arXiv subjects

S. I. Bitioukov

Publications and source records attributed to S. I. Bitioukov.

2 recordsLinked to original sources

arXiv2012

The relation between frequentist confidence intervals and Bayesian credible intervals

We investigate the relation between frequentist and Bayesian approaches. Namely, we find the "frequentist" Bayes prior π_{f}(λ,x_{obs}) = -\frac{\int_{-\infty}^{x_{obs}}\frac{\partial f(x,λ)}{\partial λ}dx}{f(x_{obs},λ)} (here f(x,λ) is the probability density) for which the results of frequentist and Bayes approaches to the determination of confidence intervals coincide. In many cases (but not always) the "frequentist" prior which reproduces frequentist results coincides with the Jeffreys prior.

physics.data-an↗

arXiv2012

Modified frequentist determination of confidence intervals for Poisson distribution

We propose modified frequentist definitions for the determination of confidence intervals for the case of Poisson statistics. We require that 1-β^{'} \geq \sum_{n=o}^{n_{obs}+k} P(n|λ) \geq α^{'}. We show that this definition is equivalent to the Bayesian method with prior π(λ) \sim λ^{k}. Other generalizations are also considered. In particular, we propose modified symmetric frequentist definition which corresponds to the Bayes approach with the prior function π(λ) \sim 1/2(1 + \frac{n_{obs}}λ). Modified frequentist definitions for the case of nonzero background are proposed.

physics.data-an↗