Combining the analysis of multiple diagnostics and well-chosen prior information in the framework of Bayesian probability theory, the Integrated Data Analysis code (IDA Fischer et al 2010 Fusion Sci. Technol. 58 675-84) can provide density and temperature radial profiles of fusion plasmas. These IDA-fitted measurements are then used for further analysis, such as discharge simulations and other experimental data analysis. Since IDA considers measurement data, which is frequently fragmentary, with statistical and systematic uncertainties, which are often difficult to quantify, from a heterogeneous set of diagnostics, the fitted profiles and their gradients may be in contradiction to well-established expectations from transport theory. Using the modeling suite ASTRA coupled with the quasi-linear transport solver TGLF, we have created a loop in which simulated profiles and their uncertainties are fed back into IDA as an additional prior, thus providing constraints about the physically reasonable parameter space. We apply this physics-motivated prior to several different plasma scenarios and find improved heat flux match, while still matching the experimental data. This work feeds into a broader effort to make IDA more robust against measurement uncertainties or lack of measurements by combining multiple transport solvers with different levels of complexity and computing costs in a multi-fidelity approach.