Bayes’ Theorem can be written in two different ways, in terms of probabilities, and in terms of odds ratios.
Bayes’ Theorem in the probability form is used to characterize the ‘Tasteability’ of the individual taste categories in terms of the four graded taste parameters – Appearance, Aroma, Mouthfeel, and Flavor.
It does this by computing the conditional probability of a taste event, given a joint set of graded taste parameters:
When written in the odds ratio form (see below), Bayes’ theorem relates the odds ratio in favour of the ‘Tasteability’ category (TCAT) given the taste data (POST_OR), to the odds ratio in favour of the TCAT in the absence of any taste data (PRE_OR). The factor that relates the two is the Likelihood Ratio (LR).
As the LR increases, so too do the odds in favor of the TCAT ( categories A,B,C, or D ), given the graded set of taste parameters ( columns B-E ) – the higher the odds (POST_OR), the greater the probability ( Pr( A | BCDE ) ) that the graded taste set Characterizes the given TCAT.
