Vol: 30 Page: 281

Authors:
Wiktor Oktaba

Title:
 On inference in the mathematical statistics in aspect of the mathematical logic and the therory of probability

Language: Polish

Keywords:
statistical inference
formal logic
incomplete enumeration logic
metamathematics
set theory
estimation
verification of hypotheses
decision theory
history
methodology of mathematics
bayesian and "classical" inference
philosophical controversies
subjective probability
mathematical logic in informatics
neo-bayesian statistics

Summary:
The dominant role of the mathematical logic and the theory of probability in inferences in mathematical statistics are presented. Some historical outlines of the domains mentioned above as well as well as approaches of the Polish Mathematical School and specially Polish Logical School are given. Problems of the mathematical statistics and its relation to the theory of probability are described. Different inference theories corresponding to some interpretation of probability: bayesian, subjective, Fisherian and that of Neyman, E.S. Pearson ones are presented.