The Cost of Accumulating Evidence in Perceptual Decision Making
Open accessAbstract
Decision making often involves the accumulation of information over time, but acquiring information typically comes at a cost. Little is known about the cost incurred by animals and humans for acquiring additional information from sensory variables due, for instance, to attentional efforts. Through a novel integration of diffusion models and dynamic programming, we were able to estimate the cost of making additional observations per unit of time from two monkeys and six humans in a reaction time (RT) random-dot motion discrimination task. Surprisingly, we find that the cost is neither zero nor constant over time, but for the animals and humans features a brief period in which it is constant but increases thereafter. In addition, we show that our theory accurately matches the observed reaction time distributions for each stimulus condition, the time-dependent choice accuracy both conditional on stimulus strength and independent of it, and choice accuracy and mean reaction times as a function of stimulus strength. The theory also correctly predicts that urgency signals in the brain should be independent of the difficulty, or stimulus strength, at each trial.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The factors that determine when to stop gathering information and commit to a final decision, as well as which options to sample from, remain an active area of investigation.
“the factors that determine when to stop gathering information and commit to a final decision, as well as which options to sample from, remain an active area of investigation1,4,9–11.”
From Interpretable abstractions of artificial neural networks predict behavior and neural activity during human information gathering (2026) · cites this paper as [4]
A flat decision bound does not capture the shape of the reaction-time distributions and the mean reaction time on error trials.
“For analytic simplicity (see below), we used a flat bound (i.e., stationary rather than collapsing), which does not capture the shape of the RT distributions and the mean RT on error trials (Drugowitsch et al., 2012).”
From A common mechanism underlies changes of mind about decisions and confidence (2016) · cites this paper as Drugowitsch et al., 2012
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
A new look at the statistical model identification
Akaike, H. (1974) · IEEE Transactions on Automatic Control · doi:10.1109/tac.1974.1100705 · Cited by 51,879 · see citing works
Reinforcement Learning: An Introduction
Sutton, R. S., & Barto, A. (2005) · IEEE Transactions on Neural Networks · doi:10.1109/tnn.2004.842673 · Cited by 25,263 · see citing works
Advances in neural information processing systems 7
Cios, K. J., & Shields, M. E. (1997) · Neurocomputing · doi:10.1016/s0925-2312(97)90018-7 · Cited by 22,089 · see citing works
Advances in Neural Information Processing Systems 19
(2007) · The MIT Press eBooks · doi:10.52202/085713 · Cited by 16,037 · see citing works
Bellman, R. E. (2010) · doi:10.1515/9781400835386 · Cited by 14,588 · see citing works
(1995) · Cited by 10,558 · see citing works
(1966) · Medical Entomology and Zoology · Cited by 10,293 · see citing works
Risken, H. (1984) · Springer series in synergetics · doi:10.1007/978-3-642-61544-3 · Cited by 9,128 · see citing works
Ratcliff, R. (1978) · Psychological Review · doi:10.1037/0033-295x.85.2.59 · Cited by 4,513 · see citing works
The Neural Basis of Decision Making
Gold, J. I., & Shadlen, M. N. (2007) · Annual Review of Neuroscience · doi:10.1146/annurev.neuro.29.051605.113038 · Cited by 3,764 · see citing works
Self-citation<i>The Theory of Stochastic Processes</i>
Cox, D. R., Miller, H. D., Weiss, G., & Shuler, K. (1966) · Physics Today · doi:10.1063/1.3047872 · Cited by 3,324 · see citing works
Barto, A. (1998) · IFAC Proceedings Volumes · doi:10.1016/s1474-6670(17)38315-5 · Cited by 2,172 · see citing works
The analysis of visual motion: a comparison of neuronal and psychophysical performance
Britten, K., Shadlen, M., Newsome, W., & Movshon, J. (1992) · The Journal of Neuroscience · doi:10.1523/jneurosci.12-12-04745.1992 · Cited by 1,958 · see citing works
Self-citationBogacz, R., Brown, E., Moehlis, J., Holmes, P. J., & Cohen, J. D. (2006) · Psychological Review · doi:10.1037/0033-295x.113.4.700 · Cited by 1,845 · see citing works
Neural Basis of a Perceptual Decision in the Parietal Cortex (Area LIP) of the Rhesus Monkey
Shadlen, M. N., & Newsome, W. T. (2001) · Journal of Neurophysiology · doi:10.1152/jn.2001.86.4.1916 · Cited by 1,755 · see citing works
Self-citationRoitman, J. D., & Shadlen, M. N. (2002) · The Journal of Neuroscience · doi:10.1523/jneurosci.22-21-09475.2002 · Cited by 1,589 · cited 4× · see citing works
“…firing rate of neurons in the intraparietal cortex (LIP) seems to represent ac- cumulation of evidence over time, as this rate, as a function of time, is consistent with a diffusion process with a deterministic drift (Shadlen and Newsome, 2001; Roitman and Shadlen, 2002; Churchland et al., 2011).”
