One use case that may be of particular interest is updating a prior on a parameter B based on b,
an a statistical estimate of B (for example from a study you conducted or are reading about).
- If b is a mean or a difference in means (such as a treatment effect), the likelihood distribution will be a normal distribution
centered around b with a standard deviation equal to the standard error of b. The log-normal distribution may be a good choice of prior for positive quantities.
Quick link: Update from statistical estimate of a mean or treatment effect
- If b is a ratio, its error distribution converges to normality slowly.
In the case of a risk ratio, both risks are positive, so the error distribution of log(b), which converges faster, is often used.
In this case, you can take logs of both prior and likelihood, so that the likelihood becomes a normal distribution. A good choice for the prior
over a risk ratio is a ratio of Beta distributions, whose log is a difference of logs of betas distributions.
Quick link: Update from statistical estimate of a risk ratio (log space)
helpful for converting between 95% confidence intervals, standard errors, and p-values.