This monograph is based on ideas by A. Dempster (1967) and G. Shafer (1976). They developed probabilistic argumentation systems combining logic and probability with a unified theory of inference under uncertainty. It has numerous applications in various fields (artificial intelligence, diagnostics and reliability, among others). The book applies this new theory to statistical inference. In particular, a new principle, called by the authors assumption-based inference in statistics reasoning, is introduced and worked out. Both the Bayesian approach and the Fisher fiducial probabilities are seen as special cases of a more general theory. The authors show the possibility of a new approach to discrete probability models, continuous probability models and linear models. Basic principles are introduced and explained in part concerning simple discrete probability models. A number of illustrative examples help in understanding the theory. The book is intended to open a new view on statistical inference.