BackgroundInfluentialSelf-citationBayesian inference with probabilistic population codes
Ma, W. J., Beck, J. M., Latham, P. E., & Pouget, A. (2006) · Nature Neuroscience · doi:10.1038/nn1790 · Cited by 1,457 · see citing works
Self-citationNeal, R. M. (2003) · The Annals of Statistics · doi:10.1214/aos/1056562461 · Cited by 1,380 · see citing works
A Comparison of Sequential Sampling Models for Two-Choice Reaction Time.
Ratcliff, R., & Smith, P. L. (2004) · Psychological Review · doi:10.1037/0033-295x.111.2.333 · Cited by 1,227 · see citing works
Neuronal correlates of a perceptual decision
Newsome, W. T., Britten, K. H., & Movshon, J. A. (1989) · Nature · doi:10.1038/341052a0 · Cited by 1,177 · see citing works
Optimum Character of the Sequential Probability Ratio Test
Wald, A., & Wolfowitz, J. (1948) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177730197 · Cited by 1,162 · see citing works
Slice SamplingPreprint
Neal, R. M. (2000) · arXiv (Cornell University) · Cited by 1,151 · see citing works
Representation of Confidence Associated with a Decision by Neurons in the Parietal Cortex
Kiani, R., & Shadlen, M. N. (2009) · Science · doi:10.1126/science.1169405 · Cited by 1,027 · see citing works
Self-citationInformation theory of choice-reaction times
Laming, D. (1968) · Medical Entomology and Zoology · Cited by 952 · see citing works
The effect of stimulus strength on the speed and accuracy of a perceptual decision
Palmer, J., Huk, A. C., & Shadlen, M. N. (2005) · Journal of Vision · doi:10.1167/5.5.1 · Cited by 691 · see citing works
Self-citationDecision-making with multiple alternatives
Churchland, A. K., Kiani, R., & Shadlen, M. N. (2008) · Nature Neuroscience · doi:10.1038/nn.2123 · Cited by 671 · see citing works
Self-citationProbabilistic population codes for Bayesian decision making
Beck, J. M., Ma, W. J., Kiani, R., Hanks, T., Churchland, A. K., Roitman, J., Shadlen, M. N., Latham, P. E., & Pouget, A. (2008) · Neuron · doi:10.1016/j.neuron.2008.09.021 · Cited by 645 · see citing works
Self-citationA role for neural integrators in perceptual decision making
Mazurek, M. E., Roitman, J. D., Ditterich, J., & Shadlen, M. N. (2003) · Cerebral Cortex · doi:10.1093/cercor/bhg097 · Cited by 620 · see citing works
Self-citationGold, J. I., & Shadlen, M. N. (2002) · Neuron · doi:10.1016/s0896-6273(02)00971-6 · Cited by 547 · see citing works
Self-citationDecision Processes in Visual Perception
(1979) · Elsevier eBooks · doi:10.1016/c2013-0-11654-6 · Cited by 511 · see citing works
Kiani, R., Hanks, T. D., & Shadlen, M. N. (2008) · The Journal of Neuroscience · doi:10.1523/jneurosci.4761-07.2008 · Cited by 500 · see citing works
Self-citationA Sequential Theory of Psychological Discrimination
Link, S. W., & Heath, R. A. (1975) · Psychometrika · doi:10.1007/bf02291481 · Cited by 492 · see citing works
Average reward reinforcement learning: Foundations, algorithms, and empirical results
Mahadevan, S. (1996) · Machine Learning · doi:10.1007/bf00114727 · Cited by 386 · see citing works
Elapsed Decision Time Affects the Weighting of Prior Probability in a Perceptual Decision Task
Hanks, T. D., Mazurek, M. E., Kiani, R., Hopp, E., & Shadlen, M. N. (2011) · The Journal of Neuroscience · doi:10.1523/jneurosci.5613-10.2011 · Cited by 378 · see citing works
Self-citationVariance as a signature of neural computations during decision making
Churchland, A. K., Kiani, R., Chaudhuri, R., Wang, X.-J., Pouget, A., & Shadlen, M. N. (2011) · Neuron · doi:10.1016/j.neuron.2010.12.037 · Cited by 350 · see citing works
Self-citationStochastic Dynamic Models of Response Time and Accuracy: A Foundational Primer
Smith, P. L. (2000) · Journal of Mathematical Psychology · doi:10.1006/jmps.1999.1260 · Cited by 271 · see citing works
Stochastic models of decisions about motion direction: Behavior and physiology
Ditterich, J. (2006) · Neural Networks · doi:10.1016/j.neunet.2006.05.042 · Cited by 233 · see citing works
Evidence for time‐variant decision making
