Normative evidence accumulation in unpredictable environments

  1. Christopher M Glaze  Is a corresponding author
  2. Joseph W Kable
  3. Joshua I Gold
  1. University of Pennsylvania, United States
  2. University of Pennsylvania, United Kingdom


In our dynamic world, decisions about noisy stimuli can require temporal accumulation of evidence to identify steady signals; differentiation to detect unpredictable changes in those signals; or both. Normative models can account for learning in these environments but have not yet been applied to faster decision processes. We present a novel, normative formulation of adaptive learning models that forms decisions by acting as a leaky accumulator with non-absorbing bounds. These dynamics, derived for both discrete and continuous cases, depend on the expected rate of change of the statistics of the evidence and balance signal identification and change detection. We found that, for two different tasks, human subjects learned these expectations, albeit imperfectly, then used them to make decisions in accordance with the normative model. The results represent a unified, empirically supported account of decision-making in unpredictable environments that provides new insights into the expectation-driven dynamics of the underlying neural signals.

Article and author information

Author details

  1. Christopher M Glaze

    Department of Neuroscience, University of Pennsylvania, Philadelphia, United States
    For correspondence
    Competing interests
    The authors declare that no competing interests exist.
  2. Joseph W Kable

    Department of Psychology, University of Pennsylvania, Philadelphia, United States
    Competing interests
    The authors declare that no competing interests exist.
  3. Joshua I Gold

    Department of Neuroscience, University of Pennsylvania, University of Pennsylvania, United Kingdom
    Competing interests
    The authors declare that no competing interests exist.


Human subjects: Informed consent, and consent to publish, was obtained from each subject prior to each experiment. Human subject protocols were approved by the University of Pennsylvania Internal Review Board.

Reviewing Editor

  1. Timothy Behrens, Oxford University, United Kingdom

Version history

  1. Received: May 19, 2015
  2. Accepted: August 30, 2015
  3. Accepted Manuscript published: August 31, 2015 (version 1)
  4. Version of Record published: September 28, 2015 (version 2)


© 2015, Glaze et al.

This article is distributed under the terms of the Creative Commons Attribution License permitting unrestricted use and redistribution provided that the original author and source are credited.


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  1. Christopher M Glaze
  2. Joseph W Kable
  3. Joshua I Gold
Normative evidence accumulation in unpredictable environments
eLife 4:e08825.

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