哈密顿蒙特卡洛采样算法在贝叶斯统计教学中的探索

Exploring Hamiltonian Monte Carlo Sampling in Bayesian Statistics Teaching

摘要: 贝叶斯统计是统计学的重要专业课程，而后验计算是本课程的重要组成部分。现有教材主要聚焦传统马尔可夫链蒙特卡洛(Markov Chain Monte Carlo, MCMC)采样算法，缺少对于一些新近发展起来的、计算效果更好的MCMC采样算法的讨论。为此，本文探讨了将哈密顿蒙特卡洛(Hamiltonian Monte Carlo, HMC)采样算法引入课程体系，以期提升教学内容的前沿性与实用性，并锻炼学生的编程实践能力。从教学实践看，这一尝试取得了良好的教学效果，有效契合了人工智能背景下统计学人才的培养需求。

Abstract: Bayesian Statistics is a crucial specialized course in statistics, and posterior computation constitutes a significant component of this curriculum. Existing textbooks primarily focus on traditional Markov Chain Monte Carlo (MCMC) sampling algorithms, lacking discussion of some recently developed, more computationally effective MCMC sampling algorithms. To address this, this paper explores incorporating the Hamiltonian Monte Carlo (HMC) sampling algorithm into the course structure. This aims to enhance the course content’s relevance to current advancements and practical utility, while also strengthening students’ practical programming skills. Teaching practice demonstrates that this initiative has achieved positive educational outcomes, effectively aligning with the training objectives for statistics professionals in the era of artificial intelligence.