Situation - Specific Inference Using the Dempster - Shafer Theory

R.A. Fisher questioned the sampling-based approach to statistical inference on the grounds that it often cannot really answer the scientific question of interest. Fisher’s fiducial argument and the Dempster-Shafer (DS) theory are inferential methods that strive towards answering these situation-specific questions. For some important problems, such as testing of a sharp null hypothesis, these alternative theories suffer from the same drawbacks as their samplingbased counterparts. The Weak Belief (WB) extension of DS is applied in such cases to achieve the best of both worlds: the desirable personal probability-based inference of DS with the additional flexibility of WB. We formulate a general framework for situation specific inference, which we call the WB-DS method. Applications of the WB-DS method are illustrated in two important statistical problems, namely large-scale simultaneous hypothesis testing and nonparametrics. We show in simulations that the WB-DS procedures, suitably calibrated, perform comparably to popular classical alternatives. Most importantly, the WB-DS method makes it possible to solve challenging statistical inference problems in a situation-specific way.