Latent Dirichlet Allocation (LDA) is a fully generative approach to language modelling which overcomes the inconsistent generative semantics of Probabilistic Latent Semantic Indexing (PLSI). This paper shows that PLSI is a maximum a posteriori estimated LDA model under a uniform Dirichlet prior, therefore the perceived shortcomings of PLSI can be resolved and elucidated within the LDA framework. Categories and Subject Descriptors I.2.7 [Artificial Intelligence]: Natural Language Processing—Language Models; H.3.3 [Information Storage and Retrieval]: Information Search and Retrieval—Retrieval Models General Terms Algorithms Keywords Language Model