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X-ray and Sunyaev-Zeldovich Effect data can be combined to determine thedistance to galaxy clusters. High-resolution X-ray data are now available fromthe 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 ofX-ray and Sunyaev-Zeldovich Effect data. The advantages of this method are thehigh computational efficiency and the ability to measure simultaneously theprobability distribution of all parameters of interest, such as the spatial andspectral properties of the cluster gas and also for derivative quantities suchas the distance to the cluster. We demonstrate this technique by applying it tothe Chandra X-ray data and the OVRO radio data for the galaxy cluster Abell611. Comparisons with traditional likelihood-ratio methods reveal therobustness of the method. This method will be used in follow-up papers todetermine the distances to a large sample of galaxy clusters.Comment: ApJ accepted, scheduled for ApJ 10 October 2004, v614 issue. Title  changed, added more convergence diagnostic tests, Figure 7 converted to lower  resolution for easier download, other minor change

Markov Chain Monte Carlo Joint Analysis ofChandraX‐Ray Imaging Spectroscopy and Sunyaev‐Zel'dovich Effect Data