x1=s1 is evidence for x2=k2 with evidence strength x3=s3=p1 (numerator x4=p2, denominator x5=p3, believer x6=k1, new odds x7=k3, old odds x8=s2); x1 is Bayesian evidence for belief / prediction / hypothesis x2, with evidence magnitude / strength (and direction), as a likelihood ratio as odds, x3 since the hypothesis predicts the evidence to degree / with probability x4 and since not-hypothesis predicts the evidence to degree / with probability x5, updating x6's belief strength / odds / confidence to posterior odds / new confidence x7 from prior odds / old confidence x8; x1 is evidence for x2 with evidence strength and direction x3 due to how much better (or worse) the hypothesis predicts the evidence (amount x4) than not-hypothesis predicts the evidence (amount x5), according to knowledge / truth / subjective probability judge / assigner / evaluator x6, who after accounting for the evidence has odds in the hypothesis x7 after prior odds x8.
This is evidence as understood in a Bayesian framework, arising from Bayes' theorem. Evidence, in terms of Bayes' rule, updates degrees of belief by decomposing the update of the probability / magnitude to the posterior (afterwards) probability of the belief into its prior (before) probability and (multiplied by) the likelihood ratio. The likelihood ratio represents how much better the belief predicts the evidence (how likely is the evidence if the hypothesis is true?) than not-belief predicts the hypothesis (how likely is the evidence if the hypothesis is false?). It is derived mathematically from probability theory. ni'o This formulation uses Bayes' rule formulation, not the Bayes' theorem style. They are equivalent, but Bayes' rule allows separation of the evidence strength from the prior odds, providing for an intuitive form of just newOdds ＝ oldOdds ⋅ evidenceStrength, since it uses odds, except in the likelihood ratio (the likelihood ratio is evidenceStrength), the numerator and the denominator are probabilities (it's a ratio of probabilities, but otherwise it's in terms of odds). The Bayes' Theorem style, an equivalent formula, does not use odds but only probability. ni'o Useful for science. ni'o See also: ni'i'e.