Data Increase and Staistical Inferences

資料增加和統計推論

凌嘉華(Chiahua Ling)

《台北海洋技術學院學報》 8卷2期 (2017/06) Pp. 102-114

摘要

In this study we follow the method of Bayesian technique with a difference. In traditional Bayesian method one assumes a prior distribution, may be a conjugate one, which is centered at super parameters. Our approach of data increase 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 (pretending 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 statistical inferences. The method is dependent on computational resources, and may be useful in applied problems.

關鍵字

Bayesian method ； prior distribution ； conjugate distribution

並列摘要

本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，這方法需要用到電腦資源而且是對應用問題有幫助的。

並列關鍵字

貝氏方法 ； 先驗分配 ； 共軛分配

參考文獻

SAS User’s Guide: Statistics, 5th ed. (1985). Sas Institute Inc., Cary, North Carolina.

Wei, G. C. G., and Tanner, M. A. (1990). “A Monte Carlo implementation of the EM algorithm and the poor man’s data augmentation algorithm.” Journal of the American Statistical Association, 85, 699-704.

SAS User’s Guide: Basics, 5th ed. (1985). Sas Institute Inc., Cary, North Carolina.

Tanner, M. A. (1991), “Tools for Statistical Inference. Observed Data and Data Augmentation Methods,” New York: Springer- Verlag.

Andrews, D. F. and Pregibon, D. (1978). Finding the outliers that matter. J. R. Statist. Soc. B 40, (pp. 85-93).