<?xml version="1.0" encoding="utf-8" standalone="yes"?><rss version="2.0" xmlns:atom="http://www.w3.org/2005/Atom" xmlns:content="http://purl.org/rss/1.0/modules/content/"><channel><title>数理统计 on s-ai-unix's Blog</title><link>https://s-ai-unix.github.io/tags/%E6%95%B0%E7%90%86%E7%BB%9F%E8%AE%A1/</link><description>Recent content in 数理统计 on s-ai-unix's Blog</description><generator>Hugo -- 0.161.1</generator><language>zh-cn</language><lastBuildDate>Tue, 03 Feb 2026 20:00:00 +0800</lastBuildDate><atom:link href="https://s-ai-unix.github.io/tags/%E6%95%B0%E7%90%86%E7%BB%9F%E8%AE%A1/index.xml" rel="self" type="application/rss+xml"/><item><title>条件期望：从统计基础到深度学习应用</title><link>https://s-ai-unix.github.io/posts/2026-02-03-conditional-expectation-from-statistical/</link><pubDate>Tue, 03 Feb 2026 20:00:00 +0800</pubDate><guid>https://s-ai-unix.github.io/posts/2026-02-03-conditional-expectation-from-statistical/</guid><description>系统综述条件期望的数学基础、统计推导过程及其在机器学习和深度学习中的深刻应用</description></item><item><title>数理统计重要定理系列：Rao-Blackwell定理与充分统计量的威力</title><link>https://s-ai-unix.github.io/posts/2026-02-03-statistical-foundations-rao-blackwell-theorem-sufficient-statistics/</link><pubDate>Tue, 03 Feb 2026 08:45:00 +0800</pubDate><guid>https://s-ai-unix.github.io/posts/2026-02-03-statistical-foundations-rao-blackwell-theorem-sufficient-statistics/</guid><description>深入解读Rao-Blackwell定理的历史背景、数学原理和实际应用，揭示如何利用充分统计量改进估计量的方差</description></item><item><title>数理统计重要定理系列：最大熵原理与高斯分布的自然选择</title><link>https://s-ai-unix.github.io/posts/2026-02-03-maximum-entropy-principle-gaussian-distribution/</link><pubDate>Tue, 03 Feb 2026 08:36:00 +0800</pubDate><guid>https://s-ai-unix.github.io/posts/2026-02-03-maximum-entropy-principle-gaussian-distribution/</guid><description>深入探讨最大熵原理的数学基础、严格证明及其深刻含义，揭示为什么在已知均值和方差的条件下，高斯分布是自然界最合理的选择</description></item><item><title>数理统计重要定理系列：Neyman-Pearson引理与最优假设检验理论</title><link>https://s-ai-unix.github.io/posts/2026-02-03-statistical-foundations-neyman-pearson-lemma-hypothesis-testing-framework/</link><pubDate>Tue, 03 Feb 2026 08:35:00 +0800</pubDate><guid>https://s-ai-unix.github.io/posts/2026-02-03-statistical-foundations-neyman-pearson-lemma-hypothesis-testing-framework/</guid><description>系统介绍Neyman-Pearson引理的历史背景、数学推导和实际应用，揭示假设检验理论中最优检验的构造原理</description></item><item><title>数理统计重要定理系列：KL散度的信息论本质与统计应用</title><link>https://s-ai-unix.github.io/posts/2026-02-03-kl-divergence-information-theory/</link><pubDate>Tue, 03 Feb 2026 08:30:00 +0800</pubDate><guid>https://s-ai-unix.github.io/posts/2026-02-03-kl-divergence-information-theory/</guid><description>系统综述KL散度（Kullback-Leibler散度）的历史背景、数学推导、核心性质及其在信息论、统计推断和机器学习中的深刻应用</description></item><item><title>数理统计重要定理系列：大数定律与中心极限定理的深度解读</title><link>https://s-ai-unix.github.io/posts/2026-02-03-statistical-foundations-law-of-large-numbers-and-central-limit-theorem/</link><pubDate>Tue, 03 Feb 2026 08:30:00 +0800</pubDate><guid>https://s-ai-unix.github.io/posts/2026-02-03-statistical-foundations-law-of-large-numbers-and-central-limit-theorem/</guid><description>系统梳理大数定律和中心极限定理的历史背景、数学推导和实际应用，揭示这两个统计基石如何在随机性与确定性之间架起桥梁</description></item><item><title>数理统计重要定理系列：Fisher信息矩阵的几何、统计与应用</title><link>https://s-ai-unix.github.io/posts/2026-02-03-fisher-information-matrix/</link><pubDate>Tue, 03 Feb 2026 08:23:00 +0800</pubDate><guid>https://s-ai-unix.github.io/posts/2026-02-03-fisher-information-matrix/</guid><description>系统综述Fisher信息矩阵的历史背景、数学推导、几何解释及其在统计推断、机器学习中的深刻应用</description></item><item><title>数理统计重要定理系列：Cramér-Rao下界的深刻意义与应用</title><link>https://s-ai-unix.github.io/posts/2026-02-03-cramer-rao-lower-bound/</link><pubDate>Tue, 03 Feb 2026 08:16:00 +0800</pubDate><guid>https://s-ai-unix.github.io/posts/2026-02-03-cramer-rao-lower-bound/</guid><description>系统综述Cramér-Rao下界定理的历史背景、严格推导过程及其在参数估计中的深刻应用，深入浅出地理解估计量方差的理论极限</description></item><item><title>概率论与数理统计：机器学习的概率基石</title><link>https://s-ai-unix.github.io/posts/2026-01-25-probability-statistics-ml-guide/</link><pubDate>Sun, 25 Jan 2026 12:00:00 +0800</pubDate><guid>https://s-ai-unix.github.io/posts/2026-01-25-probability-statistics-ml-guide/</guid><description>从赌场轮盘到神经网络：系统性地介绍概率论和数理统计在机器学习中的核心应用，包含完整的数学推导和直观的几何可视化</description></item></channel></rss>