函數型資料分析為近年發展的統計方法。函數型資料是在一段特定時間上，我們只在離散的時間點上收集觀測值。例如:氣象觀測站所收集到的每月氣溫、雨量資料，即是一種常見的函數型資料。函數型資料主要有三種特色，共同趨勢性、觀測個體反應強度不同，觀測個體時間特色上的差異。本文研究主要是使用，Brumback與Lindstrom在2004所提出的自模型迴歸族(self-modeling)當作模型架構來處理函數型資料的趨勢性與個體反應強度。而為了處理函數型資料的時間差異性，我們在模型中加入時間轉換函數(time transformation function)，處理函數型資料的時間差異性步驟，這個過程稱為同步化。經過同步化的處理後，能幫助研究者更清楚資料的特性。模型中除了時間轉換函數的部份，其餘模型中的參數我們是利用馬可夫鏈蒙地卡羅法中的Gibbs Sampling來進行參數的抽樣，並以取出的抽樣值來估計參數。時間轉換函數的部份，我們使用概似懲罰函數(penalized likelihood function)來估計時間轉換函數的參數部份。由於函數型資料擁有趨勢性，我們預期不同類別的資料，會呈現不同的趨勢性，我們將利用此一特色當做分類上的標準。 關鍵詞:函數型資料分析、曲線同步化、曲線區別分析、馬可夫鏈蒙地卡羅法。 / Functional data are random curves observed in a period of time at discrete time points.They often exhibit a common shape, but with variations in amplitude and phase across curves.To estimate the common shape,some adjustment for synchronization is often made,which is also known as time warping or curve registration.In this thesis,splines are used to model the warping functions and the common shape. Certain parameters are allowed to be random.For the estimation of the random parameters,priors are proposed so that samples from the posteriors can be obtained using Markov chain Monte Carlo methods.For the estimation of non-random parameters, a penalized likelihood approach is used. It is found via simulation studies that for a set of random curves with a common shape,the estimated common shape function looks like the true function up to a location-scale transform,and the curve alignment based on estimated time warping functions looks reasonable.For two groups of random curves which differ in the group common shape functions,synchronization also improves the discrimination between groups in some cases. Key words: functional data analysis,curve registration,curve discrimination,markov chain monte carlo method.

意識的議題古老而難解，但是近年來認知神經科學領域對此議題的探討已經熱烈展開，本研究之主要目的即在探索視覺意識與大腦功能性連結之間的關係。 根據一項人臉知覺的實驗結果，本研究依照線性對非線性、局部對整體等兩項條件所構成的四個取向，分別擬定用以反映視覺意識的腦電波指標。結果發現，線性的局部指標—即γ波的強度，以及線性的整體指標—即γ波的相位耦合程度，兩者皆無法有效反映視覺意識。然而，非線性的局部指標—即吸子的相關維度，在特定通道上可以反映視覺意識；至於非線性的整體指標—即廣義的同步化程度，乃為四者中最能穩定反映視覺意識的指標。 除了得到上述若干可以有效反映視覺意識的腦電波指標之外，本研究實質上整合了認知神經科學、非線性動力系統理論、小波轉換理論以及小世界理論等當代思維，因此文中亦做出大量而深入的理論探討，並且提出對現有相關研究在邏輯或方法上的改進與澄清。 / Consciousness is an ancient and puzzling mystery. Until recently, scientists have made little significant progress on it. This study is aimed to search for the neural correlates of visual awareness. / Based on empirical data from an experiment of face perception, this study explores linear vs. nonlinear and local vs. global human EEG indexes of visual awareness. The results indicate that neither linear local index, i.e. γ-band power, nor linear global index, i.e. γ-band phase coherence, can reveal the participant’s state of awareness validly. However, nonlinear local index, i.e. correlation dimension of attractor, can be a valid index of visual awareness, but only on specific channels. Last but not least, nonlinear global index, i.e. generalized synchrony, can be the most valid and efficient index of visual awareness. / In addition to the empirical findings listed above, this study, an interdisciplinary combination of cognitive neuroscience, chaos theory, wavelet transform and small-world theory, also presents numerous theoretical discussions and modifications to other related studies logically or methodologically.