Proceedings of the Particle Physics and Early Universe Conference (PPEUC). For this paper: postscript PPEUC CMB index 1 Likelihood Analysis.. ... Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh, EH9 3HJ, U.K. Max Tegmark . ... We discuss the problems of applying Maximum Likelihood methods to the CMB and how one can make it both efficient and optimal. ... A much fuller account of most of this work is available ( Tegmark, Taylor & Heavens (1997) ). ...