Figure 1. Testing ideal observer predictions in perceptual decision-making.

(a) Schematic drawing of rate discrimination task. Rats initiate trials by poking into a center port. Trials consist of visual stimuli presented via a panel of diffused LEDs, auditory stimuli presented via a centrally positioned speaker, or multisensory stimuli presented from both. Rats are rewarded with a 24 μL drop of water for reporting high-rate stimuli (greater than 12.5 Hz) with rightward choices and low-rate stimuli (lower than 12.5 Hz) with leftward choices. (b) Timeline of task events. (c) Example stimulus on auditory (top), visual (middle), and multisensory trials (bottom). Stimuli consist of a stream of events separated by long (100 ms) or short (50 ms) intervals. Multisensory stimuli consist of visual and auditory streams carrying the same underlying rate. Visual, auditory, and multisensory trials were randomly interleaved (40% visual, 40% auditory, and 20% multisensory). (d) Schematic outlining the computations of a Bayesian ideal observer. Stimulus belonging to a true category c with a true underlying rate s gives rise to noisy observations $x_A$ and $x_V$, which are then integrated with each other and with prior beliefs to form a multisensory posterior belief about the category, and further combined with reward information to form expected action values $Q_L,Q_R$. The ideal observer selects the action $\widehat{a}$ with maximum expected value. Lightning bolts denote proposed sources of noise that can give rise to (red) or exacerbate (gray) lapses, causing deviations from the ideal observer. (e) Posterior beliefs on an example trial assuming flat priors. Solid black line denotes true rate, and blue and green dotted lines denote noisy visual and auditory observations, with corresponding unisensory posteriors shown in solid blue and green. Solid red denotes the multisensory posterior, centered around the maximum a posteriori rate estimate in dotted red. Shaded fraction denotes the probability of the correct choice being rightward, with μ denoting the category boundary. (f) Ideal observer predictions for the psychometric curve, that is, proportion of high-rate choices for each rate. Inverse slopes of the curves in each condition are reflective of the posterior widths on those conditions, assuming flat priors. The value on the abscissa corresponding to the curve’s midpoint indicates the subjective category boundary, assuming equal rewards and flat priors.