fiducial inference on a restricted class of models on which "fiducial" procedures would be well-defined and useful. Donald A. S. Fraser developed a general theory for structural inference based on group theory and applied this to linear models. The theory formulated by Fraser has close links to decision theory and Bayesian statistics and can provide optimal frequentist decision rules if they exist. Inference topics The topics below are usually included in the area of statistical inference. Statistical assumptions Statistical decision theory Estimation theory Statistical hypothesis testing Revising opinions in statistics Design of experiments, the analysis of variance, and regression Survey sampling Summarizing statistical data Predictive inference Predictive inference is an approach to statistical inference that emphasizes the prediction of future observations based on past observations. Initially, predictive inference was based on observable parameters and it was the main purpose of studying probability, but it fell out of favor in the 20th century due to a new parametric approach pioneered by Bruno de Finetti. The approach modeled phenomena as a physical system observed with error (e.g., celestial mechanics). De Finetti's idea of exchangeability—that future observations should behave like past observations—came to the attention of the English-speaking world with the 1974 translation from French of his 1937 paper, and has since been propounded by such statisticians as Seymour Geisser. See also Algorithmic inference Induction (philosophy) Informal inferential reasoning Information field theory Population proportion Philosophy of statistics Prediction interval Predictive analytics Predictive modelling Stylometry Notes References Citations Sources . Cox, D. R. (2006). Principles of Statistical Inference, Cambridge University Press. . Fisher, R. A. (1955), "Statistical methods and scientific induction", Journal of the Royal Statistical Society, Series B, 17, 69–78. (criticism of statistical theories of Jerzy Neyman and Abraham Wald) Freedman, D. A. (2010). Statistical Models and Causal Inferences: A Dialogue with the Social Sciences (Edited by David Collier, Jasjeet Sekhon, and Philip B. Stark), Cambridge University Press. Reprinted as Konishi S., Kitagawa G. (2008), Information Criteria and Statistical Modeling, Springer. Le Cam, Lucian. (1986) Asymptotic Methods of Statistical Decision Theory, Springer. Moore, D. S.; McCabe, G. P.; Craig, B. A. (2015), Introduction to the Practice of Statistics, Eighth Edition, Macmillan. (reply to Fisher 1955) Peirce, C. S. (1877–1878), "Illustrations of the logic of science" (series), Popular Science Monthly, vols. 12–13. Relevant individual papers: (1878 March), "The Doctrine of Chances", Popular Science Monthly, v. 12, March issue, pp. 604–615. Internet Archive Eprint. (1878