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Merged
mmcky merged 3 commits into from
Jul 19, 2026
Merged

[action-translation] resync: imp_sample.md #116

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deb93a2
🔄 resync imp_sample.md
mmcky Jul 18, 2026
1d3e640
Add missing 'import matplotlib as mpl' for the i18n font config
mmcky Jul 18, 2026
0ebf120
Restore trailing newline (engine issue tracked in QuantEcon/action-tr…
mmcky Jul 19, 2026
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6 changes: 6 additions & 0 deletions .translate/state/imp_sample.md.yml
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Original file line number Diff line number Diff line change
@@ -0,0 +1,6 @@
source-sha: b8ed85c7e8b8c17f5f59c74b3cb829470363ca8b
synced-at: "2026-07-18"
model: claude-sonnet-5
mode: RESYNC
section-count: 7
tool-version: 0.17.0
15 changes: 12 additions & 3 deletions lectures/imp_sample.md
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Expand Up @@ -9,6 +9,16 @@ kernelspec:
display_name: Python 3
language: python
name: python3
translation:
title: 似然比过程的均值
headings:
Overview: 概述
Mathematical expectation of likelihood ratio: 似然比的数学期望
Importance sampling: 重要性采样
Selecting a sampling distribution: 选择抽样分布
Approximating a cumulative likelihood ratio: 近似累积似然比
Distribution of sample mean: 样本均值的分布
Choosing a sampling distribution: 选择抽样分布
---

# 似然比过程的均值
Expand All @@ -34,6 +44,7 @@ import numpy as np
from numba import jit, vectorize, prange
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 @@ -263,13 +274,12 @@ estimate(g_a, g_b, h_a, h_b, T=10, N=10000)
下面的代码使用蒙特卡洛和重要性采样方法生成估计值的分布。

```{code-cell} ipython3
@jit(parallel=True)
def simulate(p_a, p_b, q_a, q_b, N_simu, T=1):

μ_L_p = np.empty(N_simu)
μ_L_q = np.empty(N_simu)

for i in prange(N_simu):
for i in range(N_simu):
μ_L_p[i] = estimate(p_a, p_b, p_a, p_b, T=T)
μ_L_q[i] = estimate(p_a, p_b, q_a, q_b, T=T)

Expand Down Expand Up @@ -468,4 +478,3 @@ plt.show()
注意，即使在$T = 1$时，使用重要性抽样的均值估计比直接用$g$进行抽样的偏差更大。

因此，我们的模拟表明，对于我们的问题，直接使用$g$进行蒙特卡洛近似会比使用$h_3$作为重要性抽样分布更好。

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