貝氏定理應用於分佈參數推估之自動更新法

貝氏推估法爲有關工程設計上囘歸值分析實用方法之一，可應用各組數據集合隨時更新各分佈模式之機率與囘歸值之分佈情形，作為判斷模式正確性與囘歸值信賴區間之用。但在其更新過程中，需以試誤法反覆決定參數範圍，卽耗費人力時間又易使分析流於主觀。爲彌補此一缺陷，本文提議利用預先設定之邊界率比作爲指標，而以常態分佈函數更新參數範圍、機率之自動推估方法。文中以實測波高做為應用實例，由更新過程中參數範圍與機率之改變情形，及由囘歸值分佈範圍與機率等推估結果與一般更新方法之比較，來檢定本方法之實用性。結果說明，本文提議之自動更新方式可促使囘歸值之推估作業自動化，實質改善囘歸值推估分析之作業時效，加述貝氏推估法在囘歸值分析問題上之推廣應用。

關鍵字

貝氏推估；自動更新；常態分佈函數；邊界機率比；分佈模式；分佈參數；囘歸值

並列摘要

Bayesian estimator is one of the practicable methods to regress the return values for the design criteria. According to a new available data set, it can be used to update the following items at the same updating procedure: (1) the probability of the distribution models, (2) the range and probability of the distribution parameters, as well as (3) the expectation and probability of the return values. Nevertheless, to get the good resolution of distribution histogram with the general updating procedure, the analyst must stay at his seat and keep his time to decide recurrently how to revise the initial settings for the range and probability of the distribution parameters. To eliminate this trouble, an auto-updating scheme is established for Bayesian estimator in this paper. By setting the marginal probability ratio, the revising procedure based on the normal function for the prior range and probability of parameters is proposed for this scheme. Through the examining on the updating probability histogram, it is proved that this scheme would exactly complete the revising procedure with the inputting data set. Meanwhile, this scheme also gives the perfect agreement with the results of the general updating procedure. Accordingly, this auto-updating scheme is supposed to make a substantial improvement on Bayesian estimator, when this method is used to investigate the fitness of distribution model and regress the return values.

並列關鍵字

Bayesian estimator ； Auto-updating ； Normal function ； Marginal probability ratio ； Distribution model ； Distribution parameter ； Return value

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