On the Role of Quantiles in Quantum Mechanics

The implications of describing quantum effects with the help of concepts originating from classical continuum mechanics is to this day a matter of contention. Its manifestations outside of canonical theory in particular, such as the de-Broglie-Bohm theory, continue to be highly controversial. The continued refinement of measurement techniques and, arguably, the emergence of the weak measurement scheme now serves as a driver for empirical results becoming available on behalf of such interpretations. In this thesis we explore how such results and the theoretical apparatus behind it can be understood from a purely statistical perspective. We provide a generalisation to this approach, gauging its usefulness beyond the position-focused representation the hydrodynamical approach is usually centred on. We then go on to promote a scheme that allows one to produce the mentioned experimental results in a simpler and more accessible way, comparing the two approaches in terms of accuracy and efficiency in the process.