This paper provides an overview of statistical machine translation (SMT) and introduces the publicly available SMT toolkit EGYPT. It begins by explaining the Bayes decision rule, which is used to structure probability distributions into three components: the language model, the alignment model, and the lexicon model. The paper describes the system components and reports results from the VERBMOBIL and HANSARDS tasks, demonstrating that the statistical approach significantly reduces error rates compared to other translation methods. The authors discuss the challenges and advantages of using statistics in computational linguistics, the importance of prior knowledge in modeling, and the role of alignment models in translating between source and target languages. They also detail the training and search processes, including the use of the EM algorithm for parameter estimation and the bottom-to-top search strategy for generating the most likely target sentence. The paper concludes with experimental results showing the effectiveness of SMT in real-world translation tasks, particularly in the presence of speech input and ungrammatical input.This paper provides an overview of statistical machine translation (SMT) and introduces the publicly available SMT toolkit EGYPT. It begins by explaining the Bayes decision rule, which is used to structure probability distributions into three components: the language model, the alignment model, and the lexicon model. The paper describes the system components and reports results from the VERBMOBIL and HANSARDS tasks, demonstrating that the statistical approach significantly reduces error rates compared to other translation methods. The authors discuss the challenges and advantages of using statistics in computational linguistics, the importance of prior knowledge in modeling, and the role of alignment models in translating between source and target languages. They also detail the training and search processes, including the use of the EM algorithm for parameter estimation and the bottom-to-top search strategy for generating the most likely target sentence. The paper concludes with experimental results showing the effectiveness of SMT in real-world translation tasks, particularly in the presence of speech input and ungrammatical input.