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🌐 [translation-sync] [likelihood_var.md] Update np.random → Generator API #225

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🌐 [translation-sync] [likelihood_var.md] Update np.random → Generator API #225

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53a2610
Update translation: lectures/likelihood_var.md
mmcky Jul 31, 2026
90a62da
Update translation: .translate/state/likelihood_var.md.yml
mmcky Jul 31, 2026
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8 changes: 4 additions & 4 deletions .translate/state/likelihood_var.md.yml
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Original file line number Diff line number Diff line change
@@ -1,6 +1,6 @@
source-sha: 1abb15f5fc0273ea02b47850f447b3c224255123
synced-at: "2026-07-18"
source-sha: aff1ee4613dfc79e79a578069473a5765fddc716
synced-at: "2026-07-31"
model: claude-sonnet-5
mode: RESYNC
mode: UPDATE
section-count: 6
tool-version: 0.17.0
tool-version: 0.24.0
36 changes: 19 additions & 17 deletions lectures/likelihood_var.md
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Expand Up @@ -78,6 +78,8 @@ import quantecon as qe
from numba import jit
from typing import NamedTuple, Optional, Tuple
from collections import namedtuple

rng = np.random.default_rng()
```

## VAR模型设置
Expand Down Expand Up @@ -233,7 +235,7 @@ def log_likelihood_path(X, model):

return log_L

def simulate_var(model, T, N_paths=1):
def simulate_var(model, T, rng, N_paths=1):
"""
从VAR模型中模拟路径
"""
Expand All @@ -243,13 +245,13 @@ def simulate_var(model, T, N_paths=1):

for i in range(N_paths):
# 生成初始状态
x = mvn.rvs(mean=model.μ_0, cov=model.Σ_0)
x = mvn.rvs(mean=model.μ_0, cov=model.Σ_0, random_state=rng)
x = np.atleast_1d(x)
paths[i, 0] = x

# 向前模拟
for t in range(T):
w = np.random.randn(m)
w = rng.standard_normal(m)
x = model.A @ x + model.C @ w
paths[i, t+1] = x

Expand Down Expand Up @@ -337,7 +339,7 @@ model_g = create_var_model(A_g, C_g)
# 从模型f进行模拟
T = 200
N_paths = 100
paths_from_f = simulate_var(model_f, T, N_paths)
paths_from_f = simulate_var(model_f, T, rng, N_paths)

L_ratios_f = compute_likelihood_ratio_var(paths_from_f, model_f, model_g)

Expand Down Expand Up @@ -399,8 +401,8 @@ print("模型g的特征值:", np.linalg.eigvals(A_g))
T = 50
N_paths = 50

paths_from_f = simulate_var(model2_f, T, N_paths)
paths_from_g = simulate_var(model2_g, T, N_paths)
paths_from_f = simulate_var(model2_f, T, rng, N_paths)
paths_from_g = simulate_var(model2_g, T, rng, N_paths)

# 计算似然比
L_ratios_ff = compute_likelihood_ratio_var(paths_from_f, model2_f, model2_g)
Expand Down Expand Up @@ -429,7 +431,7 @@ plt.tight_layout()
plt.show()
```

让我们应用{doc}`likelihood_ratio_process`中描述的Neyman-Pearson频率主义决策规则，当$\log L_T \geq 0$时选择模型$f$，当$\log L_T < 0$时选择模型$g$
让我们应用 {doc}`likelihood_ratio_process` 中描述的Neyman-Pearson频率主义决策规则，当$\log L_T \geq 0$时选择模型$f$，当$\log L_T < 0$时选择模型$g$

```{code-cell} ipython3
fig, ax = plt.subplots()
Expand Down Expand Up @@ -468,11 +470,11 @@ def model_selection_analysis(T_values, model_f, model_g, N_sim=500):

for T in T_values:
# 从模型 f 模拟
paths_f = simulate_var(model_f, T, N_sim//2)
paths_f = simulate_var(model_f, T, rng, N_sim//2)
L_ratios_f = compute_likelihood_ratio_var(paths_f, model_f, model_g)

# 从模型 g 模拟
paths_g = simulate_var(model_g, T, N_sim//2)
paths_g = simulate_var(model_g, T, rng, N_sim//2)
L_ratios_g = compute_likelihood_ratio_var(paths_g, model_f, model_g)

# 决策规则：如果 log L_T >= 0 则选择 f
Expand Down Expand Up @@ -698,12 +700,12 @@ def create_samuelson_var_model(a, b, γ, G, σ, stationary_init=False,

return model, G_obs, info

def simulate_samuelson(model, G_obs, T, N_paths=1):
def simulate_samuelson(model, G_obs, T, rng, N_paths=1):
"""
模拟萨缪尔森模型
"""
# 模拟状态路径
states = simulate_var(model, T, N_paths)
states = simulate_var(model, T, rng, N_paths)

# 使用G矩阵提取可观测值
if N_paths == 1:
Expand Down Expand Up @@ -746,8 +748,8 @@ T = 50
N_paths = 50

# 获取状态和观测值
states_f, obs_f = simulate_samuelson(model_sam_f, G_obs_f, T, N_paths)
states_g, obs_g = simulate_samuelson(model_sam_g, G_obs_g, T, N_paths)
states_f, obs_f = simulate_samuelson(model_sam_f, G_obs_f, T, rng, N_paths)
states_g, obs_g = simulate_samuelson(model_sam_g, G_obs_g, T, rng, N_paths)

output_paths_f = obs_f[:, :, 0]
output_paths_g = obs_g[:, :, 0]
Expand Down Expand Up @@ -799,10 +801,10 @@ ax.set_title(r'$\log L_t$ (真实模型 = g)')
plt.show()
```

在左图中,数据由$f$生成,似然比趋向正无穷。
在左图中，数据由 $f$ 生成，似然比趋向正无穷。

在右图中,数据由$g$生成,似然比趋向负无穷。
在右图中，数据由 $g$ 生成，似然比趋向负无穷。

在这两种情况下,为了数值稳定性,我们对对数似然比过程设置了上下限阈值,因为它们会很快增长到无界。
在这两种情况下，为了数值稳定性，我们对对数似然比过程设置了上下限阈值，因为它们会很快增长到无界。

在这两种情况下,似然比过程最终都能帮助我们选择正确的模型。
在这两种情况下，似然比过程最终都能帮助我们选择正确的模型。
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