Skip to main content
SpringerLink
Log in

Evidence Accumulation in a Laplace Domain Decision Space

  • Published:
Computational Brain & Behavior Aims and scope Submit manuscript

Abstract

Evidence accumulation models of simple decision-making have long assumed that the brain estimates a scalar decision variable corresponding to the log likelihood ratio of the two alternatives. Typical neural implementations of this algorithmic cognitive model assume that large numbers of neurons are each noisy exemplars of the scalar decision variable. Here, we propose a neural implementation of the diffusion model in which many neurons construct and maintain the Laplace transform of the distance to each of the decision bounds. As in classic findings from brain regions including LIP, the firing rate of neurons coding for the Laplace transform of net accumulated evidence grows to a bound during random dot motion tasks. However, rather than noisy exemplars of a single mean value, this approach makes the novel prediction that firing rates grow to the bound exponentially; across neurons, there should be a distribution of different rates. A second set of neurons records an approximate inversion of the Laplace transform; these neurons directly estimate net accumulated evidence. In analogy to time cells and place cells observed in the hippocampus and other brain regions, the neurons in this second set have receptive fields along a “decision axis.” This finding is consistent with recent findings from rodent recordings. This theoretical approach places simple evidence accumulation models in the same mathematical language as recent proposals for representing time and space in cognitive models for memory.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

Notes

  1. Zhang and Maloney (2012) provide an outstanding discussion of the centrality of log likelihood to understanding cognitive psychology.

  2. When z = a/2, the prior is uninformative.

  3. In many experiments, such as the random dot motion task discussed extensively below, it may be difficult to make a connection to the normative sequential sampling model.

  4. For our purposes, it is sufficient to consider real values of s.

  5. To see this, set \(\alpha (t) = \frac {dx}{dt}\) and multiply both sides of Eq. 9 by \(\frac {dt}{dx}\).

  6. This implies the ordinal variable \(n \propto \log \overset {*}{x}\).

  7. An increase in receptive field width would appear as increase in the width of the central ridge in Fig. 2b. This spread is not visible due to the properties of the recording method used in that study; an increase in receptive field width with peak time is observed in time cell studies using other recording techniques (Jin et al. 2009; Salz et al. 2016; Mello et al. 2015; Tiganj et al. 2018).

  8. More precisely, we implemented \(X_{t+{\Delta }} = X_{t} + A {\Delta } + c \sqrt {\Delta } \mathcal {N}(0,1)\). The value of Δ was set to .001, A was 1.25, .83, and .625 across conditions. X(0) = 0 and we terminated the decision when X = 1.

  9. Because the growth/decay of the units is not at the same rate for each neuron, we would expect additional principal components to capture this residual.

References

  • Atkinson, R.C., & Shiffrin, R.M. (1968). Human memory: a proposed system and its control processes. In Spence, K.W., & Spence, J.T. (Eds.) The psychology of learning and motivation, (Vol. 2 pp. 89–105). New York: Academic Press.

  • Balcı, F., & Simen, P. (2016). A decision model of timing. Curr. Opin. Behav. Sci., 8, 94–101.

    Google Scholar 

  • Beck, J.M., Ma, W.J., Kiani, R., Hanks, T., Churchland, A.K., Roitman, J., Pouget, A. (2008). Probabilistic population codes for bayesian decision making. Neuron, 60(6), 1142–1152.

    PubMed  PubMed Central  Google Scholar 

  • Bogacz, R., Brown, E., Moehlis, J., Holmes, P., Cohen, J.D. (2006). The physics of optimal decisionmaking: a formal analysis of models of performance in two-alternative forced-choice tasks. Psychol. Rev., 113 (4), 700–765.

    PubMed  Google Scholar 

  • Bolkan, S.S., Stujenske, J.M., Parnaudeau, S., Spellman, T.J., Rauffenbart, C., Abbas, A.I., Kellendonk, C. (2017). Thalamic projections sustain prefrontal activity during working memory maintenance. Nat. Neurosci., 20(7), 987–996. https://doi.org/10.1038/nn.4568.

    PubMed  PubMed Central  Google Scholar 

  • Britten, K.H., Shadlen, M.N., Newsome, W.T., Movshon, J.A. (1992). The analysis of visual motion: a comparison of neuronal andpsychophysical performance. J. Neurosci., 12(12), 4745–4765.

