Bayes Factors from Marginal Likelihoods

Compute Bayes factors from marginal likelihoods.

# S3 method for brmsfit
bayes_factor(x1, x2, log = FALSE, ...)

Arguments

x1

A brmsfit object

x2

Another brmsfit object based on the same responses.

log

Report Bayes factors on the log-scale?

...

Additional arguments passed to bridge_sampler.

Details

Computing the marginal likelihood requires samples of all variables defined in Stan's parameters block to be saved. Otherwise bayes_factor cannot be computed. Thus, please set save_all_pars = TRUE in the call to brm, if you are planning to apply bayes_factor to your models.

The computation of Bayes factors based on bridge sampling requires a lot more posterior samples than usual. A good conservative rule of thumb is perhaps 10-fold more samples (read: the default of 4000 samples may not be enough in many cases). If not enough posterior samples are provided, the bridge sampling algorithm tends to be unstable, leading to considerably different results each time it is run. We thus recommend running bayes_factor multiple times to check the stability of the results.

More details are provided under bridgesampling::bayes_factor.

See also

bridge_sampler, post_prob

Examples

if (FALSE) {
# model with the treatment effect
fit1 <- brm(
  count ~ zAge + zBase + Trt,
  data = epilepsy, family = negbinomial(),
  prior = prior(normal(0, 1), class = b),
  save_all_pars = TRUE
)
summary(fit1)

# model without the treatment effect
fit2 <- brm(
  count ~ zAge + zBase,
  data = epilepsy, family = negbinomial(),
  prior = prior(normal(0, 1), class = b),
  save_all_pars = TRUE
)
summary(fit2)

# compute the bayes factor
bayes_factor(fit1, fit2)
}