A predictive approach to nonparametric inference for adaptive sequential sampling of psychophysical experiments

Journal of Mathematical Psychology

Volumn 56, Issue 3, 2012, Pages 179-195

  Poppe, Stephan ^a   Benner, Philipp ^a   Elze, Tobias ^b  

^a MAX PLANCK INSTITUTE FOR MATHEMATICS IN THE SCIENCES   (Germany)

^b SCHEPENS EYE RESEARCH INSTITUTE   (United States)

Author keywords

Active learning; Adaptive sequential sampling; Efficient statistical computations; Optimal design; Predictive inference; Psychophysics

Indexed keywords

EID: 84862630777     PISSN: 00222496     EISSN: 10960880     Source Type: Journal    
DOI: 10.1016/j.jmp.2012.04.002     Document Type: Article

References (38)

1. Barry D., Hartigan J.A. Product partition models for change point problems. The Annals of Statistics 1992, 20(1):260-279.
2. Berger J.O. Statistical decision theory and Bayesian analysis 1993, Springer-Verlag, New York. 2nd ed.
3. Bernardo J.M. Expected information as expected utility. The Annals of Statistics 1979, 7(3):686-690.
4. Bernardo J.M., Smith A.F.M. Bayesian theory 1995, Wiley, Chichester.
5. Cavagnaro D.R., Myung J.I., Pitt M.A., Kujala J.V. Adaptive design optimization: a mutual information-based approach to model discrimination in cognitive science. Neural Computation 2010, 22:887-905.
6. Chaloner K., Verdinelli I. Bayesian experimental design: a review. Statistical Science 1995, 10(3):273-304.
7. Cronbach, L. J. (1953). A consideration of information theory and utility theory as tools for psychometric problems. Tech. rep. 1. Illinois University at Urbana, Bureau of Research and Service.
8. de Finetti B. La prévision: ses lois logiques, ses sources subjectives. Annales de l'Institut Henri Poincaré 1937, 7(2):1-68.
9. de Finetti B. Theory of probability: a critical introductory treatment 1974, Vol. 1. Wiley, London, New York, NY.
10. de Finetti B. On the condition of partial exchangeability. Studies in inductive logic and probability 1980, 193-205. University of California Press, Berkeley. R.C. Jeffrey (Ed.).
11. DeGroot M.H. Uncertainty, information, and sequential experiments. The Annals of Mathematical Statistics 1962, 33(2):404-419.
12. DeGroot M.H. Optimal statistical decisions, Wiley Classics Library 2004, Wiley-Interscience, Hoboken, NJ.
13. Eggenberger F., Pólya G. Über die statistik verketteter vorgänge. ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 1923, 3(4):279-289.
14. Elze T., Song C., Stollhoff R., Jost J. Chinese characters reveal impacts of prior experience on very early stages of perception. BMC Neuroscience 2011, 12:14.
15. Endres D., Földiák P. Bayesian bin distribution inference and mutual information. IEEE Transactions on Information Theory 2005, 51(11):3766-3779.
16. Endres D., Oram M., Schindelin J., Foldiak P. Bayesian binning beats approximate alternatives: estimating peri-stimulus time histograms. Advances in neural information processing systems 2008, vol. 20:393-400. MIT Press, Cambridge, MA.
17. Fernhead P. Exact and efficient Bayesian inference for multiple changepoint problems. Statistics and Computing 2006, 16(2):203-213.
18. Geisser S. Predictive inference: an introduction 1993, Chapman & Hall, London.
19. Hartigan J.A. Partition models. Communications in Statistics-Theory and Methods 1990, 19(8):2745-2756.
20. Hutter M. Exact Bayesian regression of piecewise constant functions. Bayesian Analysis 2007, 2(4):635-664.
21. Kontsevich L.L., Tyler C.W. Bayesian adaptive estimation of psychometric slope and threshold. Vision Research 1999, 39(16):2729-2737.
22. Kujala J.V. Obtaining the best value for money in adaptive sequential estimation. Journal of Mathematical Psychology 2010, 54:475-480.
23. Kujala J.V., Lukka T.J. Bayesian adaptive estimation: the next dimension. Journal of Mathematical Psychology 2006, 50:369-389.
24. Kuss M., Jakel F., Wichmann F.A. Bayesian inference for psychometric functions. Journal of Vision 2005, 5(5):8.
25. Lauritzen, S. L. (1974). On the interrelationships among sufficiency, total sufficiency and some related concepts. Tech. rep. 18. Stanford University. Department of Statistics.
26. Leek M. Adaptive procedures in psychophysical research. Attention, Perception & Psychophysics 2001, 63:1279-1292.
27. Levitt H. Transformed up-down methods in psychoacoustics. The Journal of the Acoustical Society of America 1971, 49(2B):467-477.
28. Lindley D.V. On a measure of the information provided by an experiment. The Annals of Mathematical Statistics 1956, 27(4):986-1005.
29. Link G. Representation theorems of the de finetti type for (partially) symmetric probability measures. Studies in inductive logic and probability 1980, 207-231. University of California Press, Berkeley. R.C. Jeffrey (Ed.).
30. MacKay D.J.C. Information-based objective functions for active data selection. Neural Computation 1992, 4:590-604.
31. McKee S., Klein S., Teller D. Statistical properties of forced-choice psychometric functions: implications of probit analysis. Attention, Perception & Psychophysics 1985, 37(4):286-298.
32. Müller P., Berry D.A., Grieve A.P., Smith M., Krams M. Simulation-based sequential Bayesian design. Journal of Statistical Planning and Inference 2007, 137(10):3140-3150. special issue: Bayesian inference for stochastic processes.
33. Roberts H.V. Probabilistic prediction. Journal of the American Statistical Association 1965, 60(306):50-62.
34. Taylor M.M., Creelman C.D. Pest: efficient estimates on probability functions. The Journal of the Acoustical Society of America 1967, 41(4A):782-787.
35. Watson A., Fitzhugh A. The method of constant stimuli is inefficient. Attention, Perception & Psychophysics 1990, 47(1):87-91.
36. Watson A., Pelli D. Quest: a Bayesian adaptive psychometric method. Attention, Perception & Psychophysics 1983, 33:113-120.
37. Wichmann F., Hill N. The psychometric function: I. Fitting, sampling, and goodness of fit. Attention, Perception & Psychophysics 2001, 63:1293-1313.
38. Yao Y.-C. Estimation of a noisy discrete-time step function: Bayes and empirical Bayes approaches. The Annals of Statistics 1984, 12(4):1434-1447.