Robust versus optimal strategies for two-alternative forced choice tasks

Journal of Mathematical Psychology

Volumn 54, Issue 2, 2010, Pages 230-246

  Zacksenhouse, M ^a   Bogacz, R ^b   Holmes, P ^c  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

^b UNIVERSITY OF BRISTOL   (United Kingdom)

^c Princeton University   (United States)

Author keywords

Decision making; Drift diffusion models; Info gap; Optimal decision making; Robust decision making; Two alternative forced choice; Uncertainties

Indexed keywords

EID: 77949873882     PISSN: 00222496     EISSN: 10960880     Source Type: Journal    
DOI: 10.1016/j.jmp.2009.12.004     Document Type: Article

References (61)

1. In: Abramowitz M., and Stegun I. (Eds). Handbook of mathematical functions with formulas, graphs, and mathematical tables (1972), Dover Publications, New York
2. Akaike H. Likelihood of a model and information criteria. Journal of Econometrics 16 (1981) 3-14
3. Ben-Haim Y. Information gap decision theory: Decisions under severe uncertainty. 2nd ed. (2006), Academic Press, New York
4. Ben-Tal A., and Nemirovski A. Selected topics in robust convex optimization. Mathematical Programming 112 (2008) 125-158
5. Bogacz R., Brown E., Moehlis J., Holmes P., and Cohen J. The physics of optimal decision making: A formal analysis of models of performance in two alternative forced choice tasks. Psychological Review 113 4 (2006) 700-765
6. Bogacz, R., Hu, P., Cohen, J., & Holmes, P. (2009). Do humans select the speed-accuracy tradeoff maximizing reward rate? The Quarterly Journal of Experimental Psychology [in press]. Published online Sept 10th, 2009, doi:10.1080/17470210903091643
7. Bohil C., and Maddox W. On the generality of optimal versus objective classifier feedback effects on decision criterion learning in perceptual categorization. Memory & Cognition 31 2 (2003) 181-198
8. Britten K., Shadlen M., Newsome W., and Movshon J. Responses of neurons in macaque MT to stochastic motion signals. Visual Neuroscience 10 (1993) 1157-1169
9. Buhusi C., and Meck W. What makes us tick? functional and neural mechanisms of interval timing. Nature 6 (2005) 755-765
10. Busemeyer J., and Myung I. An adaptive approach to human decision making: Learning theory, decision theory, and human performance. Journal of Experimental Psychology: General 121 2 (1992) 177-194
11. Busemeyer J., and Rapoport A. Psychological models of deferred decision making. Journal of Mathematical Psychology 32 (1988) 91-134
12. Busemeyer J., and Townsend J. Decision field theory: A dynamic-cognitive approach to decision making in an uncertain environment. Psychological Review 100 (1993) 432-459
13. Carmel Y., and Ben-Haim Y. Info-gap robust-satisfying model of foraging behavior: Do foragers optimize or satisfice?. American Naturalist 166 5 (2005) 633-641
14. Cohen J., Dunbar K., and McClelland J. On the control of automatic processes: A parallel distributed processing model of the Stroop effect. Psychological Review 97 3 (1990) 332-361
15. Conover W. Practical nonparametric statistics (1980), Wiley, New York
16. Cox D. Renewal theory. Monographs on applied probability and statistics (1962), Methuen, London
17. Ditterich J. Evidence for time-variant decision making. European Journal of Neuroscience 24 (2006) 3628-3641
18. Ditterich J. Stochastic models of decisions about motion direction: Behavior and psysiology. Neural Networks 19 (2006) 981-1012
19. Diederich A., and Busemeyer J. Simple matrix methods for analyzing diffusion models of choice probability, choice response time, and simple response time. Journal of Mathematical Psychology 47 (2003) 304-322
20. Eckhoff P., Holmes P., Law C., Connolly P., and Gold J. On diffusion processes with variable drift rates as models for decision making during learning. New Journal of Physics 10 (2008) 10.1088/1367-2630/10/1/015006
21. Edwards W. Models for statistics, choice reaction times, and human information processing. Journal of Mathematical Psychology 2 (1965) 312-329
22. Frazier, P., & Yu, A. (2007). Sequential hypothesis testing under stochastic deadlines. In Advances in neural information processing systems. Neural Information Processing Systems Foundation, downloadable from http://books.nips.cc/nips20.html
23. Gardiner C. Handbook of stochastic methods. second ed. (1985), Springer, New York
24. Gibbon J. Scalar expectancy theory and Weber's law in animal timing. Psychological Review 84 3 (1977) 279-325
25. Gigerenzer G. Decision making: Nonrational theories. In: Smelser N., and Bates P. (Eds). International encyclopedia of the social and behavioral sciences Vol. 4 (2001), MIT Press, Cambridge, MA 3304-4409
26. Gigerenzer G. The adaptive toolbox. In: Gigerenzer G., and Selten R. (Eds). Bounded rationality: The adaptive toolbox (2002), MIT Press, Cambridge, MA
27. Gigerenzer G., and Goldstein D. Reasoning the fast and frugal way: Models of bounded rationality. Psychological Review 103 (1996) 650-669
