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研究生:吳佳靜
研究生(外文):Jia-Jing Wu
論文名稱:整數型時間序列之因果關係檢定:應用於環境健康議題
論文名稱(外文):Causality Test for Integer-valued Time Series Models with Applications to Environmental Health
指導教授:陳婉淑
指導教授(外文):CATHY CHEN, WOAN-SHU
口試委員:蔡恆修許英麟
口試委員(外文):TSIA, HENG-HSIUHSU, YING-LIN
口試日期:2017-06-07
學位類別:碩士
校院名稱:逢甲大學
系所名稱:統計學系
學門:數學及統計學門
學類:統計學類
論文種類:學術論文
論文出版年:2017
畢業學年度:105
語文別:英文
論文頁數:40
中文關鍵詞:貝氏理論過度分散整數型時間序列廣義卜瓦松模型馬可夫鏈蒙地卡羅法(MCMC)勝算比
外文關鍵詞:Bayesian inferenceOver-dispersionInteger-valued time seriesGeneralized PoissonMarkov chain Monte Carlo methodPosterior odds ratio
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流感併發肺炎是常見的公共衛生問題,而其感染後的後果嚴重可導致住院或死亡,探討暴露於空氣中的細懸浮粒子對於支氣管與肺部所造成的影響是一個重要議題。本研究抽取台灣2009到2015年間北中南11個行政區並分為五個年齡層的流感併發肺炎的病例,研究細懸浮粒子(PM2.5)和流感併發肺炎病例之間的因果關係。此處,流感併發肺炎的病例為整數值,在過去許多相關的文獻中往往沒有考慮到整數型時間序列的特徵,這些特徵包含:離散性、相依性以及過度分散的問題,而採納常態分配或純卜瓦松分配的假設。考慮上述因素,在配適整數型廣義卜瓦松自迴歸條件變異數(INGARCHX)模型下,本研究採用貝氏方法檢定Granger因果關係並描述整數型時間序列的相關性與過度分散的特徵。本研究採納對數線性廣義卜瓦松INGARCHX模型(Log linear generalized Poisson),此模型涵蓋對數線性卜瓦松INGARCHX模型,而此處X表示共變數,目的在於檢定PM2.5對流感併發肺炎病例是否存在有顯著的因果關係。我們採用貝氏適應性馬可夫鏈蒙地卡羅法(MCMC)方法對模型的參數作估計,並利用事後勝算比決定共變數PM2.5是否為顯著的重要因素,我們同時應用勝算比計算事後虛無假設的機率,並使用此機率判斷準則做為比較模型的依據。由事後機率檢定的結果顯示,流感併發肺炎的病例與PM2.5在台灣西南部包含雲林、嘉義、台南、高雄、屏東等地區的0-4、5-14、15-24此三年齡層具有顯著的因果關係,而在新北市、彰化、雲林、嘉義、台南、高雄、屏東等地區特別是壯年族群(25-64)與老年族群(≥65)更為明顯,表示暴露在環境中的PM2.5可能會增加流感併發肺炎之風險。細懸浮粒子等空氣汙染問題已對健康造成明顯的影響,避免暴露於空氣汙染環境非常重要,尤其是對於壯年族群與老年族群。
Influenza is caused by viruses of respiratory tract infection. Serious outcomes of influenza infection can result in hospitalization due to severe illness and life-threatening complications or even death. Human seasonal influenza is prevalent in Taiwan, with the most common air pollutant, particulate matter (pm), being related to an increased risk of health deterioration and respiratory symptoms in the individuals with existing lung illness. Fine suspended particles (PM2.5), such as second-hand smoke, have an aerodynamic diameter of suspended particles that is less than or equal to 2.5um. Suspended particles can exist in the atmosphere for a long time and accumulate in the trachea or lung through breathing. Ho, Wang, and Liu (2010) show that human infections are caused by the swine H1N1 virus, which was reported in Mexico in April 2009. The virus also causes severe illnesses and deaths in younger people, with many deaths due to severe pneumonia. Schwartz et al. (2015) use an instrumental variable approach, including back trajectories, as an instrument for variations in PM2.5 uncorrelated with other predictors of death. They also use a propensity score as an alternative causal modeling analysis. They note a causal association of PM2.5 with mortality, with a 0.53% and a 0.50% increase in daily deaths using the instrumental variable and the propensity score, respectively. Paulin and Hansel (2016) report that existing research suggests that pm exposure can negatively influence lung development and has an important impact on lung function in both children and adults, as well as in those with and without existing lung disease. Chen, G. et al. (2017) propose that controlling PM2.5 concentrations could be effective for decreasing the risk of exposure and subsequent transmission of influenza.
Contents

