Language models and probability of relevance

D is a document, {Ti} are query terms. The whole represents the probability that the query could have been generated from the language model representing the document (here simplified to the P (Ti|D) values), but with a smoothing parameter λ, which allows terms some chance of coming from a general language model (the P (Ti) values). The conception is that the user has a document in mind, and that s/he generates the query from this document; the equation then represents the probability that the document that the user had in mind was in fact this one. Hiemstra [1] gives the same equation a slightly different justification. The basic assumption is the same (the user is assumed to have a specific document in mind and to generate the query on the basis of this document), but instead of smoothing, the user is assumed to assign a binary importance value to each term position in the query. An important term-position is filled with a term from the document; a non-important one is filled with a general language term. If we define λi = P (term position i is important), then we get