A Different Method of Data Increase

資料增加的不同方法

10.6202/THJ.201712_(13).0007

凌嘉華(Chiahua Ling)

Bayesian method ； prior distribution ； conjugate distribution ； 貝氏方法 ； 先驗分配 ； 共軛分配

慈惠學報

13期（2017 / 12 / 01）

89 - 97

英文

In traditional Bayesian method one assumes a prior distribution which is centered at super parameters. Our approach of data increase is supposed to help for small samples or cases. We use prior distributions, centered at the given observations 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.

傳統的貝氏方法是假設有先驗分配和以超參數為中心。我們用小樣本作資料增加擴大，用以觀察值中心的先驗分配來產生一個較大的資料集，我們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。

1. Casella, G.,Berger, R. L.(2001).Statistical Inference.Brooks/ColeCengage Learning.
2. Casella, G.,George, E.(1992).Weibulllaining the Gibbs sampler.The AmericanStatistican,46,167-174.
3. Clayton, D.(2003).Conditional likelihood inference under complex ascertainmentusing data augmentation.Biometrika,90,976-981.
4. David, Herbert A.,Nagaraja, Haikady N.(2003).Order Statistics.WileySeries in Probability and Statistics John Wiley & Sons.
5. Hastie, T.,Tibshirani, R.,Friedman, J.(2009).The Elements of Statistical Learning: Data Mining, Inference, and Prediction.New York:Springer‐ Verlag.
6. Kamakura, W.A.,Wedel, M.,Rosa, F.D.,Mazzon, J.A.(2003).Cross Sellingthrough Database Marketing: A Mixed Data Factor Analyzer for DataAugmentation and Prediction.International Journal of Research in Marketing,20(1),45-65.
7. Kosuke, I.,David, A.V.D.(2005).A Bayesian Analysis of the Multinomial Probit Model Using Marginal Data Augmentation.Journal of Econometrics,124(2),311-344.
8. Liamputtong, L (ed.)(2010).Research methods in health: Foundations forevidence‐based practice.South Melbourne:Oxford University Press.
9. Liu, Jun S.,Wu, Ying Nian(1999).Parameter Expansion for Data Augmentation.Journal of the American Statistical Association,94(48),1264-1274.
10. Pelosi, M. K.,Sandifer, T. M.(2002).Airspace Data Set, Doing Statistics ForBusiness: Data, Inference, and Decision Making.New York:John Wiley & Sons,Inc..
11. Van Dyk, D. A.,Meng. X. ‐L.(2001).The art of data augmentation.J. Comput. Graph. Stat.,10,1-111.
12. Wei, G. C. G.,Tanner, M. A.(1990).A Monte Carlo implementation of the EMalgorithm and the poor man’s data augmentation algorithm.Journal of theAmerican Statistical Association,85,699-704.