  X-ray and Sunyaev-Zeldovich Effect data can be combined to determine the
distance to galaxy clusters. High-resolution X-ray data are now available from
the Chandra Observatory, which provides both spatial and spectral information,
and Sunyaev-Zeldovich Effect data were obtained from the BIMA and OVRO arrays.
We introduce a Markov chain Monte Carlo procedure for the joint analysis of
X-ray and Sunyaev-Zeldovich Effect data. The advantages of this method are the
high computational efficiency and the ability to measure simultaneously the
probability distribution of all parameters of interest, such as the spatial and
spectral properties of the cluster gas and also for derivative quantities such
as the distance to the cluster. We demonstrate this technique by applying it to
the Chandra X-ray data and the OVRO radio data for the galaxy cluster Abell
611. Comparisons with traditional likelihood-ratio methods reveal the
robustness of the method. This method will be used in follow-up papers to
determine the distances to a large sample of galaxy clusters.
