M. Frank Norman
Publications
Book:
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.