Early approaches to characterizing errors in target displacement during a fractionated course of radiotherapy assumed that the underlying fraction-to-fraction variability in target displacement, known as the 'treatment error' or 'random error', could be regarded as constant across patients. More recent approaches have modelled target displacement allowing for differences in random error between patients. However, until recently it has not been feasible to compare the goodness of fit of alternate models of random error rigorously. This is because the large volumes of real patient data necessary to distinguish between alternative models have only very recently become available. This work uses real-world displacement data collected from 365 patients undergoing radical radiotherapy for prostate cancer to compare five candidate models for target displacement. The simplest model assumes constant random errors across patients, while other models allow for random errors that vary according to one of several candidate distributions. Bayesian statistics and Markov Chain Monte Carlo simulation of the model parameters are used to compare model goodness of fit. We conclude that modelling the random error as inverse gamma distributed provides a clearly superior fit over all alternatives considered. This finding can facilitate more accurate margin recipes and correction strategies.