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. 2018 Oct 31;285(1890):20181722. doi: 10.1098/rspb.2018.1722

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© 2018 The Authors.

Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.

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Figure 2. — Optimal integration of current and previous sensory information. (a–d) Example of sensory representation of a 40° stimulus accompanied by a 10° estimation noise. This signal can either be integrated with a preceding stimulus of similar (a,c) or different (b,d) orientation (10° and 40° away respectively). (a,c) show representation histograms. Along with the representation of sensory estimates, we show the histograms of estimates provided by an observer who integrates current and previous signals with a 0.33 weight of the past (which is optimal for the 10° difference and non-optimal for the 40°difference). (b,d) show squared error distributions associated with each estimate of the observer: squared error grows fast for estimates which are far from the correct value (40°). In the case of small difference and optimal weight (b, pink) the observer performing integration fares better than the original set of estimates. In (e) we show how the weight of the previous stimulus should vary as function of distance between the two stimuli, for noise of 10° (continuous line) and 3° (dashed line). Panels (f,g) display the bias and root-mean-square error (RMSE) of the ideal observer employing optimal weighting of current and previous information. Again, two examples are shown assuming noise of 10° (continuous line) and 3° (dashed line). The conditions depicted in panels (a–d) are highlighted with a pink star (optimal weight for 10° difference) or a hollow circle (non-optimal weight with 40° difference) along with optimal choice for 40° (purple star). Inset (h) illustrates that RMSE is the Pythagorean sum of bias and the square root of variance.