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 \tau.

p

Numeric value of p.

sigma

Numeric value of \sigma.

MC

A logical evaluating to TRUE or FALSE indicating if the integrals will be approximated using Monte Carlo.

Value

A numeric value representing the result of the Bayesian shrinkage applied to the empirical coefficient d.


[Package FunctionalCalibration version 1.0.0 Index]