The paper presents a series of five statistical models for the translation process and algorithms to estimate the parameters of these models using a set of aligned sentence pairs. The authors define word-by-word alignment between such pairs and aim to find the most probable alignment. The models are trained using a large collection of aligned French-English sentences from the Canadian Hansard data. The paper discusses the limitations of the models and proposes modifications to address these issues. The authors argue that their algorithms have minimal linguistic content, making them suitable for other language pairs as well. The work is motivated by the growing availability of bilingual, machine-readable texts and the need to extract linguistically valuable information from them. The paper also introduces the concept of alignments and cepts, which are used to formalize the translation process. The models are developed in a step-by-step manner, with each model building on the previous one to improve the accuracy of the translation probabilities. The EM algorithm is used to estimate the parameters of the models, and the results show that the statistical methods can effectively extract linguistically interesting correlations from large corpora.The paper presents a series of five statistical models for the translation process and algorithms to estimate the parameters of these models using a set of aligned sentence pairs. The authors define word-by-word alignment between such pairs and aim to find the most probable alignment. The models are trained using a large collection of aligned French-English sentences from the Canadian Hansard data. The paper discusses the limitations of the models and proposes modifications to address these issues. The authors argue that their algorithms have minimal linguistic content, making them suitable for other language pairs as well. The work is motivated by the growing availability of bilingual, machine-readable texts and the need to extract linguistically valuable information from them. The paper also introduces the concept of alignments and cepts, which are used to formalize the translation process. The models are developed in a step-by-step manner, with each model building on the previous one to improve the accuracy of the translation probabilities. The EM algorithm is used to estimate the parameters of the models, and the results show that the statistical methods can effectively extract linguistically interesting correlations from large corpora.