M. Frank Norman




1972, Markov Processes and Learning Models, Academic Press, New York.


Articles and Reviews:

1961, Effects of success and failure on confidence, Psychological Reports, 9, 607-610.

1964, A two-phase model and an application to verbal discrimination learning, in R. C. Atkinson (Ed.), Studies in Mathematical Psychology, Stanford Univ. Press, Stanford, CA, 173-187.

1964, Incremental learning on random trials, Journal of Mathematical Psychology, 1, 336-350.

1966, (with J. I. Yellott, Jr.) Probability matching, Psychometrika, 31, 43-60.

1966, Limiting distributions for some random walks arising in learning models, Annals of Mathematical Statistics, 37, 393-405.

1966, An approach to free-responding on schedules that prescribe reinforcement probability as a function of interresponse time, Journal of Mathematical Psychology, 3, 235-268.

1968, (with N. V. Graham)  A central limit theorem for families of stochastic processes indexed by a small average step size parameter, and some applications to learning models, Psychometrika, 33, 441-449.

1968, Some convergence theorems for stochastic learning models with distance diminishing operators, Journal of Mathematical Psychology, 5, 61-101.

1968, Mathematical learning theory, in G. B. Dantzig and A. F. Vienott (Eds.), Mathematics of the Decision Sciences, Part 2, American Mathematical Society, Providence, R. I., 283-313.

1968, Slow learning, British Journal of Mathematical and Statistical Psychology, 21, 141-159.

1968, On the linear model with two absorbing barriers, Journal of Mathematical Psychology, 5, 225-241.

1970, A uniform ergodic theorem for certain Markov operators on Lipschitz functions on bounded metric spaces.  Zeitschrift fur Wahrscheinlichkeitstheorie und verwandte Gebiete, 15, 51-56.

1970, Limit theorems for additive learning models, Journal of Mathematical Psychology, 7, 1-11.

1970, Review of Random Processes and Learning by M. Iosifescu and R. Theodorescu, Annals of Mathematical Statistics, 41, 1381-1383.

1971, Slow learning with small drift in two-absorbing-barrier models, Journal of Mathematical Psychology, 8, 1-21.

1971, Statistical inference with dependent observations: extensions of classical procedures, Journal of Mathematical Psychology, 8, 444-451.

1973, Review of Mathematical Model Techniques for Learning Theories by G. Levine and C. J. Burke, Contemporary Psychology, 18, 100-102.

1974, Effects of overtraining, problem shifts, and probabilistic reinforcement in discrimination learning:  predictions of an attentional model, in D. H. Krantz, R. C. Atkinson, R. D. Luce, and P. Suppes (Eds.), Contemporary Developments in Mathematical Psychology, Vol. I, Freeman, San Francisco, 185-208.

1974, Markovian learning processes, SIAM Review, 16, 143-162.

1974, A central limit theorem for Markov processes that move by small steps, Annals of Probability, 2, 1065-1074.

1975, Diffusion approximation of non-Markovian processes, Annals of Probability, 3, 358-364.  (Reprinted in Li, W-H. (Ed.), Stochastic Models in Population Genetics, Dowden,  Hutchinson, & Ross, Stroudsburg, Pa., 1977, 445-451.)

1975, Approximation of stochastic processes by Gaussian diffusions, and applications to Wright-Fisher genetic models, SIAM Journal of Applied Mathematics, 29, 225-242.

1975, Limit theorems for stationary distributions, Advances in Applied Probability, 7, 561-575.

1975, An ergodic theorem for evolution in a random environment, Journal of Applied Probability, 12, 661-672.

1976, Optional shift, and discrimination learning with redundant relevant dimensions:  predictions of an attentional model, Journal of Mathematical Psychology, 14, 130-143.

1977, Ergodicity of diffusion and temporal uniformity of diffusion approximation, Journal of Applied Probability, 14, 399-404.

1977, (with S. N. Ethier)  Error estimate for the diffusion approximation of the Wright-Fisher model, Proceedings of the National Academy of Sciences, 74, 5096-5098.

1978, (with C. R. Gallistel)  What can one learn from a strength-duration curve?, Journal of Mathematical Psychology, 18, 1-24.

1981, Lectures on linear systems theory, Journal of Mathematical Psychology, 23, 1-89.

1981, Sociobiological variations on a Mendelian theme, in S. Grossberg (Ed.), Mathematical Psychology and Psychophysiology, American Mathematical Society, Providence, R. I., 187-196.

1981, A "psychological" proof that certain Markov semigroups preserve differentiability, in S. Grossberg (Ed.),  Mathematical Psychology and Psychophysiology, American Mathematical Society, Providence, R. I., 197-211.

1992, (with Jonathan Baron)  SATs, achievement tests, and high-school class rank as predictors of college performance, Educational and Psychological Measurement, 52, 1047-1055.

2001, (with S. A. Norman, L. T. Miller, H. B. Erikson, and R. McCorkle)  Development and validation of a telephone questionnaire to characterize lymphedema in women treated for breast cancer,  Physical Therapy, 81, 1192-1205.

2002, Genetic influences on behavior, in L. Nadel (Ed.), Encyclopedia of Cognitive Science, Macmillan Publishers Limited, 354-360.

2005, (with K. G. Noble and M. J. Farah)  Neurocognitive correlates of socioeconomic status in kindergarten children.  Developmental Science, 8, 74-87.

2005, A very simple model for declining mean fitness, Journal of Bioeconomics, 7, 157-160.

2006, Review of Nature via Nurture by Matt Ridley, Journal of Bioeconomics, 8, 91-94.

2009, (with Michael T. Purkey, Marc S. Levine, Brandon Prendes, and Natasha Mirza), Predictors of aspiration pneumonia following radiotherapy for head and neck cancer, Annals of Otology, Rhinology & Laryngology, 118, 811-816.