A stochastic theory of matching processes

A theory of matching processes is developed within which serial models and parallel models based on within-stage independent intercompletion times are defined. These models are then specialized to a class of processes possessing exponential intercompletion time densities and equivalence properties of parallel and serial models within this class are investigated. Nonequivalence theorems are proved that designate possible differences in “same” (+) and different (?) matching rates as important in testing parallel and serial models. An experimental paradigm is then derived with the property that if + rates are different from — rates, and if processing is self-terminating, then the parallel and serial models are distinguishable at the level of mean reaction times. The serial class of models that is tested by this paradigm includes a large number of stochastic distributions whose central assumption is additivity of element processing times. The corresponding parallel class of models is currently limited to those assuming exponential intercompletion times. A numerical example and an example of non-parametric relations predicted by the serial or parallel models are given. Some advantages and limitations of the present treatment are discussed.