#### Bayesian model selection and analysis for Cepheid star oscillations

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)