Anova-like summary for brm-model?

Interfaces brms
3

Thank you @Solomon for helping me! I am taking my old post example: How to properly compare interacting levels. The model is slightly revised, but is nice and simple leaving aside random effects, covariates etc.

# uniformly generated means
m = runif(4, 3, 18)

# random values, random means, same std. dev.
y = list()
for (i in 1:4) {
    y[[i]] = rnorm(30, m[i], 0.8)
}
y = unlist(y)

# factorial design
F1 = c(rep('A', 30), rep('B', 30))
F2 = c('I', 'J')
design_matrix = expand.grid(F1=F1, F2=F2)

# dataset
dat = cbind(design_matrix, y)

library(brms)
library(emmeans)

model1 <- brm(y ~
    F1 * F2,
    data = dat,
    chains=4, iter=4000, cores=4)

model1.emm = emmeans(model1, ~ F1 * F2)
joint_tests(model1.emm)
 # model term df1 df2  F.ratio    Chisq p.value
 # F1           1 Inf 5288.825 5288.825  <.0001
 # F2           1 Inf   18.793   18.793  <.0001
 # F1:F2        1 Inf   56.745   56.745  <.0001

I appreciate the anova-style overall effect of F1, F2, and the interaction, but credible intervals might be more in Bayesian-spirit.