A normative model (the Markovian observer) is described for a numerical decision task (an analogue of signal detection) in which the sequence of stimuli instantiates a two-state Markov chain. The expected-value observer of classical signal detection theory is a special case of the Markovian observer. An experiment is also described in which subjects performed the numerical detection task for different Markov chains of stimuli. Neither the ordinary expected-value observer nor the Markovian observer adequately described the performance of actual subjects, particularly when the stimulus sequence was random. A modification of the Markovian observer (the Markovian observer "ignorant" of the transition probabilities governing the stimulus sequence), similar to Kubovy and Healy's ideal-learner model, was simulated on a computer and provided a good qualitative fit to the data, especially to the distribution of violations of signal detection theory's single-criterion rule.

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