Berger, J., Jefferys, W., Müller, P., and Barnes, T.
Cepheid variables 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.
Available data consists of photometric and velocity information for a number of Cepheid variables, at unequally spaced points in their periods. Note that photometry and velocity are connected by nonlinear relations involving the physical parameters of interest. Bayesian analysis is used to provide inferences for useful physical features, such as the absolute luminosity of the star, its distance, its radius, and other parameters.
In the absence of reliable physical models of the pulsation of Cepheid variables, we model the photometry and velocity curves as (i) a trigonometric polynomial with an unknown number of terms; or (ii) via a wavelet basis with an unknown number of terms. Bayesian analysis allows computation of the posterior probabilities of these varying dimensional models, and results in inferences on the physical parameters that are based on `averaging' over the possible models. Computations are done using reversible-jump Markov chain Monte Carlo methodology. Postscript File (1340kB)