Diffusion theory of decision making in continuous report

Psychological Review

Volumn 123, Issue 4, 2016, Pages 125-151

  Smith, Philip L ^a  

^a UNIVERSITY OF MELBOURNE   (Australia)

Author keywords

Continuous report; Decision making; Diffusion process; Short term memory (STM); Working memory

Indexed keywords

DECISION MAKING; HUMAN; PSYCHOLOGICAL THEORY; RECALL; SHORT TERM MEMORY;

DECISION MAKING; HUMANS; MEMORY, SHORT-TERM; MENTAL RECALL; PSYCHOLOGICAL THEORY;

EID: 84959454628     PISSN: 0033295X     EISSN: None     Source Type: Journal    
DOI: 10.1037/rev0000023     Document Type: Article

References (110)

1. Abramowitz, M., & Stegun, I. (1965). Handbook of mathematical functions. New York, NY: Dover.
2. Arkfen, G. B., & Weber, H. J. (2001). Mathematical methods for physicists (5th ed.). San Diego, CA: Academic Press.
3. Ashby, F. G. (1983). A biased random walk for two choice reaction times. Journal of Mathematical Psychology, 27, 277-297.
4. Ashby, F. G. (2000). A stochastic version of general recognition theory. Journal of Mathematical Psychology, 44, 310-329.
5. Ashby, F. G., & Townsend, J. T. (1986). Varieties of perceptual independence. Psychological Review, 93, 154-179.
6. Audley, R. J., & Pike, A. R. (1965). Some alternative stochastic models of choice. British Journal of Mathematical and Statistical Psychology, 18, 207-225.
7. Baxter, M., & Rennie, A. (1996). Financial calculus: An introduction to derivative pricing. Cambridge, United Kingdom: Cambridge University Press.
8. Bays, P. M. (2014). Noise in neural populations accounts for errors in working memory. The Journal of Neuroscience, 34, 3632-3645.
9. Bays, P. M., Catalao, R. F. G., & Husain, M. (2009). The precision of visual working memory is set by allocation of a shared resource. Journal of Vision, 9, Article 7.
10. Bays, P., Gorgoraptis, N., Wee, N., Marshall, L., & Husain, M. (2011). Temporal dynamics of encoding, storage, and reallocation of visual working memory. Journal of Vision, 11, Article 6.
11. Berlin, B., & Kay, P. (1969). Basic color terms: Their universality and evolution. Berkeley, CA: University of California Press.
12. Blurton, S. P., Kesselmeir, M., & Gondan, M. (2012). Fast and accurate calculations of cumulative first-passage time distributions in Wiener diffusion models. Journal of Mathematical Psychology, 56, 470-475.
13. Bogacz, R., Brown, E., Moehlis, J., Holmes, P., & Cohen, J. D. (2006). The physics of optimal decision making: A formal analysis of models of performance in two-alternative forced choice tasks. Psychological Review, 113, 700-765.
14. Borodin, A. N., & Salminen, P. (1996). Handbook of Brownian motion-Facts and formulae. Basel: Birkhäser.
15. Brewer, N., & Smith, G. A. (1989). Developmental changes in processing speed: Influence of speed-accuracy regulation. Journal of Experimental Psychology: General, 118, 298-310.
16. Busemeyer, J., & Townsend, J. T. (1993). Decision field theory: A dynamic-cognitive approach to decision making in an uncertain environment. Psychological Review, 100, 432-459.
17. Carverhill, A. P. (1985). Flows of stochastic dynamical systems: Ergodic theory. Stochastics, 14, 273-318.
18. Cowan, N. (2001). The magical number 4 in short-term memory: A reconsideration of mental storage capacity. Behavioral and Brain Sciences, 24, 87-185.
19. Diederich, A. (1995). Intersensory facilitation of reaction time: Evaluation of counter and diffusion coactivation models. Journal of Mathematical Psychology, 39, 197-215.
20. Diederich, A., & Busemeyer, J. R. (2003). Simple matrix methods for analyzing diffusion models of choice probability, choice response time, and simple response time. Journal of Mathematical Psychology, 47, 304-322.
