  Bayesian nonparametric regression with dependent wavelets has dual shrinkage
properties: there is shrinkage through a dependent prior put on functional
differences, and shrinkage through the setting of most of the wavelet
coefficients to zero through Bayesian variable selection methods. The
methodology can deal with unequally spaced data and is efficient because of the
existence of fast moves in model space for the MCMC computation. The
methodology is illustrated on the problem of modeling the oscillations of
Cepheid variable stars; these are a class of pulsating variable stars with the
useful property that their periods of variability are strongly correlated with
their absolute luminosity. Once this relationship has been calibrated,
knowledge of the period gives knowledge of the luminosity. This makes these
stars useful as "standard candles" for estimating distances in the universe.