1 Introduction 1

2 The INGARCH Models 4

3 Bayesian approach 6
3.1 MCMC sampling scheme 7

4 Posterior odds ratios 8

5 The data and basic statistics 10

6 Analytic results 16

7 Conclusions 20

8 References 38
Berger, J.O. and Delampady, M. (1987) Testing precise hypotheses. Statistical Science, 2, 317-335.

Chen, C.W.S., Hsieh, Y.H., Su, H.C. and Wu, J.J. (2017) Causality test of ambient fine particles and human influenza cases in Taiwan: age group-specific disparity and geographic heterogeneity. Technical Report.

Chen, C.W.S. and Lee, S. (2016) Generalized Poisson autoregressive models for time series of counts. Computational Statistics & Data Analysis, 99, 51-67.

Chen, C.W.S. and Lee, S. (2017) Bayesian causality test for integer-valued time series models with applications to climate and crime data. Journal of the Royal Statistical Society Series C Applied Statistics, DOI: 10.1111/rssc.12200.

Chen, C.W.S. and So, M.K.P. (2006) On a threshold heteroscedastic model. International Journal of Forecasting, 22, 73-89.

Chen, G., Zhang, W., Li, S., Zhang, Y., Williams, G., Huxley, R., Ren, H., Cao, W. and Guo, Y. (2017) The impact of ambient fine particles on influenza transmission and the modication effects of temperature in China: A multi-city study. Environment International, 98, 82-88.

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Fokianos, K. and Tjøstheim, D. (2011) Loglinear Poisson autoregression. Journal of Multivariate Analysis, 102, 563-578.

Gelman, A., Roberts, G.O., and Gilks, W.R. (1996) Efficient Metropolis jumping rules. In Bernardo, J.M., Berger, J.O., Dawid, A.P., and Smith, A.F.M. (Eds.), Bayesian Statistics, 5, 599-607.

Hastings, W.K. (1970) Monte-Carlo sampling methods using Markov chains and their applications. Biometrika, 57, 97-109.

Ho, T.S., Wang, S.M. and Liu, C.C. (2010) Historical review of pandemic influenza A in Taiwan, 2009. Pediatr Neonatol 51, 83-88.

Jeffreys, H. (1961) Theory of probability, 3rd ed. Oxford Classic Texts in the Physical Sciences.

Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N. and Teller, E. (1953) Equations of state calculations by fast computing machines. Journal of Chemical Physics, 21, 1087-1091.

Paulin, L. and Hansel, N. (2016) Particulate air pollution and impaired lung function. F1000 Research, 5, DOI: 10.12688/f1000research.7108.1.

Schwartz, J., Austin, E., Bind, MA., Zanobetti, A. and Koutrakis, P. (2015) Estimating causal associations of fine particles with daily deaths in Boston. American Journal of Epidemiology, 182, 644-650.

Xu, H.Y., Xie, M., Goh, T.N. and Fu, X. (2012) A model for integer-valued time series with conditional over-dispersion. Computational Statistics and Data Analysis, 56, 4229-4242.

Zhu, F. (2012) Modeling overdispersed or underdispersed count data with generalized Poisson integer-valued GARCH models. Journal of Mathematical Analysis and Applications, 389, 58-71.

Zhu, F., Shi, L. and Liu, S. (2014) Influence diagnostics in log-linear integer-valued GARCH models. AStA - Advances in Statistical Analysis, 99, 311-335.
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