近年來由於基因微陣列(microarray)技術的蓬勃發展，生物學家可以在同一時間內分析成千上萬的基因，並可利用微陣列技術研究在不同環境下之基因表現差異，探索基因微妙的運作過程。多時期微陣列(time-course microarray)是在特定的一段實驗時間中，分別在不同時間點量測基因表現值，能有效瞭解基因在隨著時間而有不同的表現變化情形。而往往基因體的運作過程極為複雜，要在龐雜的基因表現數據中萃取出有意義的生物訊息與找出顯著的基因就成為統計上的熱門議題。本文以迴歸模型配適多時期的微陣列基因資料，考慮了分段線性迴歸模型，二次迴歸模型以及傅立葉迴歸模型，並以迴歸配適後的轉折點與斜率分群。藉由分群的方法，找出在不同環境下有相似表現行為的基因。

Microarray technologies in molecular biology make it possible to simultaneously measure the expression levels of thousands of genes for a certain organism, has advanced to unravel the biological insight at the genome scale and to study the behavior of massive genes simultaneously under various environment conditions. The experiment of time-course microarray is the expression profiles of genes are repeatedly measured over a time period, and is effective not only in studying gene expression profile levels cross time but also in exploring functions and interactions of genes. Since biological processes are complex systems, the major statistic strategy is how to character the behaviors of genes and identify significant genes. It is believed that genes demonstrating similar expression profiles over time might give an informative insight into underlying biological mechanisms work. This thesis intends to investigate the significant genes in time-course microarray experiment, and present regression models for clustering periodic patterns of gene expression. We consider piecewise linear regression, quadratic regression and Fourier regression function to fit the time-course microarray data, finding a best model in fitting the calorie restriction microarray data.

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