On Event Spaces and Probabilistic Models in Information Retrieval

A basic notion of probability theory is the event space, on which the probability measure is defined. A probabilistic model needs an event space. However, some classes of events (which we may want to model probabilistically) exhibit structure which does not fit well into the traditional event space notion. A simple one-to-many example is discussed at length. The information retrieval case, involving queries, documents and relevance, is analysed. The event space issue makes for some difficulty in comparing different probabilistic models in IR.