QuantEcon · mmcky · Aug 19, 2026 · Aug 18, 2026 · Aug 18, 2026 · Aug 18, 2026
diff --git a/.translate/state/aiyagari_egm.md.yml b/.translate/state/aiyagari_egm.md.yml
@@ -1,6 +1,6 @@
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-synced-at: "2026-07-22"
-model: claude-opus-4-8
-mode: NEW
+source-sha: 96ede29937a77fb0cb26b731e1eecce5e62f6726
+synced-at: "2026-08-18"
+model: claude-sonnet-5
+mode: UPDATE
 section-count: 8
-tool-version: 0.20.0
+tool-version: 0.26.0
diff --git a/.translate/state/ar1_bayes.md.yml b/.translate/state/ar1_bayes.md.yml
@@ -1,6 +1,6 @@
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-synced-at: "2026-07-18"
+source-sha: 96ede29937a77fb0cb26b731e1eecce5e62f6726
+synced-at: "2026-08-18"
 model: claude-sonnet-5
-mode: RESYNC
+mode: UPDATE
 section-count: 3
-tool-version: 0.17.0
+tool-version: 0.26.0
diff --git a/.translate/state/back_prop.md.yml b/.translate/state/back_prop.md.yml
@@ -1,6 +1,6 @@
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-synced-at: "2026-07-18"
+source-sha: 96ede29937a77fb0cb26b731e1eecce5e62f6726
+synced-at: "2026-08-18"
 model: claude-sonnet-5
-mode: RESYNC
+mode: UPDATE
 section-count: 8
-tool-version: 0.17.0
+tool-version: 0.26.0
diff --git a/.translate/state/ifp_advanced.md.yml b/.translate/state/ifp_advanced.md.yml
@@ -1,6 +1,6 @@
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-synced-at: "2026-07-29"
+source-sha: 96ede29937a77fb0cb26b731e1eecce5e62f6726
+synced-at: "2026-08-18"
 model: claude-sonnet-5
 mode: UPDATE
 section-count: 7
-tool-version: 0.24.0
+tool-version: 0.26.0
diff --git a/.translate/state/ifp_egm.md.yml b/.translate/state/ifp_egm.md.yml
@@ -1,6 +1,6 @@
-source-sha: 0bfcac8105ac8c11f06797579a9f4d565db7b53d
-synced-at: "2026-07-18"
+source-sha: 96ede29937a77fb0cb26b731e1eecce5e62f6726
+synced-at: "2026-08-18"
 model: claude-sonnet-5
-mode: RESYNC
+mode: UPDATE
 section-count: 6
-tool-version: 0.17.0
+tool-version: 0.26.0
diff --git a/.translate/state/ifp_egm_transient_shocks.md.yml b/.translate/state/ifp_egm_transient_shocks.md.yml
@@ -1,6 +1,6 @@
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-synced-at: "2026-07-22"
-model: claude-opus-4-8
-mode: NEW
+source-sha: 96ede29937a77fb0cb26b731e1eecce5e62f6726
+synced-at: "2026-08-18"
+model: claude-sonnet-5
+mode: UPDATE
 section-count: 7
-tool-version: 0.20.0
+tool-version: 0.26.0
diff --git a/.translate/state/lake_model.md.yml b/.translate/state/lake_model.md.yml
@@ -1,6 +1,6 @@
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-synced-at: "2026-07-18"
+source-sha: 96ede29937a77fb0cb26b731e1eecce5e62f6726
+synced-at: "2026-08-18"
 model: claude-sonnet-5
-mode: RESYNC
+mode: UPDATE
 section-count: 5
-tool-version: 0.17.0
+tool-version: 0.26.0
diff --git a/.translate/state/mccall_fitted_vfi.md.yml b/.translate/state/mccall_fitted_vfi.md.yml
@@ -1,6 +1,6 @@
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-synced-at: "2026-07-18"
+source-sha: 96ede29937a77fb0cb26b731e1eecce5e62f6726
+synced-at: "2026-08-18"
 model: claude-sonnet-5
-mode: RESYNC
+mode: UPDATE
