Truncated Normal Degradation Models: A Bayesian Approach

截斷式常態衰變量模型的貝氏分析

俞一唐(I-Tang Yu)

《中國統計學報》 57卷3期 (2019/09) Pp. 211-231

摘要

When using the growth curve approach to model a degradation process, one or a few components in the degradation model are assumed random to describe the unit-to-unit variability. It is constantly to assume that the vector of the random components, or after applying a transformation, follows a multivariate normal distribution. However, the normality assumption can sometimes be inappropriate in practice. In this work, we consider a larger family of distributions, say the truncated normal distributions, for the specification of the distribution of the random components in the linear degradation model instead of seeking for a suitable transformation. Under a Bayesian framework, we provide a corresponding MCMC procedure to carry out the computation. Finally, with the use of the proposed truncated normal linear degradation model, we reanalyze GaAs laser data and obtain a better fit than fitting the normal linear degradation model to the data.

關鍵字

Bayesian estimation ； degradation analysis ； truncated normal distribution

並列摘要

為了描述實驗單位與實驗單位之間的差異性，在分析衰變量資料的統計模型中通常會假設模型中的幾個參數為隨機變數，而這些隨機變數所形成的向量會進一步假設其具有多變量常態分配（或經過一些適當轉換）。然而在一些實際的例子，中這些隨機變數的分配並不對稱，使得這樣的常態假設沒有辦法被滿足。對於這些隨機變數的機率分配的假設，在本文中我們考慮一個更大的分配族－截斷式常態分配。根據此一截斷式常態衰變量模型，在貝氏分析的架構下，我們提供了所需要的MCMC演算法。利用本文所提供的方法，我們分析了一筆雷射衰變量的資料，並且得到一個比使用傳統常態衰變量模型更好的配適結果。

並列關鍵字

貝氏分析 ； 衰變量 ； 截斷式常態分配

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