论统计推理中贝叶斯归纳的哲学研究

Analysis on the Bayesian Induction in Statistic Inference

贝叶斯归纳是通过后验概率的贝叶斯定理或从相关先验分布的密度分布,以获得新信息的运算。它以在两个"估计"过程中对贝叶斯归纳的成功运用,回应了所谓"主观性"不能在标榜"客观性"的科学过程中出现的质疑。平稳估计也称稳健性估计,保证贝叶斯估计相对于先验分布的相对独立性,无需为了做一个既准确又精确的贝叶斯估计付出巨大的准确度和精度方面的代价。通过对证据的刻画、对抽样的分析以及对因果假设的检验等分析认为:该研究避免了经典方法中对结局空间及停止规则等依赖的贝叶斯归纳方法,是一种与直观相吻合的、科学的推理方法。

Bayesian Induction is one kind of Statistics Inference to use Bayesian theorem to get new Information from the data. Its nature of subjectivity that the bayesianists have during the process of inference is a target for frequentists to critics. By using the application of Bayesian inference in two kinds of estimations （MNP and BP） , Bayesian induction answered its rivals. The Principle of stable estimation guarantees its independence of prior distribution without the price of the estimations＇ unbiasness and consistency. After all, we come to a concluding that the Bayesian induction not only meets our intuitions but also avoid the dependence upon the out-space and the subjective stopping rule which appeared in the classical inference scheme.