21. Donders, F. C. (1869/1969). On the speed of mental processes. Translated by W. G. Koster, in W. G. Koster (Ed.), Attention and Performance II Acta Psychologica, 30, 412-431.
22. Eckstein, M. P., Thomas, J. P., Palmer, J., & Shimozaki, S. (2000). A signal detection model predicts the effects of set size on visual search accuracy for feature, conjunction, triple conjunction, and disjunction displays. Perception & Psychophysics, 62, 425-451.
23. Engen, T. (1971). Psychophysics I. Discrimination and detection. In J. W. Kling & L. A. Riggs (Eds.) Woodworth and Schlosberg's experimental psychology (3rd ed., pp. 11-46). New York, NY: Holt, Rinehart & Winston.
24. Fan, J. E., & Turk-Brown, N. B. (2013). Internal attention to features in visual short-term memory guides object learning. Cognition, 129, 292-308.
25. Fific, M., Little, D. R., & Nosofsky, R. M. (2010). Logical-rule models of classification response times: A synthesis of mental-architecture, random-walk, and decision-bound approaches. Psychological Review, 117, 309-348.
26. Fisher, N. I. (1993). Statistical analysis of circular data. Cambridge, United Kingdom: Cambridge University Press.
27. Fougnie, D., & Alvarez, G. A. (2011). Object features fail independently in visual working memory: Evidence for a probabilistic feature-store model. Journal of Vision, 11, Article 3.
28. Getoor, R. K., & Sharpe, M. J. (1979). Excursions of Brownian motion and Bessel processes. Zeitschrift für Wahrscheinlichkeitstheorie, 47, 83-106.
29. Gomez, P., Ratcliff, R., & Perea, M. (2007). A model of the go/no-go task. Journal of Experimental Psychology: General, 136, 347-369.
30. Graham, N. V. S. (1989). Visual pattern analyzers. New York, NY: Wiley.
31. Green, D. M., Smith, A. F., & von Gierke, S. M. (1983). Choice reaction time with a random foreperiod. Perception & Psychophysics, 34, 195-208.
32. Green, D. M., & Swets, J. A. (1966). Signal detection theory and psychophysics. New York, NY: Wiley.
33. Gunseli, E., van Moorselaar, D., & Meeter, M., & Olivers, C. N. L. (2015). The reliability of retro-cues determine working memory representations. Psychonomic Bulletin & Review, 22, 1334-1341.
34. Hamana, Y., & Matsumoto, H. (2013). The probability distributions of the first hitting times of Bessel processes. Transactions of the American Mathematical Society, 365, 5237-5257.
35. Harrison, M. (1985). Brownian motion and stochastic flow systems. New York: NY: Wiley.
36. Heath, R. A., & Kelly, L. (1988). An application of a discriminatory index for the assessment of individual differences. In R. A. Heath (Ed.), Current issues in cognitive development and mathematical psychology. Newcastle, N. S. W.: University of Newcastle.
37. Hsu, P. (1986). Brownian exit distributions of a ball. In E. Çinlar, K. L. Chung, R. K. Getoor, & J. Glover (Eds.) Seminar on stochastic processes, 1985 (pp. 108-116). Boston, MA: Birkhäuser.
38. Johnson, N. L., Kotz, S., & Balakrishnan, N. (1995). Continuous univariate distributions (Vol. 2, 2nd ed.) New York, NY: Wiley.
39. Jones, M., & Dzhafarov, E. N. (2014). Unfalsifiability and mutual translatability of major modeling schemes for choice reaction time. Psychological Review, 121, 1-32.
40. Kahneman, D. (1973). Attention and effort. Englewood Cliffs, NJ: Prentice Hall.
41. Karatzas, I., & Shreve, S. E. (1991). Brownian motion and stochastic calculus. New York, NY: Springer.
42. Karlin, S., & Taylor, H. M. (1981). A second course in stochastic processes. New York, NY: Academic Press.
