Introduction
The original Bayes proposal leads to likelihood and confidence for many simple examples. More generally it gives approximate confidence but to achieve exact confidence reliability it needs refinement of the argument and needs more than just the usual minimum of the likelihood function from observed data. A general Bayes approach provides a flexible and fruitful methodology that has blossomed in contrast to the widely-based long-standing frequentist testing with focus on the 5% level. We examine some key events in the evolution of the Bayes approach promoted as an alternative to the present likelihood based frequentist analysis of data with model, the evidence-based approach of central statistics. And we are led to focus on the bane of Bayes: parameter curvature.
Bayes 1763
Bayes (1763) examined the Binomial model \(f(y;\theta )\,=\,\left( {\begin{array}{*{20}c} n \\ \theta \\\end{array}} \right)\) θ y(1 − θ)n − y and proposed the flat prior π(θ) = 1 on [0, 1]. Then with...
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References and Further Reading
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Fraser, D.A.S. (2011). Bayesian Analysis or Evidence Based Statistics?. In: Lovric, M. (eds) International Encyclopedia of Statistical Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04898-2_133
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DOI: https://doi.org/10.1007/978-3-642-04898-2_133
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