Contents
Does prior distribution affect Bayes Factor?
As we have seen, the Bayes Factor requires us to specify a prior distribution. Even if we use the default prior in JASP, there are some underlying assumptions which may or may not be reasonable for our particular research question, and using different priors may change the conclusions we will draw.
What does the Bayes Factor tell us?
A Bayes factor is the ratio of the likelihood of one particular hypothesis to the likelihood of another. It tells us what the weight of the evidence is in favor of a given hypothesis.
What is JZS prior?
r scale The scale of the multivariate Cauchy prior (JSZ prior) for the effect size of the model. The given value by JASP is the standard value. The value expresses that we expect that there is a 50% chance of observing an absolute effect larger than the chosen value.
How do you calculate the Bayes factor?
Rearranging, the Bayes Factor is:
- B(x) = π(M1|x)
- π(M2|x) ×
- p(M2) p(M1)
- = π(M1|x)/π(M2|x)
- p(M1)/p(M2) (the ratio of the posterior odds for M1 to the prior odds for M1).
How do you calculate Bayes factor from Bic?
Using this fact, we can approximate Bayes factor between two models by their BICs BF[M1:M2]=p(data | M1)p(data | M2)≈exp(−BIC1/2)exp(−BIC2/2)=exp.
How are the posterior odds and the Bayes factor the same?
The posterior odds are the product of the prior odds and the Bayes factor. The Bayes factor is the ration of the likelihoods. Since the sensitivity and specificity are the same as in the previous example, the likelihoods are the same, and the Bayes factor is the same.
How to calculate Bayes factor for hypothesis H?
Therefore, the Bayes factor for hypothesis H given evidence E can be calculated as the ratio of the likelihoods BF = P(E | H) P(E | Hc) That is, the Bayes factor can be computed without first computing posterior probabilities or odds. Example 3.4 Continuing Example 3.1. Now suppose that 5% of individuals in a high-risk group carry the HIV virus.
What is the Bayes factor for carrying HIV?
Comparing the prior and posterior odds in favor of carrying HIV, B F = posterior odds prior odds = 0.066 0.005025 = 13.2 The odds of carrying HIV are 13.2 times greater given a positive test result than prior to taking the test. The Bayes Factor is B F = 13.2.