Waves are everywhere. Biological waves, such as gastric slow waves, and electromagnetic waves, such as TV signals and radio waves, are typical examples that we encounter in everyday life. Many waves are emitted from a point source, whose wavefront can be approximated by a line if the point source is far away. When an experimenter records a propagating wave, the data is subject to noise contamination, posing great diffculty in wave analysis. In this thesis, we consider the situation where at most one wave propagates in a two-dimensional space at any particular time and the detector recordings are noisy. We introduce two parametric generative models for wave propagation and one parametric model for noise generation, and develop a multistage procedure which identifies the number of waves in a given data set, followed by an inference on important variables, including the location of the point source, the velocity of the wave and indicator variables of spikes under the Bayesian paradigm. The procedure is illustrated with two real-life examples. The first one is a study on the effect of potassium ion channels using cultured heart cells. The other is on the propagation characteristics of the Tokohu Tsunami in 2011. / 波是無處不在的。生物波如胃慢波，以及電磁波如電視信號和無線電波，都是我們在日常生活中常遇到的波的典型例子。許多波都是點源，而當波從一個遠的點源發射， 其波陣面會近似一條直線。當實驗者記錄波數據時，數據很大機會受到雜訊污染，增加了分析波數據的難度。本文考慮在一個二維空間內，任何特定的時間中，最多只有一個波在傳播，而波數據受到雜訊污染。我們提出了兩個參數模型模擬波的產生和傳播，以及一個參數模型模擬雜訊的產生。我們並建立了一個多階段程序先識別數據中波的數量，然後根據貝葉斯理論，將尖峰訊號分類成波尖峰訊號或雜訊尖峰訊號，以及對波尖峰訊號的重要參數，包括點源的位置和波的速度進行估算。本文提出的方法將應用於兩組真實數據上。第一組是關於細胞鉀離子通道如何影響心肌培養細胞研究，而另一組則分析2011年日本東北海嘯的傳播特性。 / Lau, Yuk Fai. / Thesis M.Phil. Chinese University of Hong Kong 2015. / Includes bibliographical references (leaves 71-74). / Abstracts also in Chinese. / Title from PDF title page (viewed on 18, October, 2016). / Detailed summary in vernacular field only.
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_1291540 |
| Date | January 2015 |
| Contributors | Lau, Yuk Fai (author.), Fan, Xiaodan (thesis advisor.), Chinese University of Hong Kong Graduate School. Division of Statistics. (degree granting institution.) |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, bibliography, text |
| Format | electronic resource, electronic resource, remote, 1 online resource (ix, 74 leaves) : illustrations (some color), computer, online resource |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons "Attribution-NonCommercial-NoDerivatives 4.0 International" License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
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