calibrate_inv_exp_lambda_driven_nig: Calibrate Inverse-Exponential Prior for NIG Driven Noise

In ngme2: Linear Latent Non-Gaussian Models with Flexible Distributions

Calibrate Inverse-Exponential Prior for NIG Driven Noise

Description

Calibrate \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
...	arguments forwarded to calibrate_inv_exp_lambda_driven_nig()

Value

A list with calibrated 'lambda', solved 'nu_r', achieved 'rc_nu_r', and diagnostics.

ngme2 documentation built on May 20, 2026, 9:10 a.m.