Inductive Inference and Replications: A Bayesian Perspective

A probabilistic model is proposed to assess the value of replications. The corroboration of a theory is shown to be a function of the number of replications, the number of successful outcomes, and our initial beliefs. An adaptive control model provides the optimal policy for continuing replications, given the accumulated evidence for the theory, the precision deemed necessary, and the cost of replicating. Copyright 1994 by the University of Chicago.

[1]  K. Pearson.  The Grammar of Science , 1900 .

[2]  B. Russell.  The Principles of Mathematics , 1938 .

[3]  Karl Pearson.  On the Influence of Past Experience on Future Expectation. , 1907 .

[4]  Pierre Simon Laplace.  Essai philosophique sur les probabilités , 1921 .

[5]  H. Jeffreys,et al.  The Theory of Probability , 1896 .

[6]  Rudolf Carnap,et al.  Logical foundations of probability , 1951 .

[7]  G. Pólya.  Mathematics and Plausible Reasoning , 1958 .

[8]  Robert Rosthal,et al.  Induction and Hypothesis , 1959 .

[9]  Howard Raiffa,et al.  Games And Decisions , 1958 .

[10]  Jacob Cohen.  Statistical Power Analysis for the Behavioral Sciences , 1969, The SAGE Encyclopedia of Research Design.

[11]  M. Degroot.  Optimal Statistical Decisions , 1970 .

[12]  David B. Montgomery,et al.  A Further Step, Though Sometimes Uncertain, Toward Quantifying Buying Behavior@@@Stochastic Models of Buying Behavior , 1972 .

[13]  M. Hesse.  The Structure of Scientific Inference , 2023 .

[14]  W. Fleming,et al.  Deterministic and Stochastic Optimal Control , 1975 .

[15]  Karl R. Popper.  The Logic of Scientific Discovery. , 1977 .

[16]  M. Degroot,et al.  Probability and Statistics , 2021, Examining an Operational Approach to Teaching Probability.

[17]  P. Ellsworth.  From Abstract Ideas to Concrete Instances: Some Guidelines for Choosing Natural Research Settings. , 1977 .

[18]  Donald G. Morrison,et al.  A modified beta binomial model with applications to multiple choice and taste tests , 1979 .

[19]  Robert C. Blattberg,et al.  The Design of Advertising Experiments Using Statistical Decision Theory , 1979 .

[20]  James O. Berger.  Statistical Decision Theory , 1980 .

[21]  D. G. Morrison.  Triangle Taste Tests: Are the Subjects who Respond Correctly Lucky or Good? , 1981 .

[22]  Roy Paul Nelson.  The design of advertising , 1981 .

[23]  Alice M. Tybout,et al.  Designing Research for Application , 1981 .

[24]  Alan G. Sawyer,et al.  Statistical Power and Effect Size in Marketing Research , 1981 .

[25]  J. Lynch.  On the External Validity of Experiments in Consumer Research , 1982 .

[26]  Alice M. Tybout,et al.  The Concept of External Validity , 1982 .

[27]  Alice M. Tybout,et al.  Beyond External Validity , 1983 .

[28]  J. Overall,et al.  Applied multivariate analysis , 1983 .

[29]  W. J. Hall,et al.  Approximating Priors by Mixtures of Natural Conjugate Priors , 1983 .

[30]  J. Lynch.  The Role of External Validity in Theoretical Research , 1983 .

[31]  J. McGrath,et al.  External Validity and the Research Process: A Comment on the Calder/Lynch Dialogue , 1983 .

[32]  John Ziman,et al.  An Introduction To Science Studies , 1984 .

[33]  John G. Lynch,et al.  Validity and the research process , 1986 .

[34]  Alice M. Tybout,et al.  Confirmatory Versus Comparative Approaches to Judging Theory Tests , 1987 .

[35]  C. Ray Smith,et al.  Maximum-entropy and Bayesian methods in science and engineering , 1988 .

[36]  Siu L. Chow,et al.  Significance test or effect size , 1988 .

[37]  James O. Berger,et al.  Statistical Analysis and the Illusion of Objectivity , 1988 .

[38]  J. Berger.  Statistical Decision Theory and Bayesian Analysis , 1988 .

[39]  Kalyan Raman,et al.  Analysis of a sales force incentive plan for accurate sales forecasting and performance , 1990 .

[40]  Jacob Cohen,et al.  THINGS I HAVE LEARNED (SO FAR) , 1990 .

[41]  Robert Rosenthal,et al.  Replication in behavioral research. , 1990 .

[42]  J. Neuliep,et al.  Replication Research in the Social Sciences , 1991 .

[43]  Eva M. Hyatt,et al.  A Critical Appraisal of Demand Artifacts in Consumer Research , 1991 .

[44]  David Brinberg,et al.  Hypothesized and Confounded Explanations in Theory Tests: A Bayesian Analysis , 1992 .

[45]  James O. Berger,et al.  Ockham's Razor and Bayesian Analysis , 1992 .

[46]  Frank L. Schmidt,et al.  What do data really mean? Research findings, meta-analysis, and cumulative knowledge in psychology. , 1992 .

[47]  W. Wells.  Discovery-oriented consumer research. , 1993 .

[48]  N. L. Johnson,et al.  Continuous Univariate Distributions. , 1995 .

[49]  Sheldon M. Ross.  Introduction to Probability Models. , 1995 .