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mmcky merged 6 commits into from
Jul 19, 2026
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[action-translation] resync: likelihood_ratio_process.md #123

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🔄 resync likelihood_ratio_process.md
mmcky Jul 18, 2026
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Add missing 'import matplotlib as mpl' for the i18n font config
mmcky Jul 18, 2026
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Restore trailing newline (engine issue tracked in QuantEcon/action-tr…
mmcky Jul 19, 2026
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Add missing bibtex key Blume_Easley2006 to fix dangling citation
mmcky Jul 19, 2026
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Align quant-econ.bib to canonical union to avoid EOF merge conflicts
mmcky Jul 19, 2026
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mmcky Jul 19, 2026
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6 changes: 6 additions & 0 deletions .translate/state/likelihood_ratio_process.md.yml
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source-sha: a8966965b2649d470ea144150ca5fd5d520b5345
synced-at: "2026-07-18"
model: claude-sonnet-5
mode: RESYNC
section-count: 10
tool-version: 0.17.0
26 changes: 23 additions & 3 deletions lectures/likelihood_ratio_process.md
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Expand Up @@ -9,6 +9,26 @@ kernelspec:
display_name: Python 3 (ipykernel)
language: python
name: python3
translation:
title: 似然比过程
headings:
Overview: 概述
Likelihood Ratio Process: 似然比过程
Nature permanently draws from density g: 当自然永久从密度g中抽取时
Peculiar property: 特殊性质
Nature permanently draws from density f: 自然永久从密度f中抽样
Likelihood ratio test: 似然比检验
Likelihood ratio test::A third distribution $h$: 第三个分布 $h$
Likelihood ratio test::A helpful formula: 一个有用的公式
Hypothesis testing and classification: 假设检验和分类
Hypothesis testing and classification::Model selection mistake probability: 模型选择错误概率
Hypothesis testing and classification::Classification: 分类
Hypothesis testing and classification::Error probability and divergence measures: 误差概率和散度度量
Markov chains: 马尔可夫链
Markov chains::KL divergence rate: KL散度率
Markov chains::Simulations: 模拟
Related lectures: 相关讲座
Exercises: 练习
---

(likelihood_ratio_process)=
Expand Down Expand Up @@ -53,6 +73,7 @@ kernelspec:
```{code-cell} ipython3
import matplotlib.pyplot as plt
FONTPATH = "fonts/SourceHanSerifSC-SemiBold.otf"
import matplotlib as mpl
mpl.font_manager.fontManager.addfont(FONTPATH)
plt.rcParams['font.family'] = ['Source Han Serif SC']

Expand Down Expand Up @@ -1223,7 +1244,7 @@ plt.show()

显然，$e^{-C(f,g)T}$是误差率的上界。

在`{doc}`divergence_measures`中，我们还研究了**Jensen-Shannon散度**作为分布之间的对称距离度量。
在{doc}`divergence_measures`中，我们还研究了**Jensen-Shannon散度**作为分布之间的对称距离度量。

我们可以使用Jensen-Shannon散度来测量分布$f$和$g$之间的距离，并计算它与模型选择错误概率的协方差。

Expand Down Expand Up @@ -1622,7 +1643,7 @@ markov_results = analyze_markov_chains(P_f, P_g)

似然过程在贝叶斯学习中扮演重要角色，正如在{doc}`likelihood_bayes`中所描述的，并在{doc}`odu`中得到应用。

似然比过程是Lawrence Blume和David Easley回答他们提出的问题"如果你那么聪明，为什么不富有？" {cite}`blume2006if`的核心，这是讲座{doc}`likelihood_ratio_process_2`的主题。
似然比过程是Lawrence Blume和David Easley回答他们提出的问题"如果你那么聪明，为什么不富有？" {cite}`Blume_Easley2006`的核心，这是讲座{doc}`likelihood_ratio_process_2`的主题。

似然比过程也出现在{doc}`advanced:additive_functionals`中，其中包含了另一个关于上述似然比过程**特殊性质**的说明。

Expand Down Expand Up @@ -1755,4 +1776,3 @@ $$

```{solution-end}
```

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