Statistics Roundtable: Different Roads to Take for Data Analysis Taken from the Spring 2007 Newsletter
Abstract: Many believe that frequentist and Bayesian approaches to analyzing data have irreconcilable differences, and that one or the other should prevail and be used exclusively. The paper states that the choice of approach depends on the problem at hand as each approach has its own trade-offs and benefits depending on the circumstances. In fact, both are parametric approaches with an underlying statistical model with parameters to be estimated, and both need to connect the observed data to the parameters through a specified relationship defined by a distribution in the likelihood function. Highlighting some of the similarities and differences between the frequentist and Bayesian approaches might help more engineers and scientists using statistical methods understand some of the trade-offs in terms of parameters, data and expert opinion, interval estimates and computational intensity. One should evaluate these trade-offs on a case-by-case basis in choosing between frequentist and Bayesian approaches.
Keywords: Frequentist methods - Bayesian - Likelihood function - Maximum likelihood estimation - Least square estimation - Random variables - Sensitivity analysis - Confidence intervals