Prion diseases (mad cow disease, CJD, etc.) are a group of fatal neurodegenerative disorders associated with structural conversion of a normal, mostly\alpha-helical cellular prion protein (PrP) into a pathogenic \beta-sheet-rich conformation. Little is known about which parts of PrP undergo conformational transition and how disease associated mutations facilitate this transition. In this work, we utilize a computational statistical approach to detect unusual patterns in prion protein. (i) We construct a novel entropic index which provides a quantitative measure of context-dependent conformational flexibility of a sequence fragment. This index is used to study conformational flexibility of PrP fragments. (ii) We identify PrP fragments that show unusual intrinsic structural propensities. (iii) We estimate the statistical significance of clusters of disease-associated PrP mutations using a stochastic model of mutational process with unequal substitution rates and context-dependent mutational hot spots.