 section-count: 6
-tool-version: 0.17.0
+tool-version: 0.26.0
diff --git a/.translate/state/mccall_model.md.yml b/.translate/state/mccall_model.md.yml
@@ -1,6 +1,6 @@
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-synced-at: "2026-07-18"
+source-sha: 96ede29937a77fb0cb26b731e1eecce5e62f6726
+synced-at: "2026-08-18"
 model: claude-sonnet-5
-mode: RESYNC
+mode: UPDATE
 section-count: 7
-tool-version: 0.17.0
+tool-version: 0.26.0
diff --git a/.translate/state/mccall_model_with_sep_markov.md.yml b/.translate/state/mccall_model_with_sep_markov.md.yml
@@ -1,6 +1,6 @@
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-synced-at: "2026-07-22"
-model: claude-opus-4-8
-mode: NEW
+source-sha: 96ede29937a77fb0cb26b731e1eecce5e62f6726
+synced-at: "2026-08-18"
+model: claude-sonnet-5
+mode: UPDATE
 section-count: 9
-tool-version: 0.20.0
+tool-version: 0.26.0
diff --git a/.translate/state/mccall_persist_trans.md.yml b/.translate/state/mccall_persist_trans.md.yml
@@ -1,6 +1,6 @@
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-synced-at: "2026-07-18"
+source-sha: 96ede29937a77fb0cb26b731e1eecce5e62f6726
+synced-at: "2026-08-18"
 model: claude-sonnet-5
-mode: RESYNC
+mode: UPDATE
 section-count: 5
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+tool-version: 0.26.0
diff --git a/.translate/state/newton_method.md.yml b/.translate/state/newton_method.md.yml
@@ -1,6 +1,6 @@
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+source-sha: 96ede29937a77fb0cb26b731e1eecce5e62f6726
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 model: claude-sonnet-5
 mode: UPDATE
 section-count: 5
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+tool-version: 0.26.0
diff --git a/.translate/state/os_egm_jax.md.yml b/.translate/state/os_egm_jax.md.yml
@@ -1,6 +1,6 @@
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-synced-at: "2026-07-22"
-model: claude-opus-4-8
-mode: NEW
+source-sha: 96ede29937a77fb0cb26b731e1eecce5e62f6726
+synced-at: "2026-08-18"
+model: claude-sonnet-5
+mode: UPDATE
 section-count: 3
-tool-version: 0.20.0
+tool-version: 0.26.0
diff --git a/.translate/state/unemployment_linear.md.yml b/.translate/state/unemployment_linear.md.yml
@@ -1,6 +1,6 @@
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-synced-at: "2026-07-22"
-model: claude-opus-4-8
-mode: NEW
+source-sha: 96ede29937a77fb0cb26b731e1eecce5e62f6726
+synced-at: "2026-08-18"
+model: claude-sonnet-5
+mode: UPDATE
 section-count: 8
-tool-version: 0.20.0
+tool-version: 0.26.0
diff --git a/.translate/state/unemployment_shocks.md.yml b/.translate/state/unemployment_shocks.md.yml
@@ -1,6 +1,6 @@
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-synced-at: "2026-07-22"
-model: claude-opus-4-8
-mode: NEW
+source-sha: 96ede29937a77fb0cb26b731e1eecce5e62f6726
+synced-at: "2026-08-18"
+model: claude-sonnet-5
+mode: UPDATE
 section-count: 6
-tool-version: 0.20.0
+tool-version: 0.26.0
diff --git a/lectures/aiyagari_egm.md b/lectures/aiyagari_egm.md
@@ -85,7 +85,6 @@ translation:
 * {cite}`Carroll2006`，介绍了内生网格法
 * {cite}`Ljungqvist2012` 的第 18 章，提供了教科书式的处理
 
