Autocorrelation in intercept-only model

Interfaces brms
,
1

Hi all!

I am trying to run a simple intercept-only model for a binary outcome variable, and at this point, I am running into a problem with autocorrelation. In the toy example below, I encounter the same problem: under different priors, autocorrelation for the estimated intercept remains high.

library(brms)
library(bayesplot)
library(tidybayes)

df <- data.frame(y = rep(c(0, 0, 1), times=25))

model1 <- brm(data = df,
              family = "bernoulli", 
              formula = y ~ 1, 
              prior(normal(0, 2), class = Intercept), 
              
              iter = 10000, 
              cores=4, 
              sample_prior = TRUE,
              
              seed = 12345) 

intercept_posteriors <- brms::as_draws_df(model1) %>%
  mutate(posterior = inv_logit_scaled(b_Intercept),
         prior = inv_logit_scaled(prior_Intercept))

mcmc_trace(intercept_posteriors, pars=c("b_Intercept", "prior_Intercept"))

intercept_posteriors %>% 
  bayesplot::mcmc_acf(pars = vars(b_Intercept, prior_Intercept))

I am wondering how concerning it is. Does the autocorrelation arise because of the family = "bernoulli" specification?

  • Operating System: Windows 10
  • brms Version: ‘2.16.3’

Thanks a lot in advance for looking into it.

Best,
Alyona