Updated old blackjax code of smc_tempered_1d_bimodal.ipynb (probml#…

…1080)

* Latexified Figure 4.20

* issue resolved

* Added 8schools problem

* Updated smc figures

* `jaxopt` added

* Fig 13.12 latexified

* Latexified Fig 3.6

notebooks/book2/03/schools8_blackjax.ipynb

@@ -88,6 +88,7 @@
    "outputs": [],
    "source": [
     "# import os\n",
+    "\n",
     "# os.environ[\"LATEXIFY\"] = \"\"\n",
     "# os.environ[\"FIG_DIR\"] = \"figures\""
    ]
@@ -142,7 +143,7 @@
     },
     {
      "data": {
-      "image/png": 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\n",
+      "image/png": "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\n",
       "text/plain": [
        "<Figure size 432x288 with 1 Axes>"
       ]
@@ -171,8 +172,8 @@
     "ax.set_yticks(y_pos)\n",
     "ax.set_yticklabels(names)\n",
     "ax.invert_yaxis()  # labels read top-to-bottom\n",
-    "ax.axvline(jnp.mean(treatment_effects), color=\"r\", linestyle=\"--\")\n",
-    "\n",
+    "ax.axvline(jnp.mean(treatment_effects), color=\"r\", linestyle=\"--\", label=\"pooled MLE\")\n",
+    "ax.set_ylabel(\"$\\\\theta$\")\n",
     "sns.despine()\n",
     "pml.savefig(\"schools8_data\")\n",
     "plt.show()"
@@ -273,7 +274,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "CPU times: user 19.6 s, sys: 237 ms, total: 19.8 s\n",
+      "CPU times: user 19.5 s, sys: 256 ms, total: 19.8 s\n",
       "Wall time: 19.6 s\n"
      ]
     }
@@ -649,8 +650,8 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "CPU times: user 15.8 s, sys: 169 ms, total: 16 s\n",
-      "Wall time: 15.8 s\n"
+      "CPU times: user 16.1 s, sys: 193 ms, total: 16.3 s\n",
+      "Wall time: 16.1 s\n"
      ]
     }
    ],
@@ -1203,7 +1204,7 @@
     {
      "data": {
       "text/plain": [
-       "<matplotlib.lines.Line2D at 0x7f632c157d50>"
+       "<matplotlib.lines.Line2D at 0x7fe74837e150>"
       ]
      },
      "execution_count": 29,