Prior odds are defined as which ratio?

• A. The ratio of the likelihoods of the models given the data.
• B. The ratio of the probability of the alternative hypothesis to the null hypothesis, reflecting belief before looking at data.
• C. The ratio of the posterior probabilities of the hypotheses.
• D. The ratio of the sample sizes for two groups.

Answer: (B)

Prior odds represent your beliefs about how plausible the competing hypotheses are before you see any data. It is defined as the ratio P(H1) / P(H0): the probability of the alternative hypothesis divided by the probability of the null hypothesis, based on prior information or subjective judgment prior to observing the data. This captures how you’re leaning before the experiment or test. For example, if you start with prior odds of 3:1 in favor of the alternative, and the data later support the alternative with a Bayes factor of 2:1, your posterior odds would become 6:1 in favor of the alternative. The other options describe related quantities but not the prior odds: the Bayes factor compares data under the two models; the posterior odds come after updating with data; and the ratio of sample sizes is unrelated to hypothesis probabilities.