    PubMed  PubMed Central  Google Scholar 

  • Brody, C.D., & Hanks, T.D. (2016). Neural underpinnings of the evidence accumulator. Curr. Opin. Neurobiol., 37, 149–157. https://doi.org/10.1016/j.conb.2016.01.003.

    PubMed  PubMed Central  Google Scholar 

  • Brown, S.D., & Heathcote, A. (2008). The simplest complete model of choice response time: linear ballisticaccumulation. Cogn. Psychol., 57(3), 153–78. https://doi.org/10.1016/j.cogpsych.2007.12.002.

    PubMed  Google Scholar 

  • Brunton, B.W., Botvinick, M.M., Brody, C.D. (2013). Rats and humans can optimally accumulate evidence for decision-making. Science, 340(6128), 95–98.

    PubMed  Google Scholar 

  • Busemeyer, J.R., & Townsend, J.T. (1993). Decision field theory: a dynamic-cognitive approach todecision making in an uncertain environment. Psychol. Rev., 100(3), 432.

    PubMed  Google Scholar 

  • Campbell, M.G., Ocko, S.A., Mallory, C.S., Low, I.I.C., Ganguli, S., Giocomo, L.M. (2018). Principles governing the integration of landmark and self-motion cues in entorhinal cortical codes for navigation. Nat. Neurosci., 21(8), 1096–1106. https://doi.org/10.1038/s41593-018-0189-y.

    PubMed  PubMed Central  Google Scholar 

  • Chance, F.S., Abbott, L.F., Reyes, A.D. (2002). Gain modulation from background synaptic input. Neuron, 35(4), 773–82.

    PubMed  Google Scholar 

  • Chaudhuri, R., & Fiete, I. (2016). Computational principles of memory. Nat. Neurosci., 19(3), 394–403.

    PubMed  Google Scholar 

  • Compte, A., Brunel, N., Goldman-Rakic, P.S., Wang, X.J. (2000). Synaptic mechanisms and network dynamics underlying spatial working memory in a cortical network model. Cereb. Cortex, 10(9), 910–23.

    PubMed  Google Scholar 

  • Cook, E.P., & Maunsell, J.H. (2002). Dynamics of neuronal responses in macaque MT and VIP during motion detection. Nat. Neurosci., 5(10), 985.

    PubMed  Google Scholar 

  • Davelaar, E.J., Goshen-Gottstein, Y., Ashkenazi, A., Haarmann, H.J., Usher, M. (2005). The demise of short-term memory revisited: empirical and computational investigations of recency effects. Psychol. Rev., 112(1), 3–42.

    PubMed  Google Scholar 

  • Funahashi, S., Bruce, C.J., Goldman-Rakic, P.S. (1989). Mnemonic coding of visual space in the monkey’s dorsolateral prefrontalcortex. J. Neurophysiol., 61(2), 331–349.

    PubMed  Google Scholar 

  • Fuster, J.M., & Jervey, J.P. (1982). Neuronal firing in the inferotemporal cortex of the monkey in a visual memory task. J. Neurosci., 2, 361–375.

    PubMed  PubMed Central  Google Scholar 

  • Gallistel, C.R., & Gibbon, J. (2000). Time, rate, and conditioning. Psychol. Rev., 107(2), 289–344.

    PubMed  Google Scholar 

  • Gershman, S.J., Horvitz, E.J., Tenenbaum, J.B. (2015). Computational rationality: a converging paradigm for intelligence in brains, minds, and machines. Science, 349(6245), 273–278.

    PubMed  Google Scholar 

  • Gibbon, J., & Church, R.M. (1984). Sources of variance in an information processing theory of timing. In Roitblat, H.L., Terrace, H.S., Bever, T.G. (Eds.) Animal cognition (pp. 465–488). Hillsdale: Erlbaum.

  • Gibbon, J., Church, R.M., Meck, W.H. (1984). Scalar timing in memory. Ann. N. Y. Acad. Sci., 423 (1), 52–77.

    PubMed  Google Scholar 

  • Gold, J.I., & Shadlen, M.N. (2007). The neural basis of decision making. Annual Review Neuroscience, 30, 535–574.

    Google Scholar 

  • Goldman-Rakic, P.S. (1996). Regional and cellular fractionation of working memory. Proc. Natl. Acad. Sci. USA, 93(24), 13473–13480.

