Conditional profile probabilities under a correlated residual, via Gibbs

For one hospital-pathogen panel at one posterior draw, samples the missing latent class dimensions conditional on the observed resistance SIGNS of the tested classes (we only ever observe \(\mathrm{sign}(Z_{ed})\), never the exact latent value), via a Gibbs sampler on the truncated multivariate normal \(Z_e \sim N(\mu_e, \Omega)\), vectorized across all events in the panel simultaneously (the per-dimension conditional-normal regression coefficients depend only on \(\Omega\) – fixed across events at a given draw – so one matrix operation updates every event's Gibbs state at once).

Usage

.gibbs_conditional_profile_probs(
  mu_hp,
  Omega_hp,
  obs_panel,
  profile_bin,
  n_burnin = 10L,
  n_kept = 20L
)

Arguments

mu_hp

Numeric matrix, n_hp x Dp. Linear predictor for this draw.

Omega_hp

Numeric matrix, Dp x Dp. Residual correlation matrix for this draw (already symmetrized/regularised by the caller).

obs_panel

Numeric matrix, n_hp x Dp, values in {0, 1, NA}.

profile_bin

Integer matrix, n_profiles x Dp, 0/1 (from enumerate_binary_profiles()); row \(j\) must correspond to integer code \(j - 1\) in binary (column \(d\) = bit \(d - 1\)), which is how enumerate_binary_profiles() orders rows.

n_burnin, n_kept

Integer. Gibbs iterations discarded as burn-in and iterations kept for the empirical profile-probability count, respectively, at this single posterior draw. Total Gibbs cost scales with (n_burnin + n_kept) * n_posterior_draws_for_profiles, so correlated-residual profile generation should typically use fewer posterior draws than an identity-residual fit of the same size.

Value

Numeric matrix, n_hp x n_profiles: empirical conditional profile probability per event, rows summing to 1.

Details

At every iteration, dimensions with an observed value are drawn from a truncated normal restricted to the half-line matching the observed sign (inverse-CDF sampling); dimensions without an observed value are drawn from the unrestricted conditional normal. Because the observed dimensions are truncation-constrained at every iteration, every kept iteration's pattern is automatically consistent with the observed cells – profiles inconsistent with observed data are never visited, rather than assigned zero probability after the fact. Counting each kept iteration's full binary pattern against the enumerated profile list gives an empirical conditional profile-probability vector per event that sums to exactly 1 by construction (every iteration falls into exactly one profile).

Dp == 1 (a single-class panel) has no joint structure to speak of and is handled directly via \(\Phi(\mu_{ed})\), bypassing Gibbs entirely.