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研究生： 趙彥茹
Yen-ju Chao
論文名稱： 貝氏補值方法應用在行星資料的週期和質量上
Bayesian imputation with an application to mass-period functions of extrasolar planets
指導教授： 鄧惠文
Huei-Wen Teng
口試委員:
學位類別： 碩士
Master
系所名稱： 理學院 - 統計研究所
Graduate Institute of Statistics
畢業學年度： 100
語文別： 英文
論文頁數： 54
中文關鍵詞： 遺失值 、補值 、貝氏
外文關鍵詞： copula, Bayesian, Missing data, imputation
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    • 在日常生活中，我們常常需要搜集資料，但常遇到資料搜集的不齊全
    也就是有遺失值的產生。在這篇論文當中，我們提出了一個貝氏方法
    來解決遺失值的問題，並且將這個方法應用到行星資料的質量及週期
    上。而我們使用天文學上最常使用的柏拉圖(Pareto)模型當成基準模
    型，並且使用Frank copula 來連結兩個為柏拉圖的邊際分配。
    選模規則建議我們在這些行星資料上使用混合模型較適當。實證分析
    建議我們應該將資料做log-transformed，並且使用混合分配的模型。
    因此本篇論文將貝氏補值方法用到這些模型上。

    Missing data problems frequently occur in many field. In this
    thesis, we provide a Bayesian method for the missing data
    problem, and apply the proposed method to the mass and period
    functions for extrasolar planets. The benchmark model is
    commonly used in astronomy, and uses a Frank copula to connect
    two pareto marginal distributions.
    Empirical analysis suggests us to provide a mixture model for
    the logarithmically transformed data. We apply our Bayesian
    imputation based on these models. Model selection criterion
    suggests that our proposed mixture model fits the data better.

    Contents 1 Introduction 1 2 Methodology 3 2.1 Copula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Our Bayesian approach . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3 Metropolis-Hastings Algorithm . . . . . . . . . . . . . . . . . . . . . 6 3 Simulation studies 7 3.1 Exploratory Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . 7 3.2 Benchmark model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.2.1 Marginal distributions . . . . . . . . . . . . . . . . . . . . . . 8 3.2.2 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.3 Mixtures model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.3.1 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 4 Real data analysis 29 5 Conclusion 45 5.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 5.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 Reference 45

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