% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/prior_calibration.R
\name{calibrate_inv_exp_lambda_driven_nig}
\alias{calibrate_inv_exp_lambda_driven_nig}
\alias{calibrate_inv_exp_lambda}
\title{Calibrate Inverse-Exponential Prior for NIG Driven Noise}
\usage{
calibrate_inv_exp_lambda_driven_nig(
  r_target = 2,
  alpha = 0.1,
  c = 3,
  mu = 0,
  sigma = 1,
  h = 1,
  n_samples = 1e+05,
  nu_lower = 0.1,
  nu_upper = 100,
  tol = 0.05,
  max_iter = 30,
  max_expand = 30,
  seed = NULL
)

calibrate_inv_exp_lambda(...)
}
\arguments{
\item{r_target}{target tail inflation level \eqn{r_\text{target} > 1}}

\item{alpha}{target prior probability in \eqn{(0,1)}}

\item{c}{tail threshold for \eqn{|U|>c}, typically `2.5` or `3`}

\item{mu}{NIG drift parameter in the driven noise term}

\item{sigma}{NIG scale parameter (> 0)}

\item{h}{positive increment scaling (> 0)}

\item{n_samples}{Monte Carlo sample size used per evaluation of \eqn{R_c(\nu)}}

\item{nu_lower}{initial lower bracket for \eqn{\nu}}

\item{nu_upper}{initial upper bracket for \eqn{\nu}}

\item{tol}{relative tolerance for solving \eqn{R_c(\nu_r)=r_\text{target}}}

\item{max_iter}{maximum number of bisection iterations}

\item{max_expand}{maximum bracket expansion steps on each side}

\item{seed}{optional integer seed for reproducible calibration}

\item{...}{arguments forwarded to \code{calibrate_inv_exp_lambda_driven_nig()}}
}
\value{
A list with calibrated `lambda`, solved `nu_r`, achieved `rc_nu_r`,
  and diagnostics.
}
\description{
Calibrate \eqn{\lambda} in the prior
\eqn{\kappa = 1/\nu \sim \mathrm{Exp}(\lambda)}
using a tail-inflation target for driven NIG noise.

The calibration target is
\deqn{\Pr(R_c(\nu) > r_\text{target}) = \alpha,}
where
\deqn{R_c(\nu) = \frac{\Pr(|U| > c \mid \nu)}{\Pr(|Z| > c)},\quad Z\sim N(0,1)}
and
\deqn{U = \frac{\mu(V-h) + \sigma\sqrt{V}Z}{\sigma\sqrt{h}},\quad V\sim\mathrm{GIG}(-1/2,\nu,\nu h^2).}

The function solves \eqn{R_c(\nu_r) = r_\text{target}} using log-scale
bisection, then returns
\deqn{\lambda = -\nu_r \log(\alpha).}
}