    PubMed  PubMed Central  Google Scholar 

  • Goldman, M.S. (2009). Memory without feedback in a neural network. Neuron, 61(4), 621–634.

    PubMed  PubMed Central  Google Scholar 

  • Gothard, K.M., Skaggs, W.E., Moore, K.M., McNaughton, B.L. (1996). Binding of hippocampal CA1 neural activity to multiple reference frames in a landmark-based navigation task. J. Neurosci., 16(2), 823–35.

    PubMed  PubMed Central  Google Scholar 

  • Gothard, K.M., Hoffman, K.L., Battaglia, F.P., McNaughton, B.L. (2001). Dentate gyrus and CA1 ensemble activity during spatial reference frame shifts in the presence and absence of visual input. J. Neurosci., 21 (18), 7284–92.

    PubMed  PubMed Central  Google Scholar 

  • Hanes, D.P., & Schall, J.D. (1996). Neural control of voluntary movement initiation. Science, 274(5286), 427–430.

    PubMed  Google Scholar 

  • Hanks, T.D., Kopec, C.D., Brunton, B.W., Duan, C.A., Erlich, J.C., Brody, C.D. (2015). Distinct relationships of parietal and prefrontal cortices to evidence accumulation. Nature, 520(7546), 220.

    PubMed  PubMed Central  Google Scholar 

  • Howard, M.W., MacDonald, C.J., Tiganj, Z., Shankar, K.H., Du, Q., Hasselmo, M.E., Eichenbaum, H. (2014). A unified mathematical framework for coding time, space, and sequences in the hippocampal region. J. Neurosci., 34(13), 4692–707. https://doi.org/10.1523/JNEUROSCI.5808-12.2014.

    PubMed  PubMed Central  Google Scholar 

  • Howard, M.W., Shankar, K.H., Aue, W., Criss, A.H. (2015). A distributed representation of internal time. Psychol. Rev., 122(1), 24–53.

    PubMed  Google Scholar 

  • Howard, M.W., & Shankar, K.H. (2018). Neural scaling laws for an uncertain world. Psychol. Rev., 125, 47–58. https://doi.org/10.1037/rev0000081.

    PubMed  Google Scholar 

  • Jin, D.Z., Fujii, N., Graybiel, A.M. (2009). Neural representation of time in cortico-basal ganglia circuits. Proc. Natl. Acad. Sci., 106(45), 19156–19161.

    PubMed  PubMed Central  Google Scholar 

  • Katz, L.N., Yates, J.L., Pillow, J.W., Huk, A.C. (2016). Dissociated functional significance of decision-related activityin the primate dorsal stream. Nature, 535(7611), 285–8. https://doi.org/10.1038/nature18617.

    PubMed  PubMed Central  Google Scholar 

  • Kiani, R., Hanks, T.D., Shadlen, M.N. (2008). Bounded integration in parietal cortex underlies decisions even when viewing duration is dictated by the environment. J. Neurosci., 28(12), 3017–3029.

    PubMed  PubMed Central  Google Scholar 

  • Killeen, P.R., & Fetterman, J.G. (1988). A behavioral theory of timing. Psychol. Rev., 95(2), 274–295.

    PubMed  Google Scholar 

  • Kim, J., Ghim, J.W., Lee, J.H., Jung, M.W. (2013). Neural correlates of interval timing in rodent prefrontal cortex. J. Neurosci., 33(34), 13834–47. https://doi.org/10.1523/JNEUROSCI.1443-13.2013.

    PubMed  PubMed Central  Google Scholar 

  • Kraus, B.J., Robinson, R.J. II, White, J.A, Eichenbaum, H., Hasselmo, M.E. (2013). Hippocampal “time cells”: time versus path integration. Neuron, 78(6), 1090–101. https://doi.org/10.1016/j.neuron.2013.04.015.

    PubMed  PubMed Central  Google Scholar 

  • Laming, D. R. J. (1968). Information theory of choice-reaction times.

  • Latimer, K.W., Yates, J.L., Meister, M.L., Huk, A.C., Pillow, J.W. (2015). Single-trial spike trains in parietal cortex reveal discrete steps during decision-making. Science, 349(6244), 184–187.

    PubMed  PubMed Central  Google Scholar 

  • Lever, C., Burton, S., Jeewajee, A., O’Keefe, J., Burgess, N. (2009). Boundary vector cells in the subiculum of the hippocampal formation. J. Neurosci., 29(31), 9771–7.

