Stochastic Dynamic Models of Response Time and Accuracy: A Foundational Primer

Journal of Mathematical Psychology

Volumn 44, Issue 3, 2000, Pages 408-463

  Smith, Philip L ^a  

^a UNIVERSITY OF MELBOURNE   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034259473     PISSN: 00222496     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmps.1999.1260     Document Type: Article

References (107)

1. Abeles M., Goldstein M. H. Response of single units in the primary auditory cortex of the cat to tones and to tone pairs. Brain Research. 42:1972;337-352.
2. Arnold L. Stochastic differential equations: Theory and applications. 1974;Wiley, New York.
3. Ashby F. G. A biased random walk model for two choice reaction times. Journal of Mathematical Psychology. 27:1983;277-297.
4. Ashby F. G., Schwartz W. A stochastic version of General Recognition Theory. Journal of Mathematical Psychology. 40:1996.
5. Ashby F. G., Townsend J. T. Varieties of perceptual independence. Psychological Review. 93:1986;154-179.
6. Audley R. J., Pike A. R. Some alternative stochastic models of choice. British Journal of Mathematical and Statistical Psychology. 18:1965;207-225.
7. Bhattacharya R. N., Waymire E. C. Stochastic processes with applications. 1990;Wiley, New York.
8. Buonocore A., Giorno V., Nobile A. G., Ricciardi L. On the two-boundary first-crossing-time problem for diffusion processes. Journal of Applied Probability. 27:1990;102-114.
9. Buonocore A., Nobile A. G., Ricciardi L. M. A new integral equation for the evaluation of first-passage-time probability densities. Advances in Applied Probability. 19:1987;784-800.
10. Burbeck S. L. A physiologically motivated model for change detection in audition. Journal of Mathematical Psychology. 29:1985;106-121.
11. Burbeck S. L., Luce R. D. Evidence from auditory simple reaction times for both change and level detectors. Perception & Psychophysics. 32:1982;117-133.
12. Busemeyer J., Rapoport A. Psychological models of deferred decision making. Journal of Mathematical Psychology. 32:1988;91-134.
13. Busemeyer J., Townsend J. T. Fundamental derivations from decision field theory. Mathematical Social Sciences. 23:1992;255-282.
14. Busemeyer J., Townsend J. T. Decision field theory: A dynamic-cognitive approach to decision making in an uncertain environment. Psychological Review. 100:1993;432-459.
15. Busey T. A., Loftus G. R. Sensory and cognitive components of visual information processing. Psychological Review. 101:1994;446-469.
16. Cherkasov I. D. On the transformation of the diffusion process to a Wiener process. Theory of Probability and its Applications. 2:1957;373-377.
17. Chung K. L., Williams R. J. Introduction to stochastic integration. 1983;Birkhäuser, Boston.
18. Coltheart M., Rastle K. Serial processing in reading aloud: Evidence for dual-route models of reading. Journal of Experimental Psychology: Human Perception and Performance. 20:1994;1197-1211.
19. Cox D. R., Miller H. D. The theory of stochastic processes. 1965;Chapman & Hall, London.
20. Dahlquist G., Björck A. Numerical methods. 1974;Prentice-Hall, Englewood Cliffs.
21. de Lange H. Experiments on flicker and some calculations on an electrical analogue of the foveal systems. Physica. 18:1952;935-950.
22. de Lange H. Relationship between critical flicker frequency and a set of low frequency characteristics of the eye. Journal of the Optical Society of America. 44:1954;380-389.
23. de Lange H. Research into the dynamic nature of the human fovea-cortex systems with intermittent and modulated light. I Attenuation characteristics with white and colored light. Journal of the Optical Society of America. 48:1958;777-784.
24. Di Crescenzo A. G., Giorno V., Nobile A. G., Ricciardi L. M. On a symmetry-based constructive approach to probability densities for two-dimensional diffusion processes. Journal of Applied Probability. 32:1995;316-336.
