Conjugate Bayesian Linear Regression Fitter

Exact conjugate Normal-Inverse-Gamma (NIG) Bayesian linear regression. Fits y ~ N(X beta, sigma^2) analytically and draws i.i.d. samples from the joint posterior (beta, sigma). No Stan, milliseconds per fit, real posteriors — the package's teaching backbone (D1).

The model formula is taken from fit_spec$formula (a base R formula, default response ~ .). Posterior draws use plain parameter names (Intercept, <coef>, sigma) so they line up with resolve_draw_columns() and the generators' cleaned names out of the box.

Usage

LinearRegressionFitter(
  name = "linear_regression",
  supports_predictions = TRUE,
  supports_log_lik = TRUE,
  supports_loo = TRUE,
  supports_epred = TRUE,
  n_draws = 1000L,
  prior_mean = 0,
  prior_precision = 1e-06,
  a0 = 2,
  b0 = 1e-06
)

Arguments

name

Character string identifying the fitter.

supports_predictions

Logical; whether predictions are supported.

supports_log_lik

Logical; whether log-likelihood is supported.

supports_loo

Logical; whether LOO-CV is supported.

supports_epred

Logical; whether posterior expectation predictions (predict_epred()) are supported.

n_draws

Positive integer; number of i.i.d. posterior draws.

prior_mean

Numeric vector (length = number of coefficients, including intercept) or scalar; prior mean of beta. Recycled. Default 0.

prior_precision

Numeric scalar; prior precision of beta per unit of sigma^2 (i.e. Lambda0 = prior_precision * I). A small value gives a weak prior. Default 1e-6.

a0

Positive numeric; Inv-Gamma prior shape for sigma^2. Default 2.

b0

Positive numeric; Inv-Gamma prior rate for sigma^2. Default 1e-6.

Value

An S7 LinearRegressionFitter object.

See also

Fitter, BrmsFitter

Examples

if (FALSE) { # \dontrun{
fitter <- LinearRegressionFitter(n_draws = 500L)
} # }