43. Kent, J. T. (1978). Some probabilistic properties of Bessel functions. Annals of Probability, 6, 760-770.
44. Kent, J. T. (1980). Eigenvalue expansions for diffusion hitting times. Zeitschrift für Wahrscheinlichkeitstheorie, 52, 309-319.
45. Kool, W., Conway, A. R. A., & Turk-Browne, N. B. (2014). Sequential dynamics in visual short-term memory. Attention, Perception, & Psychophysics, 76, 1885-1901.
46. Laming, D. (1968). Information theory of choice reaction times. New York, NY: Academic Press.
47. Laming, D. (1979). A critical comparison of two random-walk models for two choice reaction time. Acta Psychologica, 43, 431-453.
48. Link, S. W. (1975). The relative judgment theory of two-choice response time. Journal of Mathematical Psychology, 12, 114-135.
49. Link, S. W., & Heath, R. A. (1975). A sequential theory of psychological discrimination. Psychometrika, 40, 77-105.
50. Luce, R. D. (1986). Response times: Their role in inferring elementary mental organization. New York, NY: Oxford University Press.
51. Ma, W. J., Husain, M., & Bays, P. M. (2014). Changing concepts of working memory. Nature Neuroscience, 17, 347-356.
52. Ma, W. J., Shen, S., Dziugaite, G., & van den Berg, R. (2015). Requiem for the max rule? Vision Research, 116, 179-193.
53. Macmillan, N. A., & Creelman, C. D. (2005). Detection theory: A user's guide (2nd ed.). Mahwah, NJ: Erlbaum.
54. Marshall, L., & Bays, P. M. (2013). Obligatory encoding of task-irrelevant features depletes working memory resources. Journal of Vision, 13, Article 21.
55. McNicol, D. (1972/2005). A primer of signal detection theory. London, United Kingdom: George Allen & Unwin. Reprinted 2005 by Erlbaum.
56. Mörters, P., & Peres, Y. (2010). Brownian motion. Cambridge, United Kingdom: Cambridge University Press.
57. Nolte, L. W., & Jaarsma, D. (1967). More on the detection of one of Morthogonal signals. Journal of the Acoustical Society of America, 41, 497-505.
58. Palmer, J., Verghese, P., & Pavel, M. (2000). The psychophysics of visual search. Vision Research, 40, 1227-1268.
59. Pearson, B., Raškevicĭus, J., Bays, P. M., Pertzov, Y., & Husain, M. (2014). Working memory retrieval as a decision process. Journal of Vision, 14, Article 2.
60. Persaud, K., & Hemmer, P. (2014). The influence of knowledge and expectations for color on episodic memory. Proceedings of the 36th Annual Conference of the Cognitive Science Society. Quebec City, Canada.
61. Purcell, B. A., Heitz, R. P., Cohen, J. Y., Schall, J. D., Logan, G. D., & Palmeri, T. J. (2010). Neurally constrained modeling of perceptual decision making. Psychological Review, 117, 1113-1143.
62. Rabbitt, P. M. A., & Rodgers, B. (1977). What does a man do after he makes an error? An analysis of response programming. Quarterly Journal of Experimental Psychology, 29, 727-743.
63. Rademaker, R. L., Tredway, C. H., & Tong, F. (2012). Introspective judgments predict the precision and likelihood of successful maintenance of visual working memory. Journal of Vision, 12, Article 21.
64. Ratcliff, R. (1978). A theory of memory retrieval. Psychological Review, 85, 59-108.
65. Ratcliff, R. (2006). Modeling response signal and response time data. Cognitive Psychology, 53, 195-237.
66. Ratcliff, R., Hasegawa, Y., Hasegawa, R., Smith, P. L., & Segraves, M. (2007). A dual diffusion model for single cell recording data from the superior colliculus in brightness discrimination task. Journal of Neurophysiology, 97, 1756-1797.
67. Ratcliff, R., & McKoon, G. (2008). The diffusion decision model: Theory and data for two-choice decision tasks. Neural Computation, 20, 873-922.