25. Di Crescenzo A., Ricciardi L. M., Giorno V., Nobile A. G. On the reduction to one dimension of first-passage-time problems for diffusion processes. Journal of Mathematical Physical Sciences. 25:1991;599-611.
26. Diederich A. Intersensory facilitation of reaction time: Evaluation of counter and diffusion coactivation models. Journal of Mathematical Psychology. 39:1995;197-215.
27. Diederich A. Dynamic stochastic models for decision making under time constraints. Journal of Mathematical Psychology. 41:1997;260-274.
28. Durbin J. Boundary-crossing probabilities for the Brownian motion and Poisson processes and techniques for computing the power of the Kolmogorov-Smirnov test. Journal of Applied Probability. 8:1971;431-453.
29. Edwards W. Optimal strategies for seeking information: Models for statistics, choice reaction time, and human information processing. Journal of Mathematical Psychology. 2:1965;312-329.
30. Emerson P. L. Simple reaction time with Markovian evolution of Gaussian discriminal processes. Psychometrika. 35:1970;99-109.
31. Ethier S. N., Kurtz T. G. Markov processes: Characterization and convergence. 1986;Wiley, New York.
32. Feller W. An introduction to probability theory and its applications. 1971;Wiley, New York.
33. Fortet R. Les fonctions aléatoires du type de Markoff associées à certaines équations linéaires aux derivées partielles du type parabolique. Journal de Mathématiques Pures et Appliquées. 1943.
34. Gardiner C. W. Handbook of stochastic methods. 1985;Springer-Verlag, Berlin.
35. Gerstein G. L., Butler R. A., Erulkar S. D. Excitation and inhibition in cochlear nucleus. I. Tone-burst stimulation. Journal of Neurophysiology. 31:1968;526-536.
36. Gillund G., Shiffrin R. M. A retrieval model for both recognition and recall. Psychological Review. 91:1984;1-67.
37. Giorno V., Nobile A. G., Ricciardi L. M., Sato S. On the evaluation of first-passage-time probability densities via non-singular integral equations. Advances in Applied Probability. 21:1989;200-236.
38. Green D. M., Swets J. A. Signal detection theory and psychophysics. 1966;Wiley, New York.
39. Gutiérrez Jáimez R., Román Román P., Torres Ruiz F. A note on the Volterra integral equation for the first-passage-time probability. Journal of Applied Probability. 32:1995;635-648.
40. Heath R. A. A tandem random-walk model for psychological discrimination. British Journal of Mathematical and Statistical Psychology. 34:1981;76-92.
41. Heath R. A. A general nonstationary diffusion model for two choice decision making. Mathematical Social Sciences. 23:1992;283-309.
42. Hildreth J. D. Bloch's law and a Poisson counting model for simple reaction time to light. Perception & Psychophysics. 26:1979;153-162.
43. Hirsch M. W., Smale S. Differential equations, dynamical systems, and linear algebra. 1974;Academic Press, New York.
44. Hockley W. E., Murdock B. B. A decision model for accuracy and response latency in recognition memory. Psychological Review. 34:1987;341-358.
45. Humphreys M. S., Bain J. D., Pike R. Different ways to cue a coherent memory system: A theory for episodic, semantic, and procedural tasks. Psychological Review. 96:1989;208-223.
46. Karatzas I., Shreve S. E. Brownian motion and stochastic calculus. 1991;Springer-Verlag, New York.
47. Karlin S., Taylor H. M. A first course in stochastic processes. 1975;Academic Press, New York.
48. Karlin S., Taylor H. M. A second course in stochastic processes. 1981;Academic Press, Orlando.
49. Kinchla R. A. Temporal channel uncertainty in detection: A multiple observations analysis. Perception & Psychophysics. 16:1969;802-811.
50. Kinchla R. A. Detecting target elements in multi-element visual arrays: A confusability model. Perception & Psychophysics. 15:1974;149-158.
