Departement of Theoretical Philosophy
Interval Estimates and Interpretation:
An Evaluation of Four Approaches to Interval Estimation
This thesis evaluates four approaches to interval estimation: Bayesianism, frequentist confidence intervals, the fiducial argument, and likelihoodism. Statistical tools should contribute to the goal of science of giving rise to reasonable beliefs. With this purpose of statistics in mind two criteria are formulated which a good approach to interval estimation should satisfy. First, an interval estimate should allow for the interpretation that it contains the true parameter value with a certain degree of reliance. Second, the values contained by the interval estimate should be the most plausible candidates for being equal to the true parameter value compared to the values outside the interval or region. Bayesian credible regions satisfy both of the criteria, but at the cost of being fundamentally subjective and requiring the formulation of a prior. The other three frequentist approaches do not require a prior distribution, but do either satisfy at most one of the two criteria or are not truly convincing (i.e. the fiducial argument).
|Last modified:||04 September 2015 1.47 p.m.|