DSpace community: 統計研究所

多子群體對數常態廣義有限失效母體模型之階層貝氏可靠度分析;Hierarchical Bayesian Reliability Analysis of Multi-Subpopulation Lognormal Generalized Limited Failure Population Models

Tue, 20 Oct 2026 08:22:40 GMT

title: 多子群體對數常態廣義有限失效母體模型之階層貝氏可靠度分析;Hierarchical Bayesian Reliability Analysis of Multi-Subpopulation Lognormal Generalized Limited Failure Population Models abstract: 本文探討半導體與電子產品中，兼具早衰（infant mortality）與長期磨耗（wear-out）雙重失效模式之多子群體（sub-populations）產品的壽命分析。早衰失效多源於製程疏失或原料缺陷所產生的瑕疵品（defective units），因其在檢驗階段仍能正常運作而難以偵測，嚴重影響企業售後維修成本。為有效分析此類資料，本文基於廣義有限失效母體（generalized limited failure population， GLFP）模型，針對實務上多家不同廠牌製造所形成的多子群體資料進行深入探討。在兩失效模式皆服從獨立對數常態壽命分布之假設下，利用資料增補 (data augmentation) 的方法建構完整概似函數(complete likelihood function)，並結合共軛結構優勢，於階層貝氏架構（hierarchical Bayesian framework）下引入三種不同的隨機效應模型（random-effects models），以精準捕捉並描述廠牌間的產品異質性。此方法不僅能在大量設限（censoring）資料下發揮資訊借用（borrowing the strength）的功效，且可同時提供各廠牌產品完整的可靠度推論，並大幅提升馬可夫鏈蒙地卡羅（Markov chain Monte Carlo， MCMC）演算法之計算效率。經由模擬結果驗證，本方法在模型選擇上具有高度穩健性。最後，本文應用 Backblaze 公司之硬碟資料進行分析，藉由四種壽命指標評比各廠牌產品之優劣，作為企業優化線上品管與進貨決策的參考依據。;This thesis considers product lifetime analysis for multiple sub-populations in semiconductor and electronic products. These products usually exhibit infant mortality and long-term wear-out failure modes. Infant mortality failures typically originate from defective units caused by manufacturing or raw material flaws. Because these units function normally during the initial screening stage， they are difficult to detect， which severely impacts post-sale warranty and maintenance costs. To effectively analyze such lifetime data， this study builds upon the generalized limited failure population (GLFP) model to conduct an in-depth investigation into multi-subpopulation data generated by various brands in practice. Under the assumption that both failure modes follow independent lognormal lifetime distributions， a complete likelihood function is constructed using data augmentation. Taking advantages of conjugate structures， three random-effects models are introduced within a hierarchical Bayesian framework to precisely capture and characterize the product heterogeneity among different brands. The proposed approach not only borrows strength under heavy censoring to provide comprehensive reliability inferences for each brand， but also substantially enhances the computational efficiency of the Markov chain Monte Carlo (MCMC) algorithm. Simulation results demonstrate that the proposed method possesses high robustness in model selection. Finally， the methodology is applied to real-world hard drive data from Backblaze. By evaluating the performance of each brand across four lifetime metrics， this study provides a valuable quantitative basis for enterprises to optimize online quality control and future procurement decisions.

矩陣自迴歸模型之貝氏變數選擇與估計;Bayesian Variable Selection and Estimation for Matrix Autoregressive Model

Tue, 20 Oct 2026 08:22:23 GMT

title: 矩陣自迴歸模型之貝氏變數選擇與估計;Bayesian Variable Selection and Estimation for Matrix Autoregressive Model abstract: 本研究以期望最大化變數選取（expectation-maximization variable selection， EMVS）架構為基礎，提出三種貝氏變數選取方法，用以辨識矩陣自迴歸（matrix autoregressive， MAR）模型之係數矩陣中具有影響力的係數。所提出的方法分別為 EMVS+、EMVS$^{*}$ 與自適應期望最大化變數選取（adaptive EMVS，簡記為 AEMVS），三者採用不同的係數選取與估計策略。本研究透過廣泛的模擬實驗，評估各方法在變數選取與預測方面的表現。此外，本文亦將這些方法應用於 OECD 資料庫中 1996 年至 2019 年的總體經濟季資料，以及 2022 年至 2024 年經同步處理的多國金融報酬日資料。數值結果顯示，三種所提出的方法在不同的 MAR 模型設定下各自展現不同的優勢，並可作為稀疏 MAR 模型估計之穩健替代方法。;This study proposes three Bayesian variable selection procedures for identifying influential coefficients in the coefficient matrices of matrix autoregressive (MAR) models based on the expectation-maximization variable selection (EMVS) framework. The proposed procedures， namely EMVS+， EMVS$^*$， and AEMVS (adaptive EMVS)， differ in their strategies for coefficient selection and estimation. Extensive simulation studies are conducted to evaluate their variable-selection and predictive performance. The methods are further applied to quarterly macroeconomic data obtained from the OECD database from 1996 to 2019 and synchronized multi-country financial daily return data from 2022 to 2024. The numerical results show that the three proposed procedures exhibit different strengths across different MAR settings and provide robust alternatives for sparse MAR estimation.

