A Comparison of Classical and Bayesian Probability and Statitics (3)[Srovnání klasické a Bayesovské pravděpodobnosti a statistiky (3.)]

Statistics has been developing for almost 250 years - since the publication of an essay which included one theorem called Bayes' after the author. This whole period (since 1763 to this day) has been accompanied by a duel between the supporters of a subjective concept of probability and those who refuse everything but a purely objective concept of probability as well as statistics. While the 18th and 19th centuries accepted the importance of the subjective (let us say Bayesian) way of thinking for the development of probability and statistics without a problem, in the 20th century the classic (frequentist) way took over and has been dominant in teaching and textbooks to this day. Only in the second half of the 20th century did the situation begin to change slowly. Reasons for that are partly described in the present article, but arguments and simple examples supporting the Bayesian way in comparison with the classic one are clear and generally respected worldwide. Unsuspected new computing possibilities have caused an explosive development of Bayesian statistics, which has infiltrated almost all the areas of statistics and a number of other scientific fields. It is not possible to expect a retreat of the different philosophical or pedagogical positions of the fighting schools of thought (even though it is really needed), but the use of advantages of both the approaches is methodologically not only possible, but even expected. Part of the teaching of statistics must be prepared for these changes, but it has not been the case in the Czech Republic at all so far.