Computes Credible Intervals for Bayesian Wavelet Shrinkage
Description
Computes Bayesian wavelet shrinkage credible intervals for
nonparametric regression.
The method uses cumulants to derive Bayesian credible intervals for
wavelet regression estimates.
The first four cumulants of the posterior distribution of the
estimates are expressed in terms of the observed data and integer
powers of the mother wavelet functions.
These powers are closely approximated by linear combinations of
wavelet scaling functions at an appropriate finer scale.
Hence, a suitable modification of the discrete wavelet transform allows
the posterior cumulants to be found efficiently for any data set.
Johnson transformations then yield the credible intervals themselves.
Barber, S., Nason, G.P. and Silverman, B.W. (2002)
.