| dc.contributor.advisor | 黃佳慧<br>洪芷漪 | zh_TW |
| dc.contributor.advisor | Huang, Chia-Hui<br>Hong, Jyy-I | en_US |
| dc.contributor.author (Authors) | 吳典倚 | zh_TW |
| dc.contributor.author (Authors) | Wu, Tien-Yi | en_US |
| dc.creator (作者) | 吳典倚 | zh_TW |
| dc.creator (作者) | Wu, Tien-Yi | en_US |
| dc.date (日期) | 2025 | en_US |
| dc.date.accessioned | 1-Sep-2025 16:30:48 (UTC+8) | - |
| dc.date.available | 1-Sep-2025 16:30:48 (UTC+8) | - |
| dc.date.issued (上傳時間) | 1-Sep-2025 16:30:48 (UTC+8) | - |
| dc.identifier (Other Identifiers) | G0111751011 | en_US |
| dc.identifier.uri (URI) | https://nccur.lib.nccu.edu.tw/handle/140.119/159320 | - |
| dc.description (描述) | 碩士 | zh_TW |
| dc.description (描述) | 國立政治大學 | zh_TW |
| dc.description (描述) | 應用數學系 | zh_TW |
| dc.description (描述) | 111751011 | zh_TW |
| dc.description.abstract (摘要) | 在許多應用領域中，計數資料經常會出現大量的零值，導致傳統的卜
瓦松或負二項迴歸模型無法有效地處理過多零值（excess zeros）的情形。因此，需要透過零膨脹模型（Zero-Inflated Models）來處理此類資料，該模型認為觀察值零來自兩種不同的生成機制：結構零以及隨機零。本研究針對具有時間特徵之零膨脹計數資料，提出一個具備AR(1) 結構的時間性零膨脹卜瓦松模型，並採用貝式方法進行推論。本模型在邏輯斯與計數兩部分共享一組具有時間自相關的隨機效應，以捕捉潛在的時間相依結構。我們引入Pólya-Gamma 隨機變數，使後驗分布得以轉換為條件共軛形式，進一步提升MCMC 抽樣的效率與穩定性。透過模擬研究驗證，在不同觀察期與自相關強度下，模型皆能提供穩定且準確的參數估計。最後，本研究將模
型應用於2020 年佛羅里達州COVID-19 死亡資料，說明其在處理實際零膨
脹時間性計數資料上的實用性與可行性。 | zh_TW |
| dc.description.abstract (摘要) | In many applied fields, count data often contain an excessive number of zeros, making it difficult for traditional Poisson or negative binomial regression models to handle such zero inflation effectively. To solve this problem, zero-inflated models are commonly used. These models assume that observed zeros come from two distinct sources: structural zeros and random zeros. This study proposes a Bayesian zero-inflated Poisson (ZIP) model with a temporal feature, incorporating an AR(1) structure to account for time dependence. In the proposed model, a shared set of temporally autocorrelated random effects is introduced in both the logistic and count components to capture the underlying temporal dependence. To facilitate efficient posterior sampling, we adopt the Pólya-Gamma data augmentation approach, which transforms the posterior into a conditionally conjugate form and improves the efficiency and stability of MCMC sampling. Simulation studies under various time lengths and autocorrelation strengths demonstrate that the model provides stable and accurate parameter estimates. Finally, the model is applied to the daily COVID-19 death counts of Florida from June to July 2020, demonstrating its usefulness in analyzing zero-inflated temporal count data. | en_US |
| dc.description.tableofcontents | 致謝 i
中文摘要 ii
Abstract iii
Contents iv
List of Tables vi
List of Figures vii
1 Introduction 1
2 Literature Review 4
2.1 Markov Chain Monte Carlo Methods 4
2.2 Metropolis-Hastings Algorithm 6
2.3 Random Effects and Temporal Structure 7
3 Bayesian Zero-Inflated Poisson Model 11
3.1 The Zero-Inflated Poisson Model 11
3.2 Pólya-Gamma Data Augmentation 14
3.3 Posterior Inference for the ZIP Model 16
4 Numerical Studies 24
4.1 Simulation 24
4.2 Real Data Analysis 27
5 Conclusion and Discussion 34
Appendix Derivation of Posterior Sampling Steps 36
Bibliography 39 | zh_TW |
| dc.format.extent | 2295065 bytes | - |
| dc.format.mimetype | application/pdf | - |
| dc.source.uri (資料來源) | http://thesis.lib.nccu.edu.tw/record/#G0111751011 | en_US |
| dc.subject (關鍵詞) | 零膨脹卜瓦松模型 | zh_TW |
| dc.subject (關鍵詞) | AR(1) 結構 | zh_TW |
| dc.subject (關鍵詞) | 貝式推論 | zh_TW |
| dc.subject (關鍵詞) | Pólya-Gamma增補 | zh_TW |
| dc.subject (關鍵詞) | 計數資料分析 | zh_TW |
| dc.subject (關鍵詞) | 隨機效應 | zh_TW |
| dc.subject (關鍵詞) | Zero-inflated Poisson model | en_US |
| dc.subject (關鍵詞) | AR(1) structure | en_US |
| dc.subject (關鍵詞) | Bayesian inference | en_US |
| dc.subject (關鍵詞) | Pólya-Gamma augmentation | en_US |
| dc.subject (關鍵詞) | count data analysis | en_US |
| dc.subject (關鍵詞) | random effect | en_US |
| dc.title (題名) | 具有 AR(1) 結構之時間性零膨脹卜瓦松模型的貝式分析 | zh_TW |
| dc.title (題名) | Bayesian Analysis of a Temporal Zero-Inflated Poisson Model with First-Order Autoregressive Structure | en_US |
| dc.type (資料類型) | thesis | en_US |
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