The vector space model assumes terms in a document are independent of one another. We know that this is not true, for example, the terms ``water'' and ``pistol'' in ``water pistol'' have a dependency relation, but in practice making this assumptions simplifies things greatly for the engineer.
Latent Semantic Indexing (LSI) was developed and patented by the Bellcore group comprising Susan Dumais et al. A description of it can be found in [DDL+90]. The most successful probabilistic retrieval system is the University of Massachusetts INQUERY system [CCH92], which uses a Bayesian belief network to determine relevance probability. Mercure [BSD97] uses a neural net approach to match queries with documents.