午餐講座預告｜貝葉斯主義：“不會消亡的理論”

2024/2025第一學期

午餐系列講座

摘要：貝葉斯統計曾被描繪成異端範式和主觀學說，如今它已從這一完全 (或彻底可悲) 的遺忘中脫穎而出，成為席捲廣義統計和數據科學世界的一股浪潮。此次講座將採用非技術性的敘述風格，簡易地介紹貝葉斯方法，並誠摯地邀請年輕學者和研究生加入研究和實踐這一擁有數百年歷史的新穎統計、認識論和哲學範式的行列。討論從貝葉斯統計的起源（貝葉斯定理）開始，講述這一框架是如何以及（可能）為何被創建和再度出現。貝葉斯統計曾被稱為逆概率方法，或許更恰當地稱之為Laplacian 統計。貝葉斯統計在其發展歷程中經歷了低谷與高峰，部分原因在於其計算的複雜性和先驗分佈的主觀性。然而，隨著計算技術的突破，特別是在1980年代和1990年代初期，幾個看似不相關的點被連接起來，創造了Markov chain Monte Carlo（MCMC）方法；這完全改變了該領域的格局，並徹底革新了貝葉斯統計的估計方法。與採用虛無假設顯著性檢驗（NHST）的經典頻率主義統計不同，貝葉斯統計通常使用貝葉斯因子、概率（而非令人困惑且問題重重的p值）和可信區間（而非置信區間）來進行推斷。隨著先驗信息被整合到當前的估計過程中，貝氏方法在認識論上與信息處理和更新的方式完美契合。如果時間允許，本次講座將使用簡單的例子來說明在經典回歸框架下，貝葉斯方法通常是如何實踐的。

Abstact: Once portrayed as a heretical paradigm and subjective doctrine, Bayesian statistics has emerged from abject oblivion to become a tidal wave to sweep through the world of statistics and data science, broadly defined. Using a non-technical narrative style, this talk gives a very gentle introduction to Bayesian methods and serves as a cordial invitation for junior scholars and graduate students to join the effort to research and practice the centuries-old novel statistical, epistemological, and philosophical paradigm. The discussion begins with the origin of Bayesian statistics, the Bayes theorem, and recounts how and (possibly) why this framework was created and reemerged. Formerly called the inverse probability approach, and probably more appropriately—Laplacian statistics—Bayesian statistics has undergone the nadir and zenith of its practice, due in part to its computational complexity and subjective assignment of priors. 

With the computational breakthroughs, especially those in the 1980s and early 1990s, several seemingly unrelated dots were connected to create the Markov chain Monte Carlo (MCMC) methods. This has completely changed the landscape in the field and revolutionized the estimation methods for Bayesian statistics. Unlike the classical frequentist framework with the null hypothesis significance testing (NHST), Bayesian statistics usually uses Bayes factors, probabilities (not the confusing and problematic p-values), and credible intervals (not confidence intervals) to make inferences. Along with prior information integrated into the current iteration of estimation, the Bayesian approach dovetails well with how information is processed and updated epistemologically. Time permitting, this talk will use simple examples to illustrate how the Bayesian approach is usually practiced under the classical regression framework.

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編輯：賴晟盛

審核：UMSociology