-
 ### 预备知识
 
 我们使用以下导入：
@@ -163,7 +162,6 @@ $$
 
 其中 $s$ 是最优储蓄策略函数。
 
-
 ### 厂商
 
 厂商在规模报酬不变的条件下，通过雇用资本和劳动来生产产出。
@@ -498,7 +496,7 @@ def capital_supply(household, prices, key,
 ```{code-cell} ipython3
 household = create_household()
 prices = Prices(r=0.01, w=1.0)
-key = jax.random.PRNGKey(42)
+key = jax.random.key(42)
 
 with qe.Timer():
     K_supply = capital_supply(household, prices, key)
@@ -555,7 +553,7 @@ def compute_equilibrium(firm, household, key,
 ```{code-cell} ipython3
 firm = Firm()
 household = create_household()
-key = jax.random.PRNGKey(42)
+key = jax.random.key(42)
 
 with qe.Timer():
     K_star = compute_equilibrium(firm, household, key)
@@ -736,4 +734,4 @@ print(f"\nGini coefficient: {gini:.4f}")
 2. 为每个状态定义收入水平。
 3. 重新计算均衡。
 4. 额外的异质性如何影响财富分布？
-```
+```
diff --git a/lectures/ar1_bayes.md b/lectures/ar1_bayes.md
@@ -58,7 +58,6 @@ translation:
 
 - 将其视为从 $\{y_t\}$ 随机过程的[平稳分布](https://intro.quantecon.org/ar1_processes.html)中抽取的随机变量
 
-
 ### 模型设定
 
 统计模型的第一个组成部分是
@@ -147,12 +146,10 @@ logger = logging.getLogger('pymc')
 logger.setLevel(logging.CRITICAL)
 ```
 
-
 ## 估计
 
 让我们转向估计问题，先从似然函数开始。
 
-
 ### 似然函数
 
 对于来自AR(1)模型的样本 $\{y_t\}_{t=0}^T$，似然函数可以**分解**如下：
@@ -241,7 +238,6 @@ plt.show()
 
 可以看到，初始条件异常地大——该序列迅速脱离这个初始值，并在一个较低的区间内波动。
 
-
 ### PyMC实现
 
 在本节中，我们使用PyMC分别在关于 $y_0$ 的两种假设下计算后验分布——首先是条件化假设，然后是平稳性假设。
@@ -400,10 +396,10 @@ summary_y0
 
 fig, ax = plt.subplots()
 ax.hist(ρ_cond, bins=50, density=True, alpha=0.5,
-        label='条件化假设')
+        label='conditioning assumption')
 ax.hist(ρ_stat, bins=50, density=True, alpha=0.5,
-        label='平稳性假设')
-ax.axvline(ρ_true, color='k', linestyle='--', lw=2, label='真实值')
+        label='stationary assumption')
+ax.axvline(ρ_true, color='k', linestyle='--', lw=2, label='true value')
 ax.set_xlabel('ρ')
 ax.legend()
 plt.show()
@@ -497,7 +493,7 @@ NUTS_kernel = numpyro.infer.NUTS(AR1_model)
 
 # 运行MCMC
 mcmc = numpyro.infer.MCMC(NUTS_kernel, num_samples=50000, num_warmup=10000, progress_bar=False)
-mcmc.run(rng_key=random.PRNGKey(1), data=y)
+mcmc.run(rng_key=random.key(1), data=y)
 ```
 
 我们绘制轨迹图和后验分布图。
@@ -549,7 +545,7 @@ NUTS_kernel = numpyro.infer.NUTS(AR1_model_y0)
 
