*Top:* Outline of a trial. Participants clicked on a mouse button and a yellow dot was flashed

ms later at the center of the screen, with

drawn from a block-dependent distribution (estimation phase). The subject then pressed the mouse button for a matching duration of

ms (reproduction phase). Performance feedback was then displayed according to an error map

.

*Bottom:* Generative model for the time interval reproduction task. The interval

is drawn from the probability distribution

(the

*objective distribution*). The stimulus induces in the observer the noisy sensory measurement

with conditional probability density

(the

*sensory likelihood*), with

a sensory variability parameter. The action

subsequently taken by the ideal observer is assumed to be the ‘optimal’ action

that minimizes the subjectively expected loss ();

is therefore a deterministic function of

,

. The subjectively expected loss depends on terms such as the prior

and the loss function (squared subjective error map

), which do not necessarily match their objective counterparts. The chosen action is then corrupted by motor noise, producing the observed response

with conditional probability density

(the

*motor likelihood*), where

is a motor variability parameter.

## PubMed Commons