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This is again relevant to https://discourse.mc-stan.org/t/rank-plots-dont-save-you-from-symmetric-non-stationary-chains/37624/4
I suppose this would be relevant for all rank-based plots?
Using this to make my own version of split chains makes the problems super obvious:
n = 1000
chain1 <- -2 + 0.003 * 1:n + arima.sim(list(ar = 0.7), n = n, sd = 0.5)
chain2 <- 1 + -0.003 * 1:n + arima.sim(list(ar = 0.7), n = n, sd = 0.5)
# Split chains into first and second half
midpoint <- n/2
chains <- as_draws_array(list(
chain1_first = list(theta = chain1[1:midpoint]),
chain1_second = list(theta = chain1[(midpoint+1):n]),
chain2_first = list(theta = chain2[1:midpoint]),
chain2_second = list(theta = chain2[(midpoint+1):n])
))
mcmc_rank_overlay(chains, )
mcmc_rank_ecdf(chains, plot_diff = TRUE)
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