Bayesian inference on a proportion believed to be a simple fraction.
This article considers the problem of making inference on a proportion when there is reason to believe that the proportion is a simple fraction. By a simple fraction we mean a fraction that, when put in lowest terms, has a small denominator. After discussing the history of Bayesian inference on a pr...
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| Language: | English |
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2007
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| Online Access: | http://ezproxy.villanova.edu/login?url=https://digital.library.villanova.edu/Item/vudl:176355 |
| Summary: | This article considers the problem of making inference on a
proportion when there is reason to believe that the proportion
is a simple fraction. By a simple fraction we mean a fraction
that, when put in lowest terms, has a small denominator. After
discussing the history of Bayesian inference on a proportion, we
propose a class of otherwise noninformative priors that incorporates
the idea that the proportion is likely to be a simple fraction,
and we explore the impact of the choice of parameter. We propose
the posterior mode as a point estimator, and we study the
behavior of this estimator both asymptotically and for small sample
sizes. We illustrate our approach by applying it both to the
famous problem of estimating the probability that the sun will
rise again tomorrow and to examples from the scientific work of
the Augustinian friar Gregor Mendel. |
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