Likelihood ratio
How much more probable the evidence is under one hypothesis than another.
What it means
A likelihood ratio compares the probability of the observed data under one hypothesis to its probability under a competing hypothesis, quantifying the strength of evidence the data provide for one over the other. In Bayesian terms it is exactly the factor by which the prior odds are multiplied to obtain the posterior odds, making it the natural currency of belief updating. In diagnostics, a high positive likelihood ratio means a result is much more expected when the condition is present than absent, sharply raising the probability of disease. It separates the evidential weight of data from the prior, clarifying that the same result updates beliefs differently depending on where one started.
Examples
A diagnostic finding ten times more likely in sick than healthy people carries a positive likelihood ratio of 10, multiplying the pre-test odds tenfold.
A spam filter sees the word 'invoice'. If it turns up in a fifth of spam and a twentieth of real mail, that one word multiplies the odds of spam fourfold.
A forensic scientist reports the fibres are far more expected if the suspect's coat is the source than if it is not. That ratio, not guilt, is what the evidence weighs.
First described in Neyman & Pearson; likelihoodist tradition (Edwards, Royall).