 # 运行MCMC
 mcmc2 = numpyro.infer.MCMC(NUTS_kernel, num_samples=50000, num_warmup=10000, progress_bar=False)
-mcmc2.run(rng_key=random.PRNGKey(1), data=y)
+mcmc2.run(rng_key=random.key(1), data=y)
 ```
 
 我们再次绘制轨迹图和后验分布图。

diff --git a/lectures/back_prop.md b/lectures/back_prop.md
@@ -4,9 +4,9 @@ jupytext:
     extension: .md
     format_name: myst
     format_version: 0.13
-    jupytext_version: 1.11.5
+    jupytext_version: 1.16.7
 kernelspec:
-  display_name: Python 3
+  display_name: Python 3 (ipykernel)
   language: python
   name: python3
 translation:
@@ -381,7 +381,7 @@ N = 3  # 层数
 layer_sizes = [1, ] * (N + 1)
 param_scale = 0.1
 step_size = 0.01
-params = init_network_params(layer_sizes, random.PRNGKey(1))
+params = init_network_params(layer_sizes, random.key(1))
 ```
 
 ```{code-cell} ipython3
@@ -482,12 +482,12 @@ f_val = f(grid)
 
 ```{code-cell} ipython3
 indices = jnp.arange(M)
-key = random.PRNGKey(0)
+key = random.key(0)
 
 def train(params, grid, f_val, key, num_epochs=300):
     for epoch in range(num_epochs):
         key, _ = random.split(key)
-        random_permutation = random.permutation(random.PRNGKey(1), indices)
+        random_permutation = random.permutation(random.key(1), indices)
         for x, y in zip(grid[random_permutation], f_val[random_permutation]):
             params = update_la(params, x, y)
 
@@ -529,8 +529,6 @@ Image(fig.to_image(format="png"))
 * 在本讲所考虑的情况下，步长和训练轮数等其他参数可能与网络层数一样重要或更重要
 * 实际上，由于 $f$ 是 $x$ 的线性函数，使用恒等映射作为激活函数的单层网络可能效果最好。
 
-
-
 ## 示例2
 
 我们使用与前一个示例相同的设置，其中

diff --git a/lectures/ifp_advanced.md b/lectures/ifp_advanced.md
@@ -334,7 +334,7 @@ def create_ifp(
     assert β * ER < 1, "稳定性条件不成立。"
 
     # 使用 JAX 生成随机抽取
-    key = jax.random.PRNGKey(seed)
+    key = jax.random.key(seed)
     subkey1, subkey2 = jax.random.split(key)
     η_draws = jax.random.normal(subkey1, (shock_draw_size,))
     ζ_draws = jax.random.normal(subkey2, (shock_draw_size,))
@@ -558,7 +558,7 @@ def compute_asset_stationary(
     z_idx_0_vector = jnp.zeros(num_households).astype(jnp.int32)
 
     # 对许多家庭进行向量化
-    key = jax.random.PRNGKey(seed)
+    key = jax.random.key(seed)
     keys = jax.random.split(key, num_households)
     # 在 (key, a_0, z_idx_0) 上向量化 simulate_household
     sim_all_households = jax.vmap(

diff --git a/lectures/ifp_egm.md b/lectures/ifp_egm.md
@@ -3,6 +3,8 @@ jupytext:
   text_representation:
     extension: .md
     format_name: myst
+    format_version: 0.13
+    jupytext_version: 1.17.2
 kernelspec:
   display_name: Python 3
   language: python
@@ -30,6 +32,14 @@ translation:
     Simulation: 模拟
 ---
 
+```{raw} jupyter
+<div id="qe-notebook-header" align="right" style="text-align:right;">
+        <a href="https://quantecon.org/" title="quantecon.org">
+                <img style="width:250px;display:inline;" width="250px" src="https://assets.quantecon.org/img/qe-menubar-logo.svg" alt="QuantEcon">
+        </a>
+</div>
+```
+
 # {index}`收入波动问题 III：内生网格法 <single: The Income Fluctuation Problem III: The Endogenous Grid Method>`
 
 ```{include} _admonition/gpu.md
@@ -854,7 +864,7 @@ def compute_asset_stationary(
     z_idx_0_vector = jnp.zeros(num_households).astype(jnp.int32)
 
     # 对多个家庭进行向量化
-    key = jax.random.PRNGKey(seed)
+    key = jax.random.key(seed)
     keys = jax.random.split(key, num_households)
     # 对 (key, a_0, z_idx_0) 向量化 simulate_household
     sim_all_households = jax.vmap(