    PubMed  PubMed Central  Google Scholar 

  • Link, S.W. (1975). The relative judgment theory of two choice response time. J. Math. Psychol., 12(1), 114–135.

    Google Scholar 

  • Lisman, J.E., & Idiart, M.A. (1995). Storage of 7 ± 2 short-term memories in oscillatory subcycles. Science, 267, 1512–1515.

    PubMed  Google Scholar 

  • Liu, Y., Tiganj, Z., Hasselmo, M.E., Howard, M.W. (in press). A neural microcircuit model for a scalable scale-invariant representation oftime. Hippocampus.

  • Luce, R.D. (1986). Response times: their role in inferring elementary mental organization (No. 8). Oxford: Oxford University Press on Demand.

    Google Scholar 

  • Luzardo, A., Alonso, E., Mondragón, E. (2017a). A Rescorla-Wagner drift-diffusion model of conditioning and timing. PLoS Comput. Biol., 13(11), e1005796. https://doi.org/10.1371/journal.pcbi.1005796.

    PubMed  PubMed Central  Google Scholar 

  • Luzardo, A., Rivest, F., Alonso, E., Ludvig, E.A. (2017b). A drift–diffusion model of interval timing in the peak procedure. J. Math. Psychol., 77, 111–123. https://doi.org/10.1016/j.jmp.2016.10.002.

    Google Scholar 

  • MacDonald, C.J., Lepage, K.Q., Eden, U.T., Eichenbaum, H. (2011). Hippocampal “time cells” bridge the gap in memory for discontiguous events. Neuron, 71(4), 737–749.

    PubMed  PubMed Central  Google Scholar 

  • Machens, C.K., Romo, R., Brody, C.D. (2005). Flexible control of mutual inhibition: a neural model of two-interval discrimination. Science, 307(5712), 1121–1124.

    PubMed  Google Scholar 

  • Mau, W., Sullivan, D.W., Kinsky, N.R., Hasselmo, M.E., Howard, M.W., Eichenbaum, H. (2018). The same hippocampal CA1 population simultaneously codes temporal information over multiple timescales. Curr. Biol., 28, 1499–1508.

    PubMed  PubMed Central  Google Scholar 

  • McNaughton, B.L., & O’Keefe, J. (1983). The contributions of position, direction, and velocity to single unit activity in the hippocampus of freely-moving rats. Exp. Brain Res., 52(1), 41– 9.

    PubMed  Google Scholar 

  • Meister, M.L.R., Hennig, J.A., Huk, A.C. (2013). Signal multiplexing and single-neuron computations in lateral intraparietal area during decision-making. J. Neurosci., 33(6), 2254–67. https://doi.org/10.1523/JNEUROSCI.2984-12.2013.

    PubMed  PubMed Central  Google Scholar 

  • Mello, G.B., Soares, S., Paton, J.J. (2015). A scalable population code for time in the striatum. Curr. Biol., 25(9), 1113–1122.

    PubMed  Google Scholar 

  • Morcos, A.S., & Harvey, C.D. (2016). History-dependent variability in population dynamics during evidence accumulation in cortex. Nat. Neurosci., 19(12), 1672–1681.

    PubMed  PubMed Central  Google Scholar 

  • Newsome, W.T., Britten, K.H., Movshon, J.A. (1989). Neuronal correlates of a perceptual decision. Nature, 341(6237), 52.

    PubMed  Google Scholar 

  • Pastalkova, E., Itskov, V., Amarasingham, A., Buzsaki, G. (2008). Internally generated cell assembly sequences in the rat hippocampus. Science, 321(5894), 1322–7.

    PubMed  PubMed Central  Google Scholar 

  • Peixoto, D., Kiani, R., Chandrasekaran, C., Ryu, S.I., Shenoy, K.V., Newsome, W.T. (2018). Population dynamics of choice representation in dorsal premotor and primary motor cortex. bioRxiv, 283960.

  • Post, E. (1930). Generalized differentiation. Trans. Am. Math. Soc., 32, 723–781.

    Google Scholar 

  • Ratcliff, R. (1978). A theory of memory retrieval. Psychol. Rev., 85, 59–108.

