computePosterior: Internal function: Compute posterior mean and variance of...

In WALS: Weighted-Average Least Squares Model Averaging

Internal function: Compute posterior mean and variance of normal location problem

Description

Computes the posterior mean and variance of the normal location problem with fixed variance to 1, i.e. x | \gamma \sim N(\gamma, 1). The priors for \gamma are either weibull, subbotin or laplace. Their properties are briefly discussed in \insertCitemagnus2016wals;textualWALS. Default method of computePosterior uses numerical integration. This is used for the weibull and subbotin priors. For the laplace prior closed form expressions exist for the integrals. In the original MATLAB code, the Gauss-Kronrod quadrature was used for numerical integration. Here we use the default integrate which combines Gauss-Kronrod with Wynn's Epsilon algorithm for extrapolation.

Usage

computePosterior(object, ...)

## S3 method for class 'familyPrior'
computePosterior(object, x, ...)

## S3 method for class 'familyPrior_laplace'
computePosterior(object, x, ...)

Arguments

object	Object of class "familyPrior", e.g. from weibull, should contain all necessary parameters needed for the posterior.
...	Further arguments passed to methods.
x	vector. Observed values, i.e. in WALS these are the regression coefficients of the transformed regressor Z2 standardized by the standard deviation: \gamma_{2u} / s.

Details

See section "Numerical integration in Bayesian estimation step" in the appendix of \insertCitehuynhwals;textualWALS for details.

computePosterior.familyPrior_laplace() is the specialized method for the S3 class "familyPrior_laplace" and computes the posterior first and second moments of the normal location problem with a Laplace prior using the analytical formula (without numerical integration). For more details, see \insertCitedeluca2020laplace;textualWALS and the original code of Magnus and De Luca.

References

\insertAllCited

Original MATLAB code on Jan Magnus' website. https://www.janmagnus.nl/items/WALS.pdf

WALS documentation built on June 22, 2024, 9:42 a.m.