28. Gold J., and Shadlen M. Neural computations that underlie decisions about sensory stimuli. Trends in Cognitive Science 5 1 (2001) 10-16
29. Gold J., and Shadlen M. Banburismus and the brain: Decoding the relationship between sensory stimuli, decisions, and reward. Neuron 36 (2002) 299-308
30. Holmes P., Shea-Brown E., Moehlis J., Bogacz R., Gao J., Aston-Jones G., et al. Optimal decisions: From neural spikes, through stochastic differential equations, to behavior. IEICE Transactions on Fundamentals on Electronics, Communications and Computer Science E88 A 10 (2005) 2496-2503
31. Judge G., Hill R., Griffiths W., Lutkepohl H., and Lee T.-C. Introduction to the theory and practice of econometrics (1988), Wiley, New York
32. Laming D. Information theory of choice-reaction times (1968), Academic Press, New York
33. Liu Y., Holmes P., and Cohen J. A neural network model of the Eriksen task: Reduction, analysis, and data fitting. Neural Computation 20 2 (2008) 345-373
34. Luijendijk H. Practical experiment on noise perception in noisy images. Proceedings of the SPIE - The International Society for Optical Engineering 2166 (1994) 2-8
35. MacKay D. Information theory, inference and learning algorithms (2003), Cambridge University Press, Cambridge, UK
36. Maddox W., and Bohil C. Base-rate and payoff effects in multidimensional perceptual categorization. Journal of Experimental Psychology 24 6 (1998) 1459-1482
37. Mazurek M., Roitman J., Ditterich J., and Shadlen M. A role for neural integrators in perceptual decision making. Cerebral Cortex 13 11 (2003) 891-898
38. Myung I., and Busemeyer J. Criterion learning in a deferred decision making task. The American Journal of Psychiatry 102 1 (1989) 1-16
39. Rapoport A., and Burkheimer G. Models for deferred decision making. Journal of Mathematical Psychology 8 (1971) 508-538
40. Ratcliff R. A theory of memory retrieval. Psychological Review 85 (1978) 59-108
41. Ratcliff R., Cherian A., and Segraves M. A comparison of macaque behavior and superior colliculus neuronal activity to predictions from models of two choice decisions. Journal of Neurophysiology 90 (2003) 1392-1407
42. Ratcliff R., Hasegawa Y., Hasegawa R., Smith P., and Segraves M. Dual-diffusion model for single-cell recording data from the superior colliculus in a bvrightness-discrimination task. Journal of Neurophysiology 97 (2006) 1756-1774
43. Ratcliff R., and Tuerlinckx F. Estimating parameters of the diffusion model: Approaches to dealing with contaminant reaction times and parameter variability. Psychonomic Bulletin & Review 9 (2002) 438-481
44. Ratcliff R., Van Zandt T., and McKoon G. Connectionist and diffusion models of reaction time. Psychological Review 106 2 (1999) 261-300
45. Reber A. Practical nonparametric statisticsthe penguin dictionary of psychology (1995), Penguin Books, London, UK
46. Roxin A., and Ledberg A. Neurobiological models of two-choice decision making can be reduced to a one-dimensional nonlinear diffusion equation. PLoS Computational Biology 4 3 (2008) 10.1371/journal.pcbi.1000046
47. Roitman J., and Shadlen M. Response of neurons in the lateral intraparietal area during a combined visual discrimination reaction time task. Journal of Neuroscience 22 21 (2002) 9475-9489
48. Schall J. Neural basis of deciding, choosing and acting. Nature Reviews in Neuroscience 2 (2001) 33-42
49. Simen P., Cohen J., and Holmes P. Rapid decision threshold modulation by reward rate in a neural network. Neural Networks 19 (2006) 1013-1026
50. Simon H. Rational choice and the structure of environments. Psychological Review 23 (1956) 129-138
51. Simon H. Models of bounded rationality (1982), MIT Press, Cambridge, MA
52. Smith P., and Ratcliff R. Psychology and neurobiology of simple decisions. Trends in Neurosciences 27 3 (2004) 161-168
53. Stone M. Models for choice-reaction time. Psychometrika 25 (1960) 251-260
54. Usher M., and McClelland J. On the time course of perceptual choice: The leaky competing accumulator model. Psychological Review 108 (2001) 550-592
55. Wagenmakers E., van der Maas H., and Grasman R. An ez-diffusion model for response time and accuracy. Psychonomic Bulletin & Review 14 (2007) 3-22
56. Wald A. Sequential analysis (1947), Wiley, New York
57. Wald A. Statistical decision functions (1950), John Wiley & Sons, Inc
58. Wald A., and Wolfowitz J. Optimum character of the sequential probability ratio test. Annals of Mathematical Statistics 19 (1948) 326-339
59. Wang X.-J. Probabilistic decision making by slow reverberation in cortical circuits. Neuron 36 (2002) 955-968
60. Wong K., and Wang X.-J. A recurrent network mechanism of time integration in perceptual decisions. Journal of Neuroscience 26 4 (2006) 1314-1328
61. Zacksenhouse M., Nemets S., Lebedev M., and Nicolelis M. Robust-satisficing linear regression: performance/robustness tradeoff and consistency criterion. Mechanical Systems and Signal Processing 23 6 (2009) 1954-1964. http://dx.doi.org/10.1016/j.ymssp.2008.09.008 Special issue: Inverse problems, doi:10.1016/j.ymssp.2008.09.008