“…An immediate concern is that these spatial random effects are typically endowed with a multivariate Gaussian distribution using Markov random fields or Gaussian processes and, being continuous distributions, the posterior probability of any two random effects being equal will be zero. Modeling spatial random effects with discrete jumps, step changes, and discontinuities have been addressed in diverse settings (see, e.g., Gao et al, 2022;Hanson et al, 2015;Li et al, 2012Li et al, , 2015Rushworth et al, 2017;Santafé et al, 2021).…”