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| Title: | 具有 AR(1) 結構之時間性零膨脹卜瓦松模型的貝式分析
Bayesian Analysis of a Temporal Zero-Inflated Poisson Model with First-Order Autoregressive Structure |
| Authors: | 吳典倚
Wu, Tien-Yi |
| Contributors: | 黃佳慧
洪芷漪
Huang, Chia-Hui
Hong, Jyy-I
吳典倚
Wu, Tien-Yi |
| Keywords: | 零膨脹卜瓦松模型
AR(1) 結構
貝式推論
Pólya-Gamma增補
計數資料分析
隨機效應
Zero-inflated Poisson model
AR(1) structure
Bayesian inference
Pólya-Gamma augmentation
count data analysis
random effect |
| Date: | 2025 |
| Issue Date: | 2025-09-01 16:30:48 (UTC+8) |
| Abstract: | 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。
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. |
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[15] Yongyi Min and Alan Agresti. Random effect models for repeated measures of zero-inflated count data. Statistical Modelling, 5(1):1–19, April 2005.
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| Description: | 碩士
國立政治大學
應用數學系
111751011 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0111751011 |
| Data Type: | thesis |
| Appears in Collections: | [Department of Mathematical Sciences] Theses
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