The Extension of Quantity Group

數量群的延伸

凌嘉華(Chiahua Ling)

《華醫學報》 54期 (2021/06) Pp. 1-10

摘要

We use a new approach which simulates the idea of Bayesian method with a difference. In traditional Bayesian method one considers a prior distribution, may be a conjugate one, which is centered at super parameters. Our method of data augmentation is supposed to help for small samples or cases where a very few observations are available. We use prior distributions, centered at the given observations ( calling them to be super parameters ), to generate a larger artificial dataset which may be termed as second generation dataset. This larger second generation dataset is then used to draw inferences. The powerful computers, coupled with suitable numerical algorithms, caused an increased interest in nonlinear models (such as neural networks) as well as the creation of new types, such as generalized linear models and multilevel models. Increased computing power has also led to the growing popularity of computationally intensive methods based on resampling, such as permutation tests and the bootstrap, while techniques such as Gibbs sampling have made use of Bayesian models more feasible.

關鍵字

Conjugate distribution ； Gibbs sampling ； Order statistics ； Prior distribution

並列摘要

這篇研究我們使用和貝氏技術些微不同的方法，傳統的貝氏方法是假設有先驗分配（可能是共軛分配）和以超參數為中心。我們用小樣本中非常少的觀察值作資料增加擴大，用以觀察值（假設它們是超參數）為中心的先驗分配來產生一個較大的資料集（稱作第二產生資料集），這個第二產生資料集可以用來做統計推論，電腦及其演算法導致非線性模型（如神經網路）和新式演算法（如廣義線性模式、等級線性模型）的大量應用，電腦效能的增強使得需要大量計算的再取樣演算法成為時尚，如置換檢定、自助法。Gibbs取樣法也使得貝氏模型更加可行。

並列關鍵字

共軛分配 ； 次序統計量 ； 先驗分配 ； 吉布斯取樣法