Validate the Chapter 1 nesting / no-false-positive behaviour — validate_nesting

Complementary check to validate_recovery_2a(). It simulates independent two-biomarker data (all cross-biomarker covariances c_vec = 0, i.e. the Chapter 1 truth) and confirms that Model 2a does not invent cross-biomarker correlation: every posterior c_p credible interval should cover zero. This is the empirical counterpart of the algebraic fact that lambda = 0 reduces Model 2a to Chapter 1.

The packaged typhoid simulator sim_case_data() also produces independent biomarkers, so fitting Model 2a to its output is an equivalent real-data-style null check.

Usage

validate_nesting_2a(
  n = 120,
  mu_g = c(0, 3, 2.3, -4, -1),
  mu_a = c(0.2, 3.1, 2.2, -3.8, -1.1),
  sigma_g = diag(c(0.09, 0.16, 0.09, 0.16, 0.09)),
  sigma_a = diag(c(0.09, 0.16, 0.09, 0.16, 0.09)),
  noise_sd = 0.15,
  seed = 1,
  ...
)

Arguments

n: integer number of subjects. Default 120.
mu_g, mu_a, sigma_g, sigma_a: Model 2a truth (cross-block forced to zero).
noise_sd: Residual SD on the log scale. Default 0.15.
seed: RNG seed. Default 1.
...: MCMC controls forwarded to run_mod_2a().

Value

A data.frame with columns param, cov_med, cov_lo, cov_hi, and covers_zero (logical); all rows should have covers_zero = TRUE.