具長期追蹤共變數之存活資料動態預測準確度的布賴爾分數評估;Dynamic Prediction Accuracy Evaluation via Brier Score for Survival Data with Longitudinal Covariates

Tue, 20 Oct 2026 08:22:06 GMT

title: 具長期追蹤共變數之存活資料動態預測準確度的布賴爾分數評估;Dynamic Prediction Accuracy Evaluation via Brier Score for Survival Data with Longitudinal Covariates abstract: 在過去文獻中，布賴爾分數（Brier Score）多半被應用於固定共變數情境下的預測評估。然而在生物醫學研究中，個體的生物標記或臨床指標常隨追蹤時間反覆測量，形成時間相依共變數，此類資料若直接採用固定共變數評估框架，將無法全面反映模型的動態預測效能。有鑑於此，聯合模型（Joint Model）提供了一個自然的統計架構，能夠同時處理時間相依共變數與存活時間之間的關聯，並以此為基礎，進一步探討動態預測準確度的評估問題。本研究以聯合模型為工具，核心貢獻在於將布賴爾分數的應用推廣至此一動態預測情境，以動態布賴爾分數（Dynamic Brier Score）作為預測誤差的主要衡量指標。我們同時考慮參數模型（基於指數、韋伯、對數常態及對數羅吉斯分佈）與半母數模型，分別在比例風險（Proportional Hazards）模型、加速失效時間（Accelerated Failure Time）模型與比例勝算（Proportional odds）模型三類存活架構下，藉由動態布賴爾分數比較不同模型的預測準確度，以探討各存活假設下模型的預測穩健性。針對右設限資料，引入逆設限機率加權法（Inverse Probability of Censoring Weighting， IPCW）對動態布賴爾分數進行修正，以確保評估結果的正確性。透過模擬研究，針對於不同設限率及模型錯誤配適情境下，以動態布賴爾分數與整合布賴爾分數（Integrated Brier Score， IBS）作為跨模型比較的主要指標，系統性評估各模型的預測表現。此外，本研究亦以 PBC 真實臨床資料進行實例分析，以驗證模擬結論在真實資料情境下的適用性。;In the existing literature， the Brier Score has predominantly been applied to static prediction evaluation under fixed covariate settings. However， in biomedical research， individuals’ clinical indicators are often measured repeatedly over follow-up， giving rise to time-dependent covariates for which static evaluation frameworks are inadequate. The Joint Model provides a natural framework for handling such data， serving as the basis for this study. The core contribution of this study is to extend the Brier Score to this dynamic prediction setting via the Dynamic Brier Score. We consider both parametric and semi-parametric models under three survival frameworks—Proportional Hazards (PH)， Accelerated Failure Time (AFT)， and Proportional Odds (PO)—with IPCW correction for right-censoring to ensure unbiased evaluation. Simulation studies systematically evaluate predictive performance under varying censoring rates and model misspecification， using the Integrated Brier Score (IBS) as the primary summary measure. A real data analysis based on the PBC dataset is further conducted to verify the simulation findings.

Rank-Based Bayesian Variable Selection for High-Dimensional LTRC Survival Data;Rank-Based Bayesian Variable Selection for High-Dimensional LTRC Survival Data

Tue, 20 Oct 2026 08:21:49 GMT

title: Rank-Based Bayesian Variable Selection for High-Dimensional LTRC Survival Data;Rank-Based Bayesian Variable Selection for High-Dimensional LTRC Survival Data abstract: 本文提出一個可擴展的貝氏架構，用於處理具有左截斷與右設限的超高維存活分析中的變數選擇問題。基於部分秩相關估計量，我們提出一種準成對秩概似方法，並結合 sigmoid 平滑與邊界修正，以提升數值穩定性與計算效率。透過 Pólya-Gamma 資料擴增，所提出的準概似可以重新表達為一個擴增的邏輯斯迴歸模型，進而促進在全域－局部收縮先驗下的有效貝氏推論，用於稀疏變數選擇。此外，我們建立了重要的理論保證，包括後驗一致性以及高維設定下的變數選擇一致性。大量的模擬研究與真實資料應用結果顯示，與現有方法相比，所提出的方法在估計準確度與變數選擇表現上具有競爭力。;In this article， we develop a scalable Bayesian framework for variable selection in ultrahigh-dimensional survival analysis with left truncation and right censoring. Building upon the partial-rank correlation estimator， we propose a quasi-pairwise rank likelihood with sigmoid smoothing and boundary correction to improve numerical stability and computational efficiency. Through Pólya--Gamma augmentation， the proposed quasi-likelihood can be reformulated as an augmented logistic regression model， which facilitates efficient Bayesian inference under global--local shrinkage priors for sparse variable selection. We further establish important theoretical guarantees， including posterior consistency and variable selection consistency in high-dimensional settings. Extensive simulation studies and real-data applications demonstrate that the proposed method achieves competitive estimation accuracy and variable selection performance compared with existing approaches.