68. Ratcliff, R., & Smith, P. L. (2004). A comparison of sequential-sampling models for two choice reaction time. Psychological Review, 111, 333-367.
69. Ratcliff, R., & Smith, P. L. (2010). Perceptual discrimination in static and dynamic noise: The temporal relationship between perceptual encoding and decision making. Journal of Experimental Psychology: General, 139, 70-94.
70. Ratcliff, R., & Smith, P. L. (2015). Modeling simple decisions and applications using a diffusion model. In J. R. Busemeyer, Z. Wang, J. TTownsend, & A. Eidels (Eds.), The Oxford handbook of computational and mathematical psychology (pp. 35-62). Oxford, United Kingdom: Oxford University Press.
71. Ratcliff, R., Smith, P. L., & McKoon, G. (2015). Modeling response time and accuracy data. Current Directions in Psychological Science, 24, 458-470.
72. Reuter, G. E. H. (1959). Denumerable Markov processes, II. Journal of the London Mathematical Society, 34, 81-91.
73. Revus, D., & Yor, M. (1990). Continuous martingales and Brownian motion. Berlin: Springer-Verlag.
74. Rogers, L. C. G., & Williams, D. (1987/2000). Diffusions, Markov processes and martingales. Vol. 2. Itô calculus. Chichester, United Kingdom: Wiley, reprinted 2000 New York: Cambridge University Press.
75. Rouder, J. N., Yue, Y., Speckman, P. L., Pratte, M. S., & Province, J. M. (2010). Gradual growth versus shape invariance in perceptual decision making. Psychological Review, 117, 1267-1274.
76. Sewell, D. K., Lilburn, S. D., & Smith, P. L. (2014). An information capacity limitation of visual short-term memory. Journal of Experimental Psychology: Human Perception and Performance, 40, 2214-2242.
77. Shaw, M. I. (1982). Attending to multiple sources of information: I. The integration of information in decision making. Cognitive Psychology, 14, 353-409.
78. Smith, P. L. (1990). A note on the distribution of response times for a random walk with Gaussian increments. Journal of Mathematical Psychology, 34, 445-459.
79. Smith, P. L. (1998). Attention and luminance detection: A quantitative analysis. Journal of Experimental Psychology: Human Perception and Performance, 24, 105-133.
80. Smith, P. L. (2000). Stochastic dynamic models of response time and accuracy: A foundational primer. Journal of Mathematical Psychology, 44, 408-463.
81. Smith, P. L. (2015). The Poisson shot noise model of visual short-term memory and choice response time: Normalized coding by neural population size. Journal of Mathematical Psychology, 66, 41-52.
82. Smith, P. L., & Ratcliff, R. (2004). Psychology and neurobiology of simple decisions. Trends in Neurosciences, 27, 161-168.
83. Smith, P. L., & Ratcliff, R. (2009). An integrated theory of attention and decision making in visual signal detection. Psychological Review, 116, 283-317.
84. Smith, P. L., & Ratcliff, R. (2015a). An introduction to the diffusion model of decision-making. In E. J. Wagenmakers & B. U. Forstmann (Eds.), An introduction to model-based cognitive neuroscience (pp. 35-62). New York, NY: Springer.
85. Smith, P. L., & Ratcliff, R. (2015b). Diffusion and random walk processes. In James D. Wright (Ed.), International encyclopedia of the social and behavioral sciences (2nd ed., Vol. 6, pp. 395-401). Oxford: Elsevier.
86. Smith, P. L., & Sewell, D. K. (2013). A competitive interaction theory of attentional selection and decision making in brief, multielement displays. Psychological Review, 120, 589-627.
87. Smith, P. L., & Van Zandt, T. (2000). Time-dependent Poisson counter models of response latency in simple judgment. British Journal of Mathematical and Statistical Psychology, 53, 293-315.
