This paper provides an overview of statistical machine translation (SMT) and presents the publicly available SMT toolkit EGYPT. It begins with the Bayes decision rule, showing how probability distributions can be structured into three parts: the language model, the alignment model, and the lexicon model. The paper describes the components of the system and reports results on the VERBMOBIL and HANSARDS tasks. The experience from the VERBMOBIL project showed that the statistical approach resulted in significantly lower error rates than three competing translation approaches. Statistical decision theory is applied in machine translation, where the goal is to translate a text from a source language to a target language. The Bayes decision rule is used to select the most probable target string. The architecture of the statistical translation approach is based on this rule. Alignment modeling is a key issue in SMT, as it involves defining the correspondence between words in the source and target sentences. The paper discusses various alignment models, including IBM-1 to IBM-5, and the alignment template approach, which allows for word groups or phrases to be aligned. Training of SMT models is done using the EM algorithm, which optimizes the parameters of the models based on training data. The alignment templates are trained using a parallel training corpus and are determined for word classes rather than individual words. Search algorithms are used to generate the most likely target sentence. The search must consider all three knowledge sources: the alignment model, the lexicon model, and the language model. The search is based on the inverted alignment and uses a bigram language model. The EGYPT toolkit is a publicly available SMT toolkit that includes training, decoding, and visualization tools. It has been developed for the purpose of statistical machine translation and includes various modules such as GIZA, WEAVER, CAIRO, and WHITTLE. The paper presents experimental results on the VERBMOBIL and HANSARDS tasks, showing that the statistical approach results in significantly lower error rates compared to other approaches. The results show that the statistical approach is superior, especially in the presence of speech input and ungrammatical input. The paper concludes that the statistical modeling approach may be comparable to or better than the conventional rule-based approach.This paper provides an overview of statistical machine translation (SMT) and presents the publicly available SMT toolkit EGYPT. It begins with the Bayes decision rule, showing how probability distributions can be structured into three parts: the language model, the alignment model, and the lexicon model. The paper describes the components of the system and reports results on the VERBMOBIL and HANSARDS tasks. The experience from the VERBMOBIL project showed that the statistical approach resulted in significantly lower error rates than three competing translation approaches. Statistical decision theory is applied in machine translation, where the goal is to translate a text from a source language to a target language. The Bayes decision rule is used to select the most probable target string. The architecture of the statistical translation approach is based on this rule. Alignment modeling is a key issue in SMT, as it involves defining the correspondence between words in the source and target sentences. The paper discusses various alignment models, including IBM-1 to IBM-5, and the alignment template approach, which allows for word groups or phrases to be aligned. Training of SMT models is done using the EM algorithm, which optimizes the parameters of the models based on training data. The alignment templates are trained using a parallel training corpus and are determined for word classes rather than individual words. Search algorithms are used to generate the most likely target sentence. The search must consider all three knowledge sources: the alignment model, the lexicon model, and the language model. The search is based on the inverted alignment and uses a bigram language model. The EGYPT toolkit is a publicly available SMT toolkit that includes training, decoding, and visualization tools. It has been developed for the purpose of statistical machine translation and includes various modules such as GIZA, WEAVER, CAIRO, and WHITTLE. The paper presents experimental results on the VERBMOBIL and HANSARDS tasks, showing that the statistical approach results in significantly lower error rates compared to other approaches. The results show that the statistical approach is superior, especially in the presence of speech input and ungrammatical input. The paper concludes that the statistical modeling approach may be comparable to or better than the conventional rule-based approach.