Calibrate Inverse-Exponential Prior for NIG Driven Noise
Source:R/prior_calibration.R
calibrate_inv_exp_lambda_driven_nig.RdCalibrate \(\lambda\) in the prior \(\kappa = 1/\nu \sim \mathrm{Exp}(\lambda)\) using a tail-inflation target for driven NIG noise.
The calibration target is $$\Pr(R_c(\nu) > r_\text{target}) = \alpha,$$ where $$R_c(\nu) = \frac{\Pr(|U| > c \mid \nu)}{\Pr(|Z| > c)},\quad Z\sim N(0,1)$$ and $$U = \frac{\mu(V-h) + \sigma\sqrt{V}Z}{\sigma\sqrt{h}},\quad V\sim\mathrm{GIG}(-1/2,\nu,\nu h^2).$$
The function solves \(R_c(\nu_r) = r_\text{target}\) using log-scale bisection, then returns $$\lambda = -\nu_r \log(\alpha).$$
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
- r_target
target tail inflation level \(r_\text{target} > 1\)
- alpha
target prior probability in \((0,1)\)
- c
tail threshold for \(|U|>c\), typically `2.5` or `3`
- mu
NIG drift parameter in the driven noise term
- sigma
NIG scale parameter (> 0)
- h
positive increment scaling (> 0)
- n_samples
Monte Carlo sample size used per evaluation of \(R_c(\nu)\)
- nu_lower
initial lower bracket for \(\nu\)
- nu_upper
initial upper bracket for \(\nu\)
- tol
relative tolerance for solving \(R_c(\nu_r)=r_\text{target}\)
- max_iter
maximum number of bisection iterations
- max_expand
maximum bracket expansion steps on each side
- seed
optional integer seed for reproducible calibration