rheology and stability of a magmatic system. Large silicic volcanic eruptions in the geological record suggest that extensive pockets of melt-rich silicic magma must exist in the subsurface but such melt pockets have not been detected by geophysics. This has led to the question of whether the reservoirs that feed large volcanic eruptions are only melt-rich for a short time and thus would only be detected by geophysics shortly prior to an eruption. Magnetotelluric data measure the electrical resistivity of the subsurface and are sensitive to subsurface fluids and partial melts making it a powerful tool for imaging subvolcanic magma reservoirs. This study examines the ability for magnetotelluric data to accurately estimate melt fraction using both stochastic Bayesian inversion and deterministic regularized inversion. Results from synthetic modelling indicate that magnetotelluric data are best able to predict the melt fraction for the thick melt-rich layer using both inversion methods, though both methods under-estimate the true amount of melt. In addition, magnetotelluric data can accurately detect changes in melt fraction from crystal-rich mush (0.1 melt fraction) to melt-rich magma (0.9 melt fraction) for thick layers. Thickness is a key parameter which provides a method to assess the total volume of melt present, but it is difficult to estimate using smooth regularized inversions. Fixed-dimension Bayesian inversions provide estimates of layer thickness and their uncertainties and it is shown that estimates of total volume of melt are more accurate for both thin (0.2 km) and thick (1 km) layers than individual estimates of melt fraction or thickness alone. The melt fraction of the thin melt-rich layer is under-estimated using both the deterministic inversion method and the most probable solution of the Bayesian inversion. The Bayesian distribution of solutions has long tails which includes the true solution and better represents the uncertainty of the modelled parameters. As we consider past large melt-rich caldera eruptions at Taupo (New Zealand), Toba (Indonesia), Yellowstone and Long Valley (USA), our analysis suggests that thin melt-rich, potentially eruptible zones involved in large (e.g. >500 km3) eruptions could be systematically misinterpreted as thicker non-eruptible crystal-rich mush zones. Testing the sensitivity of MT to detect melt accumulation in active magmatic systems has important implications for volcanic hazard assessment and the use of Bayesian inversions allows for a better understanding of the range of possible interpretations. • Bayesian inversion is used to estimate melt fraction from synthetic MT data. • MT data can detect melt fraction from 0.1 to 0.9 (immobile to mobile) for thick layers. • Smooth inversions often underestimate melt fractions especially for thin layers. • Melt volume and melt fraction is better characterized using Bayesian inversion. • Lack of geophysical evidence for thin melt-rich lenses does not preclude them. [ABSTRACT FROM AUTHOR]