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[action-translation] resync: wald_friedman_2.md (#161)
* 🔄 resync wald_friedman_2.md * Add missing 'import matplotlib as mpl' for the i18n font config The resync kept the CJK font-configuration block but dropped the mpl import it depends on - a NameError at execution that non-strict builds swallow. Found sweeping the wave for the pattern behind zh-cn#97's December fixes. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com> * Restore trailing newline (review nit) Co-Authored-By: Claude Fable 5 <noreply@anthropic.com> --------- Co-authored-by: Claude Fable 5 <noreply@anthropic.com>
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source-sha: b27f1eb0ae52b5e20807d516a3d2f54a586e75fa
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synced-at: "2026-07-18"
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model: claude-sonnet-5
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mode: RESYNC
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section-count: 4
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tool-version: 0.17.0

lectures/wald_friedman_2.md

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display_name: Python 3 (ipykernel)
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language: python
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name: python3
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translation:
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title: 用贝叶斯方法解决弗里德曼和瓦尔德问题
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headings:
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Overview: 概述
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A Dynamic Programming Approach: 动态规划方法
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A Dynamic Programming Approach::Losses and Costs: 损失和成本
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A Dynamic Programming Approach::Digression on Type I and Type II Errors: 关于第一类和第二类错误的说明
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A Dynamic Programming Approach::Intuition: 直观理解
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A Dynamic Programming Approach::A Bellman Equation: 贝尔曼方程
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Implementation: 实现
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Analysis: 分析
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Analysis::Cost Function: 成本函数
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Analysis::Simulations: 模拟
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Analysis::Comparative Statics: 比较静态分析
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---
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(wald_friedman_2)=
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import numpy as np
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import matplotlib.pyplot as plt
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FONTPATH = "fonts/SourceHanSerifSC-SemiBold.otf"
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import matplotlib as mpl
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mpl.font_manager.fontManager.addfont(FONTPATH)
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plt.rcParams['font.family'] = ['Source Han Serif SC']
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```{note}
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在{cite:t}`Bertsekas75`中,信念是与分布$f_0$相关联的,但在这里
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我们将信念与分布 $f_1$ 关联起来,以匹配{doc}`关于Wald序贯分析的讲座<wald_friedman>`中的讨论。
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```
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\begin{aligned}
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h(\pi) &= c + \mathbb E [J(\pi')] \\
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&= c + \mathbb E_{\pi'} \min \{ \pi' L_0, (1 - \pi') L_1, h(\pi') \} \\
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&= c + \int \min \{ \kappa(z', \pi) L_0, (1 - \kappa(z', \pi) ) L_1, h(\kappa(z', \pi) ) \} f_\pi (z') dz'
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\end{aligned}
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return π_new
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```
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如同{doc}`最优增长讲座 <optgrowth>`中所述,为了近似连续的值函数
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如同{doc}`os_stochastic`中所述,为了近似连续的值函数
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* 我们在有限的 $\pi$ 值网格上进行迭代。
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* 当我们在网格点之间评估 $\mathbb E[J(\pi')]$ 时,我们使用线性插值。
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simulation_plot(wf)
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```
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由于每次抽样成本的增加,决策者在做出决定前会减少抽样次数。
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因为他用更少的抽样来做决定,他的正确判断比例下降。
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[^f1]: 决策者的行为就像他相信随机变量序列 $[z_{0}, z_{1}, \ldots]$ 是*可交换的*。关于可交换性的讨论,请参见[可交换性和贝叶斯更新](https://python.quantecon.org/exchangeable.html)
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{cite}`Kreps88`第11章。
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