To pick up the gaunlet, I’ve fitted a Bayesian Cox model with skeptical priors ~normal (mean=0, sd=0.1) for all the signs of the zodiac, except for the basal category (the sign of Capricorn). With the Capricorns I did not know very well what to do. I don’t know if a skeptical prior should be placed on the intercept and what the prior would be. The brms library uses the Student-t distribution with 3 parameters for the intercept.

In any case this is the result. The Bayes factor against a null (intercept-only) model is 8 in this example. What do you think?

```
prior <- c(set_prior("normal(0,0.1)", class = "b", coef = "zodAquarius"),
set_prior("normal(0,0.1)", class = "b", coef = "zodAries"),
set_prior("normal(0,0.1)", class = "b", coef = "zodCancer"),
set_prior("normal(0,0.1)", class = "b", coef = "zodGemini"),
set_prior("normal(0,0.1)", class = "b", coef = "zodLeo"),
set_prior("normal(0,0.1)", class = "b", coef = "zodLibra"),
set_prior("normal(0,0.1)", class = "b", coef = "zodPisces"),
set_prior("normal(0,0.1)", class = "b", coef = "zodSagittarius"),
set_prior("normal(0,0.1)", class = "b", coef = "zodScorpio"),
set_prior("normal(0,0.1)", class = "b", coef = "zodTaurus"),
set_prior("normal(0,0.1)", class = "b", coef = "zodVirgo")
)
> rstan_options (auto_write=TRUE)
> options (mc.cores=parallel::detectCores ())
> fit <- brm(SG | cens(1-Die) ~ 1 + zod, data = dat, prior=prior, family = brmsfamily("cox"),chains=4, iter=2000, save_all_pars = TRUE)
Compiling Stan program...
Start sampling
> fit2 <- brm(SG | cens(1-Die) ~ 1 , data = dat, family = brmsfamily("cox"),chains=4, iter=2000, save_all_pars = TRUE)
Compiling Stan program...
Start sampling
> summary(fit)
Family: cox
Links: mu = log
Formula: SG | cens(1 - Die) ~ 1 + zod
Data: dat (Number of observations: 2473)
Samples: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
total post-warmup samples = 4000
Population-Level Effects:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept 1.56 0.08 1.42 1.73 1.00 1803 1982
zodAquarius 0.05 0.06 -0.07 0.18 1.00 4366 3145
zodPisces 0.02 0.06 -0.11 0.13 1.00 3462 2786
zodAries -0.08 0.06 -0.20 0.04 1.00 4652 3343
zodTaurus -0.06 0.06 -0.19 0.07 1.00 3922 2963
zodGemini 0.08 0.06 -0.04 0.20 1.00 4058 3030
zodCancer -0.04 0.06 -0.16 0.08 1.00 4030 2859
zodLeo 0.11 0.07 -0.03 0.24 1.00 4300 3243
zodVirgo 0.03 0.06 -0.09 0.15 1.00 3874 2963
zodLibra -0.02 0.07 -0.15 0.11 1.00 4226 2854
zodScorpio -0.02 0.07 -0.15 0.11 1.00 4043 2882
zodSagittarius -0.15 0.07 -0.28 -0.01 1.00 4076 3180
> bayes_factor(fit,fit2)
Estimated Bayes factor in favor of fit over fit2: 8.02152
```