The Bayesian theory to discern different hypotheses when given experimental evidence (data) was developed by Rev. Thomas Bayes in 1763. Bayes' theorem allows calculation of the probability of an hypothesis Hi based on available evidence E. This is written Pr(Hi|E).
According to Bayes, for N competing and mutually exclusive hypotheses:
                              Pr          ⁡                      (                                          H                i                            |              E                        )                          =                                            PR              ⁡                              (                                  E                  |                                      H                    i                                                  )                                      ⁢                          Pr              ⁡                              (                                  H                  i                                )                                                                        ∑                              j                =                1                            N                        ⁢                                          Pr                ⁡                                  (                                      E                    |                                          H                      j                                                        )                                            ⁢                              Pr                ⁡                                  (                                      H                    j                                    )                                                                                        (        1        )            where Pr(Hi|E) is the probability of the hypothesis H given evidence E, and Pr(Hi) is the prior probability (before any evidence) of the hypothesis and the sum is over all mutually exclusive hypotheses. The term Pr(E|Hi) is either the probability of finding the evidence E given the truth of the hypothesis Hi, or the probability density function of the hypothesis Hi at a value given by the evidence E (this is also known as the ‘likelihood’). In the absence of any other prior knowledge of the system, each Pr(Hi) can be set as 1/N, the so-called “flat prior”.
The inventors of the present invention have applied Bayesian theory to develop a statistical tool for the treatment in real time of data from unknown sources which allows for comparison of the real time data with a template of previously recorded data from known sources in order to effect a decision with a given probability of the source of the real time data being generated by one of the known sources.