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 magnus2016wals;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.
computePosterior(object, ...)# S3 method for familyPrior
computePosterior(object, x, ...)
# S3 method for familyPrior_laplace
computePosterior(object, x, ...)
Object of class "familyPrior", e.g. from
weibull, should contain all necessary parameters needed
for the posterior.
Further arguments passed to methods.
vector. Observed values, i.e. in WALS these are the regression coefficients of the transformed regressor Z2 standardized by the standard deviation: \(\gamma_{2u} / s\).
See section "Numerical integration in Bayesian estimation step" in the appendix of huynhwals;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 deluca2020laplace;textualWALS and the
original code of Magnus and De Luca.
Original MATLAB code on Jan Magnus' website. https://www.janmagnus.nl/items/WALS.pdf