Hostname: page-component-89b8bd64d-j4x9h Total loading time: 0 Render date: 2026-05-08T03:57:56.751Z Has data issue: false hasContentIssue false
  • English
  • Français

What is Bayesian statistics?

Published online by Cambridge University Press:  14 June 2016

Osvaldo Marrero
Osvaldo Marrero*
Affiliation:
Department of Mathematics and Statistics, Villanova University, 800 Lancaster Avenue, Villanova, Pennsylvania 19085-1699, USA e-mail: Osvaldo.Marrero@villanova.edu
Get access

Extract

Bayesian statistics is included in few elementary statistics courses, and many mathematicians have heard of it, perhaps through collateral readings from popular literature or [1], selected as an Editor's Choice in the New York Times Book Review. ‘Bayesian statistics’ provides for a way to incorporate prior beliefs, experience, or information into the analysis of data. Bayesian thinking is natural, and that is an advantage. For example, on a summer morning, if we see dark rain clouds up in the sky, we leave home for work with an umbrella because prior experience tells us that doing so is beneficial. In general, the idea is simple; schematically, it looks like this:

(prior belief) + (data: new information) ⇒ (posterior belief).

Thus, we begin with a prior belief that we allow to be modified or informed by new data to produce a posterior belief, which then becomes our new prior, and this process is never-ending. We are always willing to update our beliefs according to new information.

Information

Type
Research Article
Information
The Mathematical Gazette , Volume 100 , Issue 548 , July 2016 , pp. 247 - 256
Copyright
Copyright © Mathematical Association 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

1.McGrayne, S. B., The theory that would not die: how Bayes' rule cracked the enigma code, hunted down Russian submarines, and emerged triumphant from two centuries of controversy. Yale University Press, New Haven, Connecticut (2011).Google Scholar
2.von Baeyer, H. C., Quantum weirdness? It's all in your mind, Scientific American 308 (6) (2013) pp. 46–51.CrossRefGoogle ScholarPubMed
3.McIntosh, L., Coates, S., Voters turn away from a Scottish nation state: dramatic poll shows slump in Salmond's support, The Times, 1 July 2014.Google Scholar
4.Albert, J., Bayesian computation with R (2nd edn.), Springer, New York (2009).Google Scholar
5.Cowles, M. K., Applied Bayesian statistics: with R and OpenBUGS examples, Springer, New York (2013).CrossRefGoogle Scholar
6.Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., Rubin, D. B., Bayesian data analysis (3rd edn.), CRC Press, Boca Raton, Florida (2014).Google Scholar
7.Hoff, P. D., A first course in Bayesian statistical methods. Springer, New York (2009).CrossRefGoogle Scholar
8.Box, G. E. P., Tiao, G. C., Bayesian inference in statistical analysis, Addison-Wesley, Reading, Massachusetts (1973).Google Scholar
9.Lindley, D. V., Introduction to probability and statistics from a Bayesian viewpoint. Part 1 Probability, Cambridge University Press (1965).Google Scholar
10.Lindley, D. V., Introduction to probability and statistics from a Bayesian viewpoint. Part 2 Inference, Cambridge University Press (1965).Google Scholar
11.Barnett, V., Comparative statistical inference (2nd edn.), Wiley, New York (1982).Google Scholar
12.Lindley, D. V., Understanding uncertainty (Revised edn.), Wiley, Hoboken, New Jersey (2014).Google Scholar
13.Lunn, D., Jackson, C., Best, N., Thomas, A., Spiegelhalter, D., The BUGS book: a practical introduction to Bayesian analysis. CRC Press, Boca Raton, Florida (2013).Google Scholar
14.Timpson, C. G., Quantum Bayesianism: A study, Studies in history and philosophy of modern physics 39 (2008) pp. 579–609.CrossRefGoogle Scholar