Probabilistic relevance model

The probabilistic relevance model^[1][2] was devised by Stephen E. Robertson and Karen Spärck Jones as a framework for probabilistic models to come. It is a formalism of information retrieval useful to derive ranking functions used by search engines and web search engines in order to rank matching documents according to their relevance to a given search query.

It is a theoretical model estimating the probability that a document d_j is relevant to a query q. The model assumes that this probability of relevance depends on the query and document representations. Furthermore, it assumes that there is a portion of all documents that is preferred by the user as the answer set for query q. Such an ideal answer set is called R and should maximize the overall probability of relevance to that user. The prediction is that documents in this set R are relevant to the query, while documents not present in the set are non-relevant.

${\displaystyle sim(d_{j},q)={\frac {P(R|{\vec {d}}_{j})}{P({\bar {R}}|{\vec {d}}_{j})}}}$