图 书 馆
流形上的扩散与测地线流：马尔可夫链蒙特卡罗微分几何Diffusions and Geodesic Flows on Manifolds: The Differential Geometry of Markov Chain Monte Carlo |
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| 课程网址: | http://videolectures.net/mlss2012_girolami_mcmc/ |
| 主讲教师: | Mark Girolami |
| 开课单位: | 格拉斯哥大学 |
| 开课时间: | 2013-01-15 |
| 课程语种: | 英语 |
| 中文简介: |  马尔可夫链蒙特卡罗方法提供了最全面的基于仿真的工具集，可以对多种统计模型进行推理。许多应用的复杂性对于激励理论，方法和相关算法不断创新的采样方法提出了巨大的挑战。在这一系列的讲座中，我们将考虑MCMC方法的最新进展，该方法利用了微分几何，经典非线性动力学和流形上的扩散等数学思想，试图提供必要的工具来应对某些最具挑战性的采样向统计学家提出的问题。将逐步介绍这些材料，以确保学生掌握基本概念，并能够在讲座结束时进一步发展理论和方法。 |
| 课程简介: | Markov Chain Monte Carlo methods provide the most comprehensive set of simulation based tools to enable inference over many classes of statistical models. The complexity of many applications presents an enormous challenge for sampling methods motivating continual innovation in theory, methodology and associated algorithms. In this series of lectures we will consider one recent advance in MCMC methodology, that has exploited mathematical ideas from differential geometry, classical nonlinear dynamics, and diffusions constrained on manifolds, in attempting to provide the tools required to attack some of the most challenging of sampling problems presented to statisticians. A step-by-step presentation of the material will be provided to ensure that students grasp the fundamental concepts and are able to then develop further theory and methodology at the end of the lectures. |
| 关 键 词: | 微分几何; 线性动力 |
| 课程来源: | 视频讲座网 |
| 数据采集: | 2020-11-16：zyk |
| 最后编审: | 2020-11-16：zyk |
| 阅读次数: | 63 |