Stopping rules in Bayesian adaptive threshold estimation

Thumbnail Image
Full text at PDC
Publication Date
Advisors (or tutors)
Journal Title
Journal ISSN
Volume Title
Google Scholar
Research Projects
Organizational Units
Journal Issue
Threshold estimation with sequential procedures is justifiable on the surmise that the index used in the so-called dynamic stopping rule has diagnostic value for identifying when an accurate estimate has been obtained. The performance of five types of Bayesian sequential procedure was compared here to that of an analogous fixed-length procedure. Indices for use in sequential procedures were: (1) the width of the Bayesian probability interval, (2) the posterior standard deviation, (3) the absolute change, (4) the average change, and (5) the number of sign fluctuations. A simulation study was carried out to evaluate which index renders estimates with less bias and smaller standard error at lower cost (i.e. lower average number of trials to completion), in both yes–no and two-alternative forced-choice (2AFC) tasks. We also considered the effect of the form and parameters of the psychometric function and its similarity with themodel function assumed in the procedure. Our results show that sequential procedures do not outperform fixed-length procedures in yes–no tasks. However, in 2AFC tasks, sequential procedures not based on sign fluctuations all yield minimally better estimates than fixed-length procedures, although most of the improvement occurs with short runs that render undependable estimates and the differences vanish when the procedures run for a number of trials (around 70) that ensures dependability. Thus, none of the indices considered here (some of which are widespread) has the diagnostic value that would justify its use. In addition, difficulties of implementation make sequential procedures unfit as alternatives to fixed-length procedures.
Alcalá-Quintana, R. and García-Pérez, M. A. (2003). Stopping rules in adaptive Bayesian threshold estimation. Paper presented at the IX Conferencia Española de Biometría, La Coruña, Spain. Alcalá-Quintana, R. and García-Pérez, M. A. (2004). The role of parametric assumptions in adaptive Bayesian estimation, Psychol. Methods 9, 250–271. Alvarez, S. L., Pierce, G. E., Vingrys, A. J., Benes, S. C., Weber, P. A. and King-Smith, P. E. (1997). Comparison of red-green, blue-yellow and achromatic losses in glaucoma, Vision Research 37, 2295–2301. Anderson, A. J. (2003). Utility of a dynamic termination criterion in the ZEST adaptive threshold method, Vision Research 43, 165–170. Anderson, A. J. and Johnson, C. A. (2002). Mechanisms isolated by frequency-doubling technology perimetry, Investigat. Ophthalmol. Vis. Sci. 43, 398–401. Anderson, A. J. and Vingrys, A. J. (2000). Interactions between flicker thresholds and luminancepedestals, Vision Research 40, 2579–2588. Anscombe, F. J. (1953). Sequential estimation, J. Roy. Stat. Soc. Series B 15, 1–29. Billock, V. A., Vingrys, A. J. and King-Smith, P. E. (1994). Opponent-color detection threshold asymmetries may result from reduction of ganglion-cell subpopulations, Visual Neuroscience 11, 99–109. Boynton, G. M. and Foley, J. M. (1999). Temporal sensitivity of human luminance pattern mechanisms determined by masking with temporally modulated stimuli, Vision Research 39, 1641–1656. Burr, D. C. and Santoro, L. (2001). Temporal integration of optic flow, measured by contrast and coherence thresholds, Vision Research 41, 1891–1899. Foley, J. M. and Yang, Y. D. (1991). Forward pattern masking: Effects of spatial-frequency and contrast, J. Opt. Soc. Amer. A 8, 2026–2037. Fredericksen, R. E. and Hess, R. F. (1998). Estimating multiple temporal mechanisms in human vision, Vision Research 38, 1023–1040. García-Pérez, M. A. (1998). Forced-choice staircases with fixed step sizes: Asymptotic and smallsample properties, Vision Research 38, 1861–1881. García-Pérez, M. A. (2001). Yes–no staircases with fixed step sizes: Psychometric properties and optimal setup, Optomet. Vision Sci. 78, 56–64. Gold, J., Benett, P. J. and Sekuler, A. B. (1999). Identification of band-pass filtered letters and faces by human and ideal observers, Vision Research 39, 3537–3560. Grigsby, S. S., Vingrys, A. J., Benes, S. C. and King-Smith, P. E. (1991). Correlation of chromatic, spatial, and temporal sensitivity in optic-nerve disease, Investigat. Ophthalmol. Visual Sci. 32, 3252–3262. Hall, J. L. (1968). Maximum-likelihood sequential procedure for estimation of psychometric