最近幾年基因微陣列晶片技術的發展，使我們得以同時研究成千上萬個基因。對於微陣列資料，基因表現值變異數與表現值之間呈現某種關連性為眾所皆知的事實。相關學者建議穩定變異數以提高挑選顯著性基因的檢定力，但大多數待轉換的資料只考慮單一時點，未慮及多時期下所製作之time-course微陣列資料。
在本論文中，將估計多時期微陣列資料之變異數函數，並建議將所有時間點下的資料合併後進行變異數穩定轉換。我們將推廣文獻上已有之Started Log (sLog), Log-Linear Hybrid (Hyb), Generalized Logarithm Transformation (glog) 和 Spread-versus-Level Plot transformation (SVL) 之變異數轉換至多時點基因資料的轉換。我們也考慮Data-Driven Haar-Fisz Transformation for Microarray (DDHFm) 和 step function 兩種無母數的轉換法來處理變異數不等的問題。由模擬可知，對於多時期微陣列資料，經由三種log轉換法後的變異數比其他轉換法來的穩定，而DDHFm法則可能較不適用於這種資料型態。本文以實際多時期微陣列資料來說明其應用。

In recent years, the development of cDNA microarray technology allows people to investigate thousands of genes simultaneously. For microarray data, it is well known that gene expression is related with its variance in some way.
Researchers do try to stabilize the variance
so that the detection power can be greatly improved.
However, none or very few researches focus on stabilizing the variance for multiple time-course microarray data.

In this thesis, we evaluate the function of variance for time course microarray data and suggest a pooled approach to stabilize the variance. We extend the existing methods, such as Started Log (sLog), Log-Linear Hybrid (Hyb), Generalized Logarithm Transformation (glog)
and Spread-versus-level plot transformation (SVL) to stabilize variance for time-course data. We also consider two nonparametric methods, Data-Driven Haar-Fisz Transformation for Microarray (DDHFm) and step function approaches, to deal with this problem. Simulation study shows that the three log transformation methods are better in stabilizing variance than another methods, and DDHFm transformation may not suitable for time-course microarray data.
A real time-course microarray data is illustrated for application.

Archer, K. J. et al. (2004) Graphical technique for identifying a monotonic variance stabilizing transformation for absolute gene intensity signals. BMC Bioinformatics, 5,60.

Ballman, K. V., Grill, D. E., Oberg, A. L. and Therneau, T. M. (2004) Faster cyclic loess: normalizing RNA arrays via linear models. Bioinformatics, 20, 2778-2786.

Fryzlewicz, P., and Nason, G. P. (2004) A Haar-Fisz algorithm for Poisson intensity estimation. Computational and Graphical Statistics, 13, 621-638.

Fryzlewicz, P. and Delouille, V. (2006) A data-driven Haar-Fisz transform for multiscale variance stabilization. Proceedings of the 13th IEEE Workshop on Statistical Signal
Processing, 17-20 July 2005.539-544.

Motakis, G. P, Nason, G. P., Fryzlewicz, P., and Rutter, G. A. (2006) Variance stabilization and normalization for one-color microarray data using a data-driven multiscale
approach. Bioinformatics, 22, 2457-2553.

Rocke, D. M. and Durbin, B. P. (2001) A model for measurement error for gene expression arrays. Computational Biology, 8, 557-569.

Rocke, D. M. and Durbin, B. P. (2003) Approximate variance-stabilizing transformations for gene-expression microarray data. Bioinformatics, 19, 966-972.

Lin, Yu-Ru (2007) A Step function approach in stabilizing variance for microarray data. Master Thesis National Cheng Kung University.

Tukey, J. W. (1977) Exploratory Data Analysis. Addison-Wesley, Reading, MA.