An integrated data analysis system based on Bayesian inference has been developed for the TJ-II stellarator. It reconstructs the electron density profile at a single time point, using data from interferometry, reflectometry, Thomson Scattering, and the Helium beam, while providing a detailed error analysis. In this work, we present a novel analysis of the ambiguity inherent in profile reconstruction from reflectometry, and show how the Integrated Data Analysis approach elegantly resolves it. Several examples of the application of the technique are provided, in both low-density discharges with and without electrode biasing, and in high-density discharges with an (L-H) confinement transition.