    Google Scholar 

  • Ratcliff, R., & McKoon, G. (2008). The diffusion decision model: theory and data for two-choice decision tasks. Neural Comput., 20(4), 873–922.

    PubMed  PubMed Central  Google Scholar 

  • Rivest, F., & Bengio, Y. (2011). Adaptive drift-diffusion process to learn time intervals. arXiv:1103.2382.

  • Roitman, J.D., & Shadlen, M.N. (2002). Response of neurons in the lateral intraparietal area during a combined visual discrimination reaction time task. J. Neurosci., 22(21), 9475–9489.

    PubMed  PubMed Central  Google Scholar 

  • Romo, R., Brody, C.D., Hernández, A., Lemus, L. (1999). Neuronal correlates of parametric working memory in the prefrontal cortex. Nature, 399(6735), 470.

    PubMed  Google Scholar 

  • Salz, D.M., Tiganj, Z., Khasnabish, S., Kohley, A., Sheehan, D., Howard, M.W., Eichenbaum, H. (2016). Time cells in hippocampal area CA3. J. Neurosci., 36, 7476–7484.

    PubMed  PubMed Central  Google Scholar 

  • Schultz, W., Dayan, P., Montague, P.R. (1997). A neural substrate of prediction and reward. Science, 275, 1593–1599.

    PubMed  Google Scholar 

  • Scott, B.B., Constantinople, C.M., Akrami, A., Hanks, T.D., Brody, C.D., Tank, D.W. (2017). Fronto-parietal cortical circuits encode accumulated evidence with a diversity of timescales. Neuron, 95(2), 385–398.

    PubMed  Google Scholar 

  • Shadlen, M.N., & Newsome, W.T. (2001). Neural basis of a perceptual decision in the parietal cortex (area LIP) of the rhesus monkey. J. Neurophys., 86(4), 1916–1936.

    Google Scholar 

  • Shankar, K.H., & Howard, M.W. (2012). A scale-invariant internal representation of time. Neural Comput., 24(1), 134–193.

    PubMed  Google Scholar 

  • Shankar, K.H., & Howard, M.W. (2013). Optimally fuzzy temporal memory. J. Mach. Learn. Res., 14, 3753–3780.

    Google Scholar 

  • Shankar, K.H., Singh, I., Howard, M.W. (2016). Neural mechanism to simulate a scale-invariant future. Neural Comput., 28, 2594– 2627.

    PubMed  Google Scholar 

  • Silver, R.A. (2010). Neuronal arithmetic. Nat. Rev. Neurosci., 11(7), 474–489.

    PubMed  PubMed Central  Google Scholar 

  • Simen, P., Balci, F., de Souza, L., Cohen, J.D., Holmes, P. (2011). A model of interval timing by neural integration. J. Neurosci., 31(25), 9238–53. https://doi.org/10.1523/JNEUROSCI.3121-10.2011.

    PubMed  PubMed Central  Google Scholar 

  • Simen, P., Rivest, F., Ludvig, E.A., Balci, F., Killeen, P. (2013). Timescale invariance in the pacemaker-accumulator family of timing models. Timing & Time Perception, 1(2), 159–188. https://doi.org/10.1163/22134468-00002018.

    Google Scholar 

  • Singh, I., Tiganj, Z., Howard, M.W. (in press). Is working memory stored along a logarithmic timeline? Converging evidence from neuroscience, behavior and models. Neurobiology of Learning and Memory.

  • Smith, P.L., & Ratcliff, R. (2004). Psychology and neurobiology of simple decisions. Trends Neurosci., 27 (3), 161–8.

    PubMed  Google Scholar 

  • Solstad, T., Boccara, C.N., Kropff, E., Moser, M.B., Moser, E.I. (2008). Representation of geometric borders in the entorhinal cortex. Science, 322(5909), 1865–8.

    PubMed  Google Scholar 

  • Sutton, R.S., & Barto, A.G. (1981). Toward a modern theory of adaptive networks: expectation and prediction. Psychol. Rev., 88, 135–171.

    PubMed  Google Scholar 

  • Tiganj, Z., Hasselmo, M.E., Howard, M.W. (2015). A simple biophysically plausible model for long time constants in single neurons. Hippocampus, 25(1), 27–37.

    PubMed  Google Scholar 

  • Tiganj, Z., Kim, J., Jung, M.W., Howard, M.W. (2017). Sequential firing codes for time in rodent mPFC. Cereb. Cortex, 27, 5663–5671.