51. La Berge D. A. A recruitment theory of simple behavior. Psychometrika. 27:1962;149-163.
52. Laming D. R. J. Information theory of choice-reaction times. 1968;Academic Press, London.
53. Legge G. Sustained and transient mechanisms in human vision: Temporal and spatial properties. Vision Research. 18:1978;69-82.
54. Link S. W. The relative judgment theory of two choice response time. Journal of Mathematical Psychology. 12:1975;114-135.
55. Link S. W. The relative judgment theory of the psychometric function. Requin J. Attention & Performance VII. 1978;619-630 Erlbaum, Hillsdale.
56. Link S. W. The wave theory of similarity and difference. 1992;Erlbaum, Hillsdale.
57. Link S. W., Heath R. A. A sequential theory of psychological discrimination. Psychometrika. 40:1975;77-105.
58. Luce R. D. Response times. 1986;Oxford Univ. Press, New York.
59. Luce R. D., Green D. M. A neural timing theory for response times and the psychophysics of intensity. Psychological Review. 79:1972;14-57.
60. MacMillan N. A., Creelman C. D. Detection theory: A user's guide. 1991;Cambridge Univ. Press, New York.
61. McClelland J. L., Rumelhart D. E. A interactive activation model of context effects in letter perception: Part I. An account of basic findings. Psychological Review. 88:1981;375-407.
62. McGill W. Neural counting mechanisms and energy detection in audition. Journal of Mathematical Psychology. 4:1967;351-376.
63. Murdock B. B. A theory for the storage and retrieval of item and associative information. Psychological Review. 89:1982;609-626.
64. Norman M. F. Lectures on linear system theory. Journal of Mathematical Psychology. 23:1981;1-81.
65. Pacut A. Some properties of threshold models of reaction latency. Biological Cybernetics. 28:1977;63-72.
66. Pacut A. Mathematical modeling of reaction latency: The structure of the models and its motivation. Acta Neurobiologiae Experimentalis. 40:1980;199-215.
67. Papoulis A. Probability, random variables, and stochastic processes. 1991;McGraw-Hill, New York.
68. Pike A. R. Stochastic models of choice behaviour: Response probabilities and latencies of finite Markov chain systems. British Journal of Mathematical and Statistical Psychology. 19:1966;15-32.
69. Pike A. R. Latency and relative frequency of response in psychophysical discrimination. British Journal of Mathematical and Statistical Psychology. 21:1968;161-182.
70. Protter P. Stochastic integration and differential equations. 1990;Springer-Verlag, Berlin.
71. Ratcliff R. A theory of memory retrieval. Psychological Review. 85:1978;59-108.
72. Ratcliff R. A note on modeling accumulation of information when the rate of accumulation changes over time. Journal of Mathematical Psychology. 21:1980;178-184.
73. Ratcliff R. A theory of order relations in perceptual matching. Psychological Review. 88:1981;552-572.
74. Reed A. V. Speed-accuracy trade-off in recognition memory. Science. 181:1973;574-576.
75. Reeves A., Sperling G. Attention gating in short term visual memory. Psychological Review. 93:1986;180-206.
76. Revus D., Yor M. Continuous martingales and Brownian motion. 1994;Springer-Verlag, Berlin.
77. Ricciardi L. M. On the transformation of diffusion processes into the Wiener process. Journal of Mathematical Analysis and Applications. 54:1976;185-199.
78. Ricciardi L. M., Sacerdote L., Sato S. Diffusion approximation and first passage time problem for a model neuron. II. Outline of a computational method. Mathematical Biosciences. 64:1983;29-44.
79. Ricciardi L. M., Sacerdote L., Sato S. On a integral equation for first-passage-time probability densities. Journal of Applied Probability. 21:1984;302-314.