Ditterich, J. (2006) · European Journal of Neuroscience · doi:10.1111/j.1460-9568.2006.05221.x · Cited by 229 · see citing works
Rorie, A. E., Gao, J., McClelland, J. L., & Newsome, W. T. (2010) · PLoS ONE · doi:10.1371/journal.pone.0009308 · Cited by 195 · see citing works
Rao, R. P. N. (2010) · Frontiers in Computational Neuroscience · doi:10.3389/fncom.2010.00146 · Cited by 190 · see citing works
Marginalization in Neural Circuits with Divisive Normalization
Beck, J. M., Latham, P. E., & Pouget, A. (2011) · Journal of Neuroscience · doi:10.1523/jneurosci.1706-11.2011 · Cited by 131 · see citing works
Self-citationNearly Optimal Sequential Tests of Composite Hypotheses
Lai, T. L. (1988) · The Annals of Statistics · doi:10.1214/aos/1176350840 · Cited by 128 · see citing works
Sequential Hypothesis Testing under Stochastic Deadlines
Frazier, P. I., & Yu, A. J. (2007) · TUbilio (Technical University of Darmstadt) · Cited by 106 · see citing works
Moreno‐Bote, R. (2010) · Neural Computation · doi:10.1162/neco.2010.12-08-930 · Cited by 99 · see citing works
Self-citationA Gridding Method for Bayesian Sequential Decision Problems
Brockwell, A., & Kadane, J. B. (2003) · Journal of Computational and Graphical Statistics · doi:10.1198/1061860032274 · Cited by 58 · see citing works
A Bayesian approach to diffusion process models of decision-making
Vandekerckhove, J., Tuerlinckx, F., & Lee, M. D. (2008) · Lirias · Cited by 44 · see citing works
Flagged first, then by citations
Research works printed but not linked: 1
- Wald A 1947 Sequential analysis New York, London J. Wiley & sons, Chapman & Hall
Cited by
Sorted by citations
Diffusion decision model: Current issues and history
Ratcliff, R., Smith, P. L., Brown, S. D., & McKoon, G. (2016) · Trends in Cognitive Sciences · doi:10.1016/j.tics.2016.01.007 · Cited by 1,630 · see citing works
“cases where it is possible to set different boundaries for each difficulty level, human decision makers seem fairly efficient at setting those many boundaries in an optimal manner [74,75].”
BackgroundChoice Certainty Is Informed by Both Evidence and Decision Time
Kiani, R., Corthell, L., & Shadlen, M. N. (2014) · Neuron · doi:10.1016/j.neuron.2014.12.015 · Cited by 470 · see citing works
Self-citationSuboptimality in perceptual decision making
Rahnev, D., & Denison, R. N. (2018) · Behavioral and Brain Sciences · doi:10.1017/s0140525x18000936 · Cited by 342 · see citing works
Not Noisy, Just Wrong: The Role of Suboptimal Inference in Behavioral Variability
Beck, J. M., Ma, W. J., Pitkow, X., Latham, P. E., & Pouget, A. (2012) · Neuron · doi:10.1016/j.neuron.2012.03.016 · Cited by 316 · see citing works
Self-citationA common mechanism underlies changes of mind about decisions and confidence
van den Berg, R., Anandalingam, K., Zylberberg, A., Kiani, R., Shadlen, M. N., & Wolpert, D. M. (2016) · eLife · doi:10.7554/elife.12192 · Cited by 270 · see citing works
Self-citationA neural mechanism of speed-accuracy tradeoff in macaque area LIP
Hanks, T., Kiani, R., & Shadlen, M. N. (2014) · eLife · doi:10.7554/elife.02260 · Cited by 222 · see citing works
Self-citationPerceptual Decision-Making as Probabilistic Inference by Neural Sampling
Haefner, R. M., Berkes, P., & Fiser, J. (2016) · Neuron · doi:10.1016/j.neuron.2016.03.020 · Cited by 207 · see citing works
Neural circuits for evidence accumulation and decision making in larval zebrafish
Bahl, A., & Engert, F. (2020) · Nature Neuroscience · doi:10.1038/s41593-019-0534-9 · Cited by 166 · see citing works
Representation of accumulating evidence for a decision in two parietal areas
de Lafuente, V., Jazayeri, M., & Shadlen, M. N. (2015) · The Journal of Neuroscience · doi:10.1523/jneurosci.2451-14.2015 · Cited by 162 · see citing works
“In particular, LIP is known to represent the accumulated evidence, combined with other factors that affect the decision, such as the previous probability, value, and costs associated with the alternatives (Seo et al., 2009; Rorie et al., 2010; Hanks et al., 2011; Drugowitsch et al., 2012).”
