Testing Randomness Online

The hypothesis of randomness is fundamental in statistical machine learning and many areas nonparametric statistics; it says that the observations are assumed to be independent coming from same unknown probability distribution. This close, certain respects, exchangeability, which postulates distribution invariant with respect their permutations. paper reviews known methods testing two hypotheses concentrating on online mode testing, when arrive sequentially. All for these based conformal martingales, defined studied detail. emphasizes conceptual practical aspects states kinds results. Validity results limit a false alarm or frequency alarms various procedures including versions CUSUM Shiryaev-Roberts procedures. Efficiency establish connections between randomness, martingales.