A Survey Of Subjective Bayesian Theory

Since the British mathematician Thomas Bayes’ s Bayesian theorem is proposed in 18 th century, modern inductive logic has entered into a new era. Today, a main research method of modern inductive logic is Bayesian method. Bayesian method which is based on subjective Bayesian theory not only has great research value, but also has much more practical value. Subjective Bayesian advocates interpret the probability as degrees of belief, it is based on the Bayesian theorem and get the posterior probability from the pretest probability, the convergence theorem for opinion ensures that the subjective probability will eventually converged.We know that, compare with the deductive logic witch is inevitable, inductive logic is still a probabilistic logic reasoning, and if we want to go all lengths to use it, we must prove its rationality. “the convergence theorem for opinion” witch is proven by Bruno De Finetti who is one of the founders of subjective Bayesian theory indicate that, we can revise the subjective degrees of belief constantly according to Bayesian theorem and the subjective probability will eventually converged. It also put subjective degrees of belief and frequency problems together, and the “subjectivity” and “objectivity” is unified too. Subjectivists saw the hope to solve the inductive rationality problem from Bayesian method, also, the solution of the inductive rationality problem and the effectiveness problem of Bayesian method are closely linked, through the line in the subjective Bayesian theories. This paper generalizes the advantages and disadvantages of the basic subjective Bayesian theories in order to summarise and reflect the solutions of the inductive rationality problem put forward by subjectivists.