80. Ricciardi L. M., Sato S. A note on the evaluation of first-passage-time probability densities. Journal of Applied Probability. 20:1983;197-201.
81. Rouder J. Assessing the roles of change discrimination and luminance integration: Evidence for a hybrid race model of perceptual decision making in luminance discrimination. Journal of Experimental Psychology: Human Perception and Performance. 26:2000;359-378.
82. Rudd M. E. A neural timing model of visual threshold. Journal of Mathematical Psychology. 40:1996;1-29.
83. Rudd M. E., Brown L. G. A model of Weber and noise gain control in the retina of the toad bufo marinus. Vision Research. 37:1997;2433-2453.
84. Schwartz W. A new model to explain the redundant signals effect. Perception & Psychophysics. 46:1989;498-500.
85. Shaw M. I. Attending to multiple sources of information: I. The integration of information in decision making. Cognitive Psychology. 14:1982;353-409.
86. Smith P. L. A note on the distribution of response times for a random walk with Gaussian increments. Journal of Mathematical Psychology. 34:1990;445-459.
87. Smith P. L. Psychophysically-principled models of visual simple reaction time. Psychological Review. 102:1995;567-593.
88. Smith P. L. Dynamic signal detection models driven by white noise integrals. Journal of Mathematical Psychology. 40:1996;369.
89. Smith P. L. Bloch's law predictions from diffusion process models of detection. Australian Journal of Psychology. 50:1998a;139-147.
90. Smith P. L. Attention and luminance detection: A quantitative analysis. Journal of Experimental Psychology: Human Perception and Performance. 24:1998b;1-29.
91. Smith, P. L, &, Van Zandt, T. (in press), Time-dependent Poisson counter models of response latency in simple judgment, British Journal of Mathematical and Statistical Psychology.
92. Smith P. L., Vickers D. The accumulator model of two-choice discrimination. Journal of Mathematical Psychology. 32:1988;135-168.
93. Smith P. L., Vickers D. Modeling evidence accumulation with partial loss in expanded judgment. Journal of Experimental Psychology: Human Perception and Performance. 15:1989;797-815.
94. Sperling G., Weichselgartner E. Episodic theory of the dynamics of spatial attention. Psychological Review. 102:1995;503-532.
95. Sperling G., Sondhi M. M. Model for visual luminance discrimination and flicker detection. Journal of the Optical Society of America. 58:1968;1133-1145.
96. Stone M. Models for choice-reaction time. Psychometrika. 25:1960;251-260.
97. Tolhurst D. J. Reaction times in the detection of gratings by human observers: A probabilistic mechanism. Vision Research. 15:1975a;1143-1149.
98. Tolhurst D. J. Sustained and transient channels in human vision. Vision Research. 15:1975b;1151-1155.
99. Townsend J. T., Ashby F. G. The stochastic modeling of elementary psychological processes. 1983;Cambridge University Press, Cambridge.
100. van Kampen N. G. Stochastic processes in physics and chemistry. 1992;Elsevier, Amsterdam.
101. Vickers D. Evidence for an accumulator model of psychophysical discrimination. Ergonomics. 13:1970;37-58.
102. Vickers D. Decision processes in visual perception. 1979;Academic Press, London.
103. Vickers D., Caudrey D., Willson R. J. Discriminating between the frequency of occurrence of two alternative events. Acta Psychologica. 35:1971;151-172.
104. Viviani P. Choice reaction times of temporal numerosity. Journal of Experimental Psychology: Human Perception and Performance. 5:1979a;157-167.
105. Viviani P. A diffusion model for discrimination of temporal numerosity. Journal of Mathematical Psychology. 19:1979b;108-136.
106. Watson A. B. Temporal sensitivity. Boff K. R., Kaufman L., Thomas J. P. Handbook of perception and human performance. 1986;6.1-6.43 Wiley, New York.
107. Wong P., Hajek B. Stochastic processes in engineering systems. 1985;Springer-Verlag, New York.