A Bayes factor is defined as the ratio of the probability of the observed data under which hypothesis to the probability under the other?

A Bayes factor is defined as the ratio of the probability of the observed data under which hypothesis to the probability under the other?

• A. The probability under the null hypothesis to the probability under the alternative.
• B. The probability under the alternative hypothesis to the probability under the null.
• C. The product of the probabilities of A and B.
• D. The difference between the probabilities of the data under the two hypotheses.

Answer: (B)

Bayes factors compare how well two competing hypotheses explain the observed data by taking the ratio of their likelihoods. It is defined as the probability of the data under the alternative hypothesis divided by the probability of the data under the null hypothesis: P(data | H1) / P(data | H0). A value greater than 1 indicates the data favor the alternative more than the null; a value less than 1 favors the null; a value around 1 means the data don’t strongly distinguish the two. These likelihoods are often marginal likelihoods, incorporating prior information about model parameters. It’s not a product or a difference of the two probabilities, and it’s not the ratio in the opposite direction.

Bayes factors compare how well two competing hypotheses explain the observed data by taking the ratio of their likelihoods. It is defined as the probability of the data under the alternative hypothesis divided by the probability of the data under the null hypothesis: P(data | H1) / P(data | H0). A value greater than 1 indicates the data favor the alternative more than the null; a value less than 1 favors the null; a value around 1 means the data don’t strongly distinguish the two. These likelihoods are often marginal likelihoods, incorporating prior information about model parameters. It’s not a product or a difference of the two probabilities, and it’s not the ratio in the opposite direction.