Advertisement

Bayes/Orthodox Comparisons

  • Roger D. Rosenkrantz
Chapter
Part of the Synthese Library book series (SYLI, volume 115)

Abstract

Our purpose in this chapter is to compare empirically the performance of Bayes and orthodox approaches to regression and related problems. Specifically, I treat the problem of identifying the degree of a polynomial and the order of a Markov chain. When we raise the degree of a polynomial or the order of a Markov chain, we improve the model’s accuracy at the cost of some simplicity. According to the Bayesian analysis of Chapter 5, there is a well-defined rate of exchange that must be exceeded for the average likelihood (or support) of the model to increase. The exact average likelihoods are computable in both cases. It is worth stressing that the Bayesian approach to such problems is unified: one compares average likelihoods. By contrast, orthodox statistics offers us a mixed bag of tricks with no single (or simple) underlying logic.

Keywords

Markov Chain Preceding Trial Homogeneous Sequence Average Likelihood Order Chain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. Anderson, T.W. and Goodman, L. A.: 1957, ‘statistical Inference About Markov Chains’, Ann. Math. Stat. 28, 89–110.CrossRefGoogle Scholar
  2. Box, G. E. P. and G. Tiao: 1973, Bayesian Inference in Statistical Analysis, Addison-Wesley, Reading, Mass., Section 2.7.Google Scholar
  3. Johnston, J.: 1972, Econometrics 2nd ed., McGraw-Hill, New York.Google Scholar
  4. Kalbfleisch, J. G. and D. A. Sprott: 1970, ‘Application of Likelihood Methods to Models Involving Large Numbers of Parameters’, J. Roy. Stat. Soc. B, 32, 175–194.Google Scholar
  5. Lindley, D. V. and G. M. El-Sayyad: 1968, ‘The Bayesian Estimation of a Linear Functional Relationship’, J. Roy. Stat. Soc, B 30, 190–202.Google Scholar

Copyright information

© D. Reidel Publishing Company, Dordrecht, Holland 1977

Authors and Affiliations

  • Roger D. Rosenkrantz
    • 1
  1. 1.Virginia Polytechnic Institute and State UniversityBlacksburgUSA

Personalised recommendations