scholarly journals Further Properties of Frequentist Confidence Intervals in Regression that Utilize Uncertain Prior Information

2013 ◽  
Vol 55 (3) ◽  
pp. 259-270 ◽  
Author(s):  
Paul Kabaila ◽  
Khageswor Giri
Keyword(s):  
Confidence Intervals ◽  
Prior Information

Confidence Intervals for Percentage Reductions

1972 ◽  
Vol 51 (2) ◽  
pp. 492-497 ◽  
Author(s):  
Alan M. Abrams ◽  
B. Jerald McClendon ◽  
Herschel S. Horowitz
Keyword(s):  
Statistical Method ◽  
Confidence Intervals ◽  
Prior Information ◽  
Treatment Effectiveness ◽  
Percentage Reduction

A method of using information from previous studies is applied to the problem of estimating treatment effectiveness of a preventive agent in terms of percentage reduction. The Bayesian statistical method allows the use of such prior information in analyzing the results of a study.

scholarly journals Bayesian Procedures for the Estimation of Mutation Rates from Fluctuation Experiments

Genetics ◽  
1996 ◽  
Vol 142 (1) ◽  
pp. 313-326
Author(s):  
Georgios Asteris ◽  
Sahotra Sarkar
Keyword(s):  
Confidence Intervals ◽  
Prior Information ◽  
Prior Probability ◽  
Bayesian Estimator ◽  
Mutation Rates ◽  
Quadratic Loss ◽  
Fluctuation Test ◽  
Bayesian Procedures ◽  
Point Estimators ◽  
Bayesian Estimators

Bayesian procedures are developed for estimating mutation rates from fluctuation experiments. Three Bayesian point estimators are compared with four traditional ones using the results of 10,000 simulated experiments. The Bayesian estimators were found to be at least as efficient as the best of the previously known estimators. The best Bayesian estimator is one that uses (1/m  2) as the prior probability density function and a quadratic loss function. The advantage of using these estimators is most pronounced when the number of fluctuation test tubes is small. Bayesian estimation allows the incorporation of prior knowledge about the estimated parameter, in which case the resulting estimators are the most efficient. It enables the straightfonvard construction of confidence intervals for the estimated parameter. The increase of efficiency with prior information and the narrowing of the confidence intervals with additional experimental results are investigated. The results of the simulations show that any potential inaccuracy of estimation arising from lumping together all cultures with more than n mutants (the jackpots) almost disappears at n = 70 (provided that the number of mutations in a culture is low). These methods are applied to a set of experimental data to illustrate their use.

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