Given a piece of evidence e0 and two hypothsese Hi and Hj, the likelihood ratio between them is the ratio of the likelihood each hypothesis assigns to e0.
For example, imagine the evidence is e0 = "Mr. Boddy was poisoned", and the hypotheses are HP = "Professor Plum did it" and HW = "Mrs. White did it." Let's say that, if Professor Plum were the killer, we're 25% sure he would have used poison. Let's also say that, if Mrs. White were the killer, there's only a 5% chance she would have used poison. Then the likelihood ratio of e0 between HP and HW is 25/5 = 5. This likelihood ratio says that HP assigns five times as much likelihood to e0 as does HW, which means that the evidence supports the "Plum did it" hypothesis five times as much as it supports the "Mrs. White did it" hypothesis.
Likelihood ratios such as 5/1 are sometimes written (5:1) to emphasize the fact that they can be multiplied by odds in order to update them, as per Bayes' rule.
For example, imagine the evidence is e0 = "Mr. Boddy was poisoned"knifed", and the hypotheses are HP = "Professor Plum did it" and HW = "Mrs. White did it." Let's say that, if Professor Plum were the killer, we're 25% sure he would have used poison.a knife. Let's also say that, if Mrs. White were the killer, there's only a 5% chance she would have used poison.a knife. Then the likelihood ratio of e0 between HP and HW is 25/5 = 5. This likelihood ratio5, which says that HP assigns five times as much likelihood to e0 as does HW, which means that the evidence supports the "Plum did it" hypothesis five times as much as it supports the "Mrs. White did it" hypothesis.
Likelihood ratios such as 5/1 are sometimes writtenA likelihood ratio of 5 denotes relative likelihoods of (5:1). to emphasize the fact that theyRelative likelihoods can be multiplied by odds in order to update them,those odds, as per Bayes' rule.
Given a piece of evidence e0 and two hypothsesehypotheses Hi and Hj, the likelihood ratio between them is the ratio of the likelihood each hypothesis assigns to e0.