Human Inferences about Sequences: A Minimal Transition Probability Model
Fig 2
Three different inference styles
Panel A shows an example of a sequence in which the statistics change abruptly: the first half, from 1 to 150, was generated with p(X|Y) = 1 – p(Y|X) = 2/3, and the second half with p(X|Y) = 1 – p(Y|X) = 1/3. In this paper, we consider different hypotheses regarding the inference algorithm used by the brain to cope with such abrupt changes (panel B). Some models assume that a single statistic generates all the observations received (“fixed belief”) while other assume volatility, i.e. that the generative statistic may change from one observation to the next with fixed probability pc (“dynamic belief”). Models with fixed belief may estimate the underlying statistic either by weighting all observations equally (“perfect integration”), or by considering all observations within a fixed recent window of N stimuli (“windowed integration”, not shown in the figure), or by forgetting about previous observations with an exponential decay ω (“leaky integration”). The heat maps show the posterior distributions of transition probabilities generating the sequence in (A) as estimated by each model. The white dash line indicates the true generative value. The insets show the estimated 2-dimensional space of transition probabilities at distinct moments in the sequence. White circles indicate the true generative values.