Bayesian_Shrinkage {FunctionalCalibration} | R Documentation |
Bayesian Shrinkage
Description
A Bayesian shrinkage method applied to empirical coefficients d
, aiming to denoise them.
The shrinkage function is defined as:
\delta(d) = \displaystyle \frac{(1 - p) \int_{\mathbb{R}} (\sigma u + d) \, g(\sigma u + d; \tau) \, \phi(u) \, du}{\frac{p}{\sigma} \phi\left( \frac{d}{\sigma} \right) + (1 - p) \int_{\mathbb{R}} g(\sigma u + d; \tau) \, \phi(u) \, du}
where \phi(x)
is the probability density function of the standard normal distribution,
and g(\theta; \tau)
is the logistic density function.
Usage
Bayesian_Shrinkage(d, tau, p, sigma, MC = FALSE)
Arguments
d |
Numeric value of the empirical coefficient to be denoised. |
tau |
Numeric value of |
p |
Numeric value of |
sigma |
Numeric value of |
MC |
A logical evaluating to |
Value
A numeric value representing the result of the Bayesian shrinkage applied to the empirical coefficient d
.