Bayesian_Shrinkage

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.

internal

Implements methods for calibrating an aggregated functional data model using
wavelets or splines. Each aggregated curve is modeled as a linear combination of
component functions and known weights. The component functions are estimated using
wavelets or splines. The package is based on dos Santos Sousa (2024) <doi:10.1515/mcma-2023-2016>
and Saraiva and Dias (2009) <doi:10.47749/T/UNICAMP.2009.471073>.

Vitor Perrone

FunctionalCalibration

Aggregated Functional Data Calibration using Splines and
Wavelets

Alex Sousa

Bayesian_Shrinkage function

<dl><dt>d</dt>
<dd>Numeric value of the empirical coefficient to be denoised.</dd>
<dt>tau</dt>
<dd>Numeric value of $\tau$.</dd>
<dt>p</dt>
<dd>Numeric value of $p$.</dd>
<dt>sigma</dt>
<dd>Numeric value of $\sigma$.</dd>
<dt>MC</dt>
<dd>A logical evaluating to <code>TRUE</code> or <code>FALSE</code> indicating if the integrals will be approximated using Monte Carlo.</dd></dl>

Arguments

Bayesian Shrinkage — Bayesian_Shrinkage

<dl>

<dt>d</dt>
<dd>Numeric value of the empirical coefficient to be denoised.</dd>


<dt>tau</dt>
<dd>Numeric value of $\tau$.</dd>


<dt>p</dt>
<dd>Numeric value of $p$.</dd>


<dt>sigma</dt>
<dd>Numeric value of $\sigma$.</dd>


<dt>MC</dt>
<dd>A logical evaluating to <code>TRUE</code> or <code>FALSE</code> indicating if the integrals will be approximated using Monte Carlo.</dd>

</dl>

Bayesian_Shrinkage: Bayesian Shrinkage

Description

Usage

Value

Arguments