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The intention of this article is to provide a concise introduction to the basic mathematical concepts of statistical translation models as they were introduced by Brown et al. (1993) in their groundbreaking work The Mathematics of Statistical Machine Translation: Parameter Estimation. We concentrate on a simplified description of the first two translation models known as IBM Model 1 and 2. It is one major aim of this work to serve as tutoring material for students of computational linguistics,doi:10.14746/il.2008.16.5 fatcat:wrrlmn7yonehde76bki2cfy7py