    PubMed  Google Scholar 

  • Tiganj, Z., Cromer, J.A., Roy, J.E., Miller, E.K., Howard, M.W. (2018). Compressed timeline of recent experience in monkey lPFC. J. Cogn. Neurosci., 30, 935–950.

    PubMed  PubMed Central  Google Scholar 

  • Tsao, A., Sugar, J., Lu, L., Wang, C., Knierim, J.J., Moser, M.B., Moser, E.I. (2018). Integrating time from experience in the lateral entorhinal cortex. Nature. https://doi.org/10.1038/s41586-018-0459-6.

    PubMed  Google Scholar 

  • Usher, M., & McClelland, J.L. (2001). The time course of perceptual choice: the leaky, competing accumulator model. Psychol. Rev., 108(3), 550–92.

    PubMed  Google Scholar 

  • Waelti, P., Dickinson, A., Schultz, W. (2001). Dopamine responses comply with basic assumptions of formal learning theory. Nature, 412(6842), 43–8.

    PubMed  Google Scholar 

  • Wald, A. (1945). Sequential tests of statistical hypotheses. Ann. Math. Stat., 16(2), 117–186.

    Google Scholar 

  • Wald, A. (1947). Foundations of a general theory of sequential decision functions. Econometrica, Journal of the Econometric Society, 15, 279–313.

    Google Scholar 

  • Wald, A., & Wolfowitz, J. (1948). Optimum character of the sequential probability ratio test. The Annals of Mathematical Statistics, 19, 326–339.

    Google Scholar 

  • Wang, X.J. (2002). Probabilistic decision making by slow reverberation in cortical circuits. Neuron, 36(5), 955–968.

    PubMed  Google Scholar 

  • Wang, X.J. (2008). Decision making in recurrent neuronal circuits. Neuron, 60(2), 215–234.

    PubMed  PubMed Central  Google Scholar 

  • Wong, K.F., Huk, A.C., Shadlen, M.N., Wang, X.J. (2007). Neural circuit dynamics underlying accumulation oftime-varying evidence during perceptual decision making. Front. Comput. Neurosci., 1, 6.

    PubMed  PubMed Central  Google Scholar 

  • Xu, M., Zhang, S.-y., Dan, Y., Poo, M.-m. (2014). Representation of interval timing by temporally scalable firing patterns in rat prefrontal cortex. Proc. Natl. Acad. Sci., 111(1), 480–485.

    PubMed  Google Scholar 

  • Zandbelt, B., Purcell, B.A., Palmeri, T.J., Logan, G.D., Schall, J.D. (2014). Response times from ensembles of accumulators. Proc. Natl. Acad. Sci, 111(7), 2848–2853.

    PubMed  PubMed Central  Google Scholar 

  • Zhang, H., & Maloney, L.T. (2012). Ubiquitous log odds: a common representation of probability and frequency distortion in perception, action, and cognition. Front. Neurosci., 6, 1.

    PubMed  PubMed Central  Google Scholar 

  • Zoltowski, D.M., Latimer, K.W., Yates, J.L., Huk, A.C., Pillow, J.W. (2018). Discrete stepping and nonlinear ramping dynamics underlie spiking responses of lip neurons during decision-making. bioRxiv, 433458.

Download references

Acknowledgements

We acknowledge helpful discussions with Bing Brunton, Josh Gold, Chandramouli Chandrasekaran, Chris Harvey, Ben Scott, and Karthik Shankar.

Funding

This work was supported by NIBIB R01EB022864, ONR MURI N00014-16-1-2832, and NIMH R01MH112169.

Author information

Authors and Affiliations

  1. Department of Psychological and Brain Sciences, Boston University, Boston, MA, USA

    Marc W. Howard, Andre Luzardo & Zoran Tiganj

  2. Department of Physics, Boston University, Boston, MA, USA

    Marc W. Howard

Authors
  1. Marc W. Howard
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Andre Luzardo
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zoran Tiganj
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Marc W. Howard.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Howard, M.W., Luzardo, A. & Tiganj, Z. Evidence Accumulation in a Laplace Domain Decision Space. Comput Brain Behav 1, 237–251 (2018). https://doi.org/10.1007/s42113-018-0016-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s42113-018-0016-2

Keywords

Search

Navigation