貝氏補值方法應用在行星資料的週期和質量上

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趙彥茹(Yen-ju Chao) 查詢紙本館藏

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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)

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摘要(中)

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。

摘要(英)

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.

關鍵字(中)

★ 遺失值
★ 補值
★ 貝氏

關鍵字(英)

★ copula
★ Bayesian
★ Missing data
★ imputation

論文目次

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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指導教授

鄧惠文(Huei-Wen Teng)

審核日期

2012-6-26

推文