Analysis of data is integral in bridging the gap between theory and experiment. My question is about the two major methods of approaching the analysis - Bayesian and Frequentist. How much do the results of the analysis depend upon the choice of the method?
For instance, consider experiments in Particle Physics. This paper by Louis Lyons states that Particle Physicists use a hybrid approach to analysis. (Frequentist hypothesis testing and Bayesian parameter estimation.) If a purely Bayesian/Frequentist approach was applied, would there be a difference in the results of the analysis? What implication would any difference have on the interpretation of data?