||The paper describes a novel statistical framework that was developed to derive radial profiles of thermodynamic quantities in the Scrape-Off Layer (SOL) of tokamak devices starting from basic properties of filamentary fluctuations that generate them. The framework changes the emphasis from interpreting and predicting diffusive/advective coefficients to describe SOL transport to understanding the statistics and dynamics of the filamentary structures. Experimental and numerical tools were developed to provide this input. In particular, it was developed a novel fast camera analysis technique based on wide angle pseudo-inversion of the light emitted by the filaments coupled with convolutional neural networks. Probability density functions for filament widths, amplitudes, waiting times and toroidal separation were obtained, finding, for example, that filaments do not have a clear modal structure. A Bayesian analysis of Langmuir probe data at the midplane shows that filaments are well matched by individual independent events and that are not generated in the SOL. 3D numerical simulations confirm that filaments that are sufficiently far apart (~5 widths) do not interact. Electromagnetic effects, important for inter-ELM filaments, show that the electrical connection to the target can be lost at sufficiently high or long enough connection lengths, leading to faster filaments and increased cross field transport. Finally, MAST and JET data were successfully matched with profiles calculated with the statistical framework.