Abstract
A conceptual variable is defined, and on this background the e-variable is given a precise definition. Also, the context of an epistemic process is defined. One can formulate a precise setting called a generalized experiment, and in this setting sufficiency and conditioning are discussed. The conditionality principle and the sufficiency principle are seen as intuitively obvious. Birnbaum’s theorem states that the likelihood principle follows from these two principles. Everything is seen in the context of an epistemic process.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Berger, J. O., & Wolpert, R. L. (1988). The likelihood principle. Hayward, CA: Institute of Mathematical Statistics.
Birnbaum, A. (1962). On the foundation of statistical inference. Journal of the American Statistical Association, 57, 269–326.
Bjørnstad, J. F. (1990) Predictive likelihood: A review. Statistical Science, 5, 242–265.
Cook, R. D. (2007). Fisher lecture: Dimension reduction in regression. Statistical Science, 22, 1–26.
Cox, D. R. (1958). Some problems connected with statistical inference. Annals of Statistics, 29, 357–372.
Cox, D. R. (1971). The choice between ancillary statistics. Journal of the Royal Statistical Society. Series B, 33, 251–255.
Fisher, R. A. (1922). On the mathematical foundations of theoretical statistics. Philosophical Transactions of the Royal Society of London. Series A 222, 309-368. Reprinted in: Fisher R. A. Contribution to Mathematical Statistics. Wiley, New York (1950)
Hastie, T., Tibshirani, R., & Friedman, J. (2009). The elements of statistical learning. Data mining, inference, and prediction. Springer series in statistics. Berlin: Springer.
Helland, I. S. (1995). Simple counterexamples against the conditionality principle. The American Statistician, 49, 351–356. Discussion 50, 382–386.
Helland, I. S. (2010). Steps towards a unified basis for scientific models and methods. Singapore: World Scientific.
Lehmann, E. L., & Casella, G. (1998). Theory of point estimation. New York: Springer.
McCullagh, P., & Han, H. (2011). On Bayes’s theorem for improper mixtures. Annals of Statistics, 39, 2007–2020.
Reid, N. (1995). The roles of conditioning in inference. Statistical Science, 10(2), 138–157.
Stigler, S. M. (1976). Discussion of “On rereading R.A. Fisher” by L.J. Savage. Annals of Statistics, 4, 498–500.
Taraldsen, G., & Lindqvist, B. H. (2010). Improper priors are not improper. The American Statistician, 64, 154–158.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer-Verlag GmbH Germany, part of Springer Nature
About this chapter
Cite this chapter
Helland, I.S. (2018). Inference in an Epistemic Process. In: Epistemic Processes. Springer, Cham. https://doi.org/10.1007/978-3-319-95068-6_3
Download citation
DOI: https://doi.org/10.1007/978-3-319-95068-6_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-95067-9
Online ISBN: 978-3-319-95068-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)