Bayesian inversion of a linear calibration posterior

Integrates a proper prior with a normal likelihood for paired posterior draws of the intercept, slope, and residual standard deviation. This avoids unstable division by slopes near zero and preserves calibration-draw pairing.

Usage

bayesian_linear_inverse(
  y,
  intercept,
  slope,
  residual_sd,
  analytical_sd = 0,
  prior,
  credible_level = 0.9,
  grid_size = 2001L,
  integration_tolerance = 0.001,
  tail_mass_tolerance = 1e-08,
  max_refinements = 4L,
  n_samples = 0L,
  seed = NULL
)

Arguments

y

Observed response value.

intercept, slope, residual_sd

Paired calibration posterior draws.

analytical_sd

Known response-space analytical standard deviation.

prior

A proper prior created by one of the d2h_prior_*() functions.

credible_level

Probability in the central credible interval.

grid_size

Odd number of grid points used for numerical integration.

integration_tolerance

Maximum permitted change in reported summaries between nested numerical grids, in precipitation-isotope units.

tail_mass_tolerance

Maximum permitted posterior mass in either outer grid cell for an unbounded prior.

max_refinements

Maximum domain-expansion attempts.

n_samples

Number of optional posterior samples to return.

seed

Required integer seed when n_samples is positive.

Value

A leafwax_inverse_grid object containing the normalized posterior, summaries, numerical and identifiability diagnostics, and optional samples.