BackgroundSelf-citationThe opportunity cost of time modulates cognitive effort
Otto, A. R., & Daw, N. D. (2019) · Neuropsychologia · doi:10.1016/j.neuropsychologia.2018.05.006 · Cited by 138 · see citing works
Confidence Is the Bridge between Multi-stage Decisions
van den Berg, R., Zylberberg, A., Kiani, R., Shadlen, M. N., & Wolpert, D. M. (2016) · Current Biology · doi:10.1016/j.cub.2016.10.021 · Cited by 125 · see citing works
Motor effort alters changes of mind in sensorimotor decision making
Burk, D., Ingram, J. N., Franklin, D. W., Shadlen, M. N., & Wolpert, D. M. (2014) · PLoS ONE · doi:10.1371/journal.pone.0092681 · Cited by 117 · see citing works
Rational use of cognitive resources in human planning
Callaway, F., van Opheusden, B., Gul, S., Das, P., Krueger, P. M., Griffiths, T. L., & Lieder, F. (2022) · Nature Human Behaviour · doi:10.1038/s41562-022-01332-8 · Cited by 121 · see citing works
Hauser, T. U., Moutoussis, M., Iannaccone, R., Brem, S., Walitza, S., Drechsler, R., Dayan, P., & Dolan, R. J. (2017) · PLOS Computational Biology · doi:10.1371/journal.pcbi.1005440 · Cited by 85 · see citing works
Relation between belief and performance in perceptual decision making
Drugowitsch, J., Moreno-Bote, R., & Pouget, A. (2014) · PLoS ONE · doi:10.1371/journal.pone.0096511 · Cited by 72 · see citing works
Self-citationKhalvati, K., Kiani, R., & Rao, R. P. N. (2021) · Nature Communications · doi:10.1038/s41467-021-25419-4 · Cited by 64 · see citing works
Niyogi, R. K., & Wong-Lin, K. (2013) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1003099 · Cited by 47 · see citing works
Striatal activation reflects urgency in perceptual decision making
van Maanen, L., Fontanesi, L., Hawkins, G. E., & Forstmann, B. U. (2016) · NeuroImage · doi:10.1016/j.neuroimage.2016.06.045 · Cited by 36 · see citing works
D’Ambrogio, S., Grohn, J., Khalighinejad, N., Mattar, M. G., Hunt, L., & Rushworth, M. F. S. (2026) · Nature Neuroscience · doi:10.1038/s41593-026-02342-9 · Cited by 1 · see citing works
- Authors
- Drugowitsch, J., Moreno-Bote, R., Churchland, A. K., Shadlen, M. N., & Pouget, A.
- Affiliations
- Inserm (FR)
- University of Geneva (CH)
- Howard Hughes Medical Institute (US)
- Venue
- The Journal of Neuroscience
- Publisher
- Society for Neuroscience
- Published
- 2012-03-14
- Volume
- 32
- Issue
- 11
- Pages
- 3612-3628
- ISSN
- 0270-6474 (ISSN-L)
- 1529-2401
- PMC
- PMC3329788
- OpenAlex
- W2129641119
- Cited by
- 577
- References
- 46
- Citations by year
- 2026: 34 · 2025: 44 · 2024: 53 · 2023: 62 · 2022: 40 · 2021: 44 · 2020: 43 · 2019: 45 · 2018: 40 · 2017: 30 · 2016: 41 · 2015: 37 · 2014: 36 · 2013: 20 · 2012: 8
- FWCI
- 16.56
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Licence
- Locations
- Journal of Neuroscience (publishedVersion, cc-by-nc-sa)
- PubMed Central (publishedVersion)
- PubMed (publishedVersion)
- Archive ouverte UNIGE (University of Geneva) (publishedVersion, other-oa)
- Cold Spring Harbor Laboratory Institutional Repository (Cold Spring Harbor Laboratory) (acceptedVersion)
- Archive ouverte UNIGE (University of Geneva) (submittedVersion, cc-by)
- Funders
- National Science Foundation (0446730)
- James S. McDonnell Foundation
- Multidisciplinary University Research Initiative (N00014-07-1-0937)
- National Institute on Drug Abuse (R01DA022780)
- National Eye Institute (R00EY019072)
- Topics
- Life Sciences › Neuroscience › Cognitive Neuroscience › Visual perception and processing mechanisms
- Life Sciences › Neuroscience › Cognitive Neuroscience › Neural and Behavioral Psychology Studies
- Social Sciences › Decision Sciences › General Decision Sciences › Decision-Making and Behavioral Economics
- Keywords
- perceptual decision making, evidence accumulation, attentional effort, diffusion models, dynamic programming, reaction time distribution, stimulus strength, choice accuracy, monkeys, human
- MeSH terms
- Animals, Haplorhini, Choice Behavior, Costs and Cost Analysis, Decision Making, Female, Humans, Male, Motion Perception, Photic Stimulation, Psychomotor Performance, Random Allocation, Reaction Time
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review