88. Smith, P. L., & Vickers, D. (1988). The accumulator model of two-choice discrimination. Journal of Mathematical Psychology, 32, 135-168.
89. Smith, P. L. Ratcliff, R., & McKoon, G. (2014). The diffusion model is not a deterministic growth model: Comment on Jones and Dzhafarov (2014). Psychological Review, 121, 679-688.
90. Sternberg, S. (1969). The discovery of processing stages: Extension of Donders' method. In W. G. Koster (Ed.), Attention and performance II, Acta Psychologica, 30, 276-315.
91. Stroock, D. W., & Varadhan, S. R. S. (1979). Multidimensional diffusion processes. Berlin, Germany; Springer-Verlag.
92. Swan, G., & Wyble, B. (2014). The binding pool: A model of shared neural resources for distinct items in visual working memory. Attention, Perception & Psychophysics, 76, 2136-2157.
93. Swensson, R. G., & Green, D. M. (1977). On the relations between random walk models of two-choice response times. Journal of Mathematical Psychology, 15, 282-391.
94. Thomas, E. A. C. (1975). A note on the sequential probability ratio test. Psychometrika, 40, 107-111.
95. Thomas, E. A. C., & Ross, B. H. (1980). On appropriate procedures for combining probability distributions within the same family. Journal of Mathematical Psychology, 21, 136-152.
96. Thurstone, L. L. (1927). A law of comparative judgment. Psychological Review, 34, 273-286.
97. Townsend, J. T., & Asbhy, F. G. (1983). Stochastic modeling of elementary psychological processes. Cambridge, United Kingdom: Cambridge University Press.
98. Usher, M., & McClelland, J. L. (2001). The time course of perceptual choice: The leaky, competing accumulator model. Psychological Review, 108, 550-592.
99. van den Berg, R., Awh, E., & Ma, W. J. (2014). Factorial comparison of working memory models. Psychological Review, 121, 124-149.
100. van den Berg, R., Shin, H., Chou, W-C., George, R., & Ma, W. J. (2012). Variability in encoding precision accounts for visual short-term memory limitations. Proceedings of the National Academy of Sciences of the United States of America, 109, 8780-8785.
101. Vickers, D. (1977). An adaptive module for simple judgments. In J. Requin (Ed.), Attention and Performance, VII (pp. 599-614). Hillsdale, NJ: Erlbaum.
102. Vickers, D., & Lee, M. D. (1998). Dynamic models of simple judgments: I. Properties of a self-regulating accumulator module. Nonlinear Dynamics, Psychology and Life Sciences, 2, 169-194.
103. Vickers, D., & Lee, M. D. (2000). Dynamic models of simple judgments: II. Properties of a self-regulating PAGAN (Parallel, Adaptive, Generalized, Accumulator Network) model for multi-choice tasks. Nonlinear Dynamics, Psychology and Life Sciences, 4, 1-31.
104. Wilken, P., & Ma, W. J. (2004). A detection theory account of change detection. Journal of Vision, 4, Article 11.
105. Williams, D. (1991). Probability with martingales. Cambridge, United Kingdom: Cambridge University Press.
106. Woodworth, R. S., & Schlosberg, H. (1954). Experimental psychology (Rev. ed.). London, United Kingdom: Methuen.
107. Yellott, J. I., Jr. (1971). Correction for guessing and the speed-accuracy tradeoff in choice reaction time. Journal of Mathematical Psychology, 8, 159-199.
108. Yellott, J. I., Jr. (1977). The relationship between Luce's Choice Axiom, Thurstone's theory of comparative judgment, and the double exponential distribution. Journal of Mathematical Psychology, 8, 159-199.
109. Yin, C., & Wang, C. (2009). Hitting time and place of Brownian motion with drift. The Open Statistics and Probability Journal, 1, 38-42.
110. Zhang, W., & Luck, S. J. (2008). Discrete fixed-resolution representations in visual working memory. Nature, 453, 233-235.