Advanced Optional Bayesian Workflows

This article describes the optional post-0.1.1 extensions. They remain contract-first: neither unrestricted formulas nor automatic model selection are introduced.

Capability audit

bayesian_backend_capabilities()
#> 
#> Optional Bayesian capabilities
#> 
#>         component installed    version usable
#>              brms      TRUE     2.23.0   TRUE
#>             rstan      TRUE     2.32.7   TRUE
#>          cmdstanr      TRUE      0.9.0   TRUE
#>               loo      TRUE     2.10.0   TRUE
#>        priorsense      TRUE      1.2.0   TRUE
#>  detectseparation      TRUE      0.4.0   TRUE
#>               SBC      TRUE 0.5.0.9000   TRUE
#>                                                          detail
#>                                               package available
#>                                               package available
#>  CmdStan 2.39.0 at C:/Users/Stefanos-PC/.cmdstan/cmdstan-2.39.0
#>                                               package available
#>                                               package available
#>                                               package available
#>                                               package available

Separate interaction priors

binary_sim <- simulate_hierarchical_binary_data(
  n_participants = 12,
  trials_per_participant = 8,
  n_items = 6,
  random_slope_sd = 0,
  seed = 2026
)

binary_contract <- create_model_contract(
  family = "binary",
  outcome_col = "selected",
  participant_col = "participant_id",
  item_col = "item_id",
  trial_col = "trial_id",
  condition_col = "condition",
  predictors = c("participant_covariate", "trial_covariate"),
  interaction = c("condition", "participant_covariate"),
  random_slope = FALSE
)

binary_prepared <- prepare_hierarchical_binary_data(
  binary_sim$data,
  binary_contract,
  condition_levels = c("control", "treatment")
)

binary_spec <- specify_binary_model_with_interaction_prior(
  binary_prepared,
  baseline = 0.35
)

interaction_prior_summary(binary_spec)
#>   family                     interaction main_effect_scale interaction_scale
#> 1 binary condition:participant_covariate              0.75               0.5
#>   interaction_tag
#> 1     interaction

The binary advanced default is normal(0, 0.75) for population main effects and normal(0, 0.50) for the single approved interaction. The duration advanced defaults are 0.35 and 0.25 respectively. These are candidate workflow defaults and still require prior-predictive review.

Full-MCMC backend selection

The advanced fitting functions accept only rstan or cmdstanr, and they always use full MCMC sampling.

fit_rstan <- fit_binary_model_backend(
  binary_spec,
  backend = "rstan"
)

fit_cmdstanr <- fit_binary_model_backend(
  binary_spec,
  backend = "cmdstanr"
)

Separation screening

separation_screen <- detect_binary_separation(binary_spec)
separation_screen
#> 
#> Binary separation screen
#>  Status: pass
#>  Separation detected: FALSE
#>  Observations: 96
#>                      coefficient separation_code infinite direction
#>                      (Intercept)               0    FALSE    finite
#>                        condition               0    FALSE    finite
#>            participant_covariate               0    FALSE    finite
#>                  trial_covariate               0    FALSE    finite
#>  condition:participant_covariate               0    FALSE    finite
#> 
#> This is a fixed-effects logistic separation screen. Grouping terms from the hierarchical specification are not included in this screening GLM. The screen neither fits nor validates the hierarchical Bayesian model.
plot(separation_screen)

The screen is a fixed-effects design diagnostic. It is not a replacement for the hierarchical Bayesian fit or its posterior diagnostics.

PSIS-LOO and model averaging

loo_a <- compute_psis_loo(fit_a)
loo_b <- compute_psis_loo(fit_b)

comparison <- compare_psis_loo(list(contract_a = loo_a, contract_b = loo_b))
comparison

weights <- compute_loo_model_weights(comparison, method = "stacking")
weights

The comparison reports predictive differences and diagnostics but never selects a model automatically.

Power-scaling sensitivity

sensitivity <- assess_powerscaled_sensitivity(
  fit_rstan,
  variable = c("b_Intercept", "b_condition")
)

sensitivity
plot(sensitivity, type = "ecdf")
plot(sensitivity, type = "quantities")

Low local sensitivity is not a proof of universal robustness.

Simulation-based calibration

plan <- create_brms_sbc_plan(
  binary_spec,
  n_sims = 50,
  backend = "cmdstanr"
)

sbc_result <- run_sbc_plan(plan)
sbc_result
plot(sbc_result, type = "rank")
plot(sbc_result, type = "ecdf")

The brms generator and brms inference backend share implementation code. An independently coded generator is preferable when the goal is to identify shared implementation defects.