functions, J. Acoust. Soc. Amer. 44, 370. Hood, D. C., Graham, N., von Wiegand, T. E. and Chase, V. M. (1997). Probed-sinewave paradigm: A test of models of light adaptation dynamics, Vision Research 37, 1177–1191. Kesten, H. (1958). Accelerated stochastic approximation, Annals Mathem. Stat. 29, 41–59. King-Smith, P. E. (1984). Efficient threshold estimates from yes–no procedures using few (about 10) trials, Amer. J. Optomet. Physiological Optics 61, 119P. King-Smith, P. E., Grigsby, S. S., Vingrys, A. J., Benes, S. C. and Supowit, A. (1994). Efficient and unbiased modifications of the QUEST threshold method: Theory, simulations, experimental evaluation and practical implementation, Vision Research 34, 885–912. Laming, D. and Mash, D. (1988). Some performance tests of QUEST on measurements of vibrotactile thresholds, Perception and Psychophysics 44, 99–107. Lankheet, M. J. M., van Doorn, A. J. and van de Grind, W. A. (2002). Spatio-temporal tuning of motion coherence detection at different luminance levels, Vision Research 42, 65–73. Leek, M. R. (2001). Adaptive procedures in psychophysical research, Perception and Psychophysics 63, 1279–1292. Lieberman, H. R. and Pentland, A. P. (1982). Microcomputer-based estimation of psychophysical thresholds: The best PEST, Behavior Res. Methods Instrumentation 14, 21–25. Majaj, N. J., Pelli, D. G., Kurshan, P. and Palomares, M. (2002). The role of spatial frequency channels in letter identification, Vision Research 42, 1165–1184. Makous, J. C., Friedman, R. M. and Vierck, C. J. (1995). A critical band filter in touch, J. Neurosci. 15, 2808–2818. Marks, B. J. (1962). Some optimal sequential schemes for estimating the mean of a cumulative normal quantal response curve, J. Roy. Stat. Soc. Series B 24, 393–400. Numerical Algorithms Group (1999). NAG Fortran Library Manual, Mark 19. Author, Oxford. Snowden, R. J. (1992). Orientation bandwidth: The effect of spatial and temporal frequency, Vision Res. 32, 1965–1974. Strasburger, H., Harvey, L. O. and Rentschler, I. (1991). Contrast thresholds for identification of numeric characters in direct and eccentric view, Perception and Psychophysics 49, 495–508. Tailby, C., Cubells, O. and Metha, A. (2001). Enhanced sensitivity for peripherally-presented collinearly-aligned stimulus elements: Contour detection of spatial summation? Clin. Exper. Optomet. 84, 354–360. Taylor, M. M. and Creelman, C. D. (1967). PEST: Efficient estimates on probability functions, J. Acoust. Soc. Amer. 41, 782–787. Treutwein, B. (1995). Adaptive psychophysical procedures, Vision Research 35, 2503–2522. Treutwein, B. (1997). YAAP: Yet another adaptive procedure, Spatial Vision 11, 129–134. Turpin, A., McKendrick, A. M., Johnson, C. A. and Vingrys, A. J. (2002). Performance of efficient test procedures for frequency-doubling technology perimetry in normal and glaucomatous eyes, Investigat. Ophthalmol. Visual Sci. 43, 709–715. Vingrys, A. J. and Pianta, M. J. (1999). A new look at threshold estimation algorithms for automated static perimetry, Optomet. Vision Sci. 76, 588–595. de Vries, S. H., Qi, X. F., Smith, R., Makous, W. and Sterling, P. (2002). Electrical coupling between mammalian cones, Current Biology 12, 1900–1907 Watson, A. B. and Pelli, D. G. (1983). QUEST: A Bayesian adaptive psychometric method, Perception and Psychophysics 33, 113–120. Wetherill, G. B. and Levitt, H. (1965). Sequential estimation of points on a psychometric function, Brit. J. Math. Stat. Psychol. 18, 1–10. von Wiegand, T. E., Hood, D. C. and Graham, N. (1995). Testing a computational model of lightadaptation dynamics, Vision Research 35, 3037–3051. Wolfson, S. S. and Graham, N. (2000). Exploring the dynamics of light adaptation: The effects of varying the flickering backgrounds duration in the probed-sinewave paradigm, Vision Research 40, 2277–2289. Yang, J. and Makous, W. (1995). Modeling pedestal experiments with amplitude instead of contrast, Vision Research 35, 1979–1989. Yang, J. and Makous, W. (1997). Implicit masking constrained by spatial inhomogeneities, Vision Research 37, 1917–1927. Yang, J. and Stevenson, S. B. (1997). Effects of spatial frequency, duration, and contrast on discriminating motion directions, J. Opt. Soc. Amer. A 14, 2041–2048. Yang, J., Qi, X. F. and Makous, W. (1995). Zero-frequency masking and a model of contrast sensitivity, Vision Research 35, 1965–1978. Yoon, G. Y. and Williams, D. R. (2002). Visual performance after correcting the monochromatic and chromatic aberrations of the eye, J. Opt. Soc. Amer. A 19, 266–275.