The Bayesian Method:from The View Of Philosophy Of Science

Bayesianism is one of the front edge research methods. It has been widely applied in statistics, economics, psychology and artificial intelligence, etc. Its reasoning model has been called Bayesian inference. Since Keynes started the modern age of induction and created the first probabilistic induction system, Bayesianism has become a strong defender of the induction and gradually developed to be a general scientific reasoning theory and method.There are two aspects for studying Bayesian method under the spectrum of science philosophy:firstly, to explore the inference mechanism and procedure of Bayesian method from the aspect of reasoning; secondly, to answer reasonable questions of Bayesian method from the aspect of methodology. Therefore, questions to be discussed include the superiority of Bayesian inference mechanism, the argument of subjective probability and objective probability, the puzzle of the old evidence and simplicity, and the possible developing direction of Bayesian method.First of all, to start from the perspectives of rationality and originality of Bayesian method, the author outlines the Bayesian method both longitudinally and horizontally. The modern logistic scholars give mathematical Bayesian method logistic meaning. Its origin was the reasonable questioning of induction in Hume’s problem. Hume’s problem vetoed the rigid reasoning pattern of the induction of simple enumeration method from logistics. The predetermined characteristics of Bayesian method make itself the main reasoning model in the modern induction. The philosophical core of Bayesian method represents in the interpretation of probability. According to the interpretation of probability, there are two categories of Bayesianism:the logistic Bayesianism and subjective Bayesianism. Because the subjectivism has obvious superiority since it avoids the paradoxes of indifference in logistism, it becomes the core theoretical basis of Bayesian method. For this reason, the Baeysian method discussed in this paper is the research method of subjective Bayesianism. Without special indication, Bayesianism mentioned in this paper refers to subjective Bayesianism. In addition, the author proves that Bayesian method is a logical historical method from the perspective of scientific methodology and therefore presents its rationality.Secondly, the author discusses the types and limitations of classical statistic induction and the application of Bayesian method in statistic induction in two chapters to prove the superiority of Bayesian induction mechanism. The resurrection of Bayesianism happens in the statistical induction area. Bayesian statistical induction avoids the subjectivity and ignore-to-prior in classical statistical inference, and therefore is a revolution of inference method. In the review of hypothesis, the Bayesian statistic inference solves the problem of deciding test statistic in classical statistic inference, averts the problem of stopping rule and its specialty in induction. When solving the estimation problem, Bayesian estimation utilizes credible interval to substitute the confidence interval, and provides a definition and reasonable explanation for classical confidence interval intuition. The application of Bayesian theory conquers the difficulty of introducing prior information in classical estimation. From the perspective of induction, the classical statistic method has been limited by the origin of its methodology-falsification, and has been faced with the questioning of lack of induction. The Bayesian method, however, as a quantification of induction and reasoning mechanism has the advantage of induction.Thirdly, the author analyzes the difficulties and challenges that the Bayesian method faces with, and points out the reasonable questioning. The Bayesian method has the difficulties of subjectivity, simplicity and the problem of old evidence. The difficulty of subjectivity lies in the problem of constraint of prior probability in Bayesian inference mechanism. The difficulty of simplicity is questioning the principle of simplicity, representing in the inconsistency of simplicity postulate and probability axioms. Foster and Sober stated that simplicity is an "ad hoc method," while Howson advocated to avoid the simplicity and thought simplicity should not be considered as an important guidance for choosing a theory. The old evidence indicates that an old evidence does not provide any confirmation for theory or assumption in the Bayesionism structure. It contradicts with our intuition. Howson uses the relatedness of evidence to prove that "evidence support" implies the relationship among data, assumption and background knowledge k. The problem of old evidence exists, only when e is made the evidence and k includes e. This is the exact reason why Bayesian inference needs further improvement and development.Last but not the least, the author explores the possible development of Bayesian method from the perspectives of logic, philosophy, and cognition. The rationality of Bayesian method leaves much space for its further development. To view from the developing process of induction logic, the rise of the logic of non-Pascal probability reveals a possible way for Bayesian method, that is, to revise or weaken the Pascal probability that Bayesianism has been insist on, and to form the non-Pascal Bayesianism. The philosophical discussion of Bayesian focuses on the selection of subjective probability interpretation and objective probability interpretation. On one hand, the author believes probability is multi-facets in application and both subjective interpretation and objective interpretation have their own areas for application. On the other hand, the subject interactive interpretation satisfies the objectivity of science inference. Through the research and application in cognitive science, Bayesian method provides hints for its own development. Especially the successful application of Bayesian inference model in cognitive phycology provides opportunity of perception redirection for Bayesian inference study. It also provides possible access to the development of Bayesian method, that is, to pursue the integrity of the probability and Bayesianism, and to attempt the blending of extensionality and non-extensionality by introducing connotation. To speak more specifically, Gigerenzer and Hoffrage brought forward a Bayesian model with frequency representation of information, which means to improve the Bayesian inference method by substituting probability representation with frequency representation. Tversky and others put forward a supporting theory for subjective probability, and built a non-extention logic for the support theory for subjective probability. It is therefore very likely that the cognitive turn of induction logic will be one of the important direction for induction logic’s development in the future.