added an optional cell block for extending the pattern to more than two levels

Author: Abhishek.6122008

docs/source/learn/core_notebooks/vector_variables.ipynb

@@ -893,6 +893,43 @@
     "Once the mapping is in place, the rest of the model looks like any other hierarchical setup.\n"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "1be8ea9b",
+   "metadata": {},
+   "source": [
+    "## Optional: Extending this pattern to more than two levels\n",
+    "\n",
+    "This example uses two levels (category and family), but the same idea works for any number of levels.  \n",
+    "The key ingredients stay the same:\n",
+    "\n",
+    "1. factorize each level of labels into integer codes  \n",
+    "2. build a mapping array from each level to the one above it  \n",
+    "3. use that mapping to index the parent vector inside the next level’s prior\n",
+    "\n",
+    "For example, if you had three levels:\n",
+    "\n",
+    "- level_0\n",
+    "- level_1\n",
+    "- level_2\n",
+    "\n",
+    "You would create the following:\n",
+    "\n",
+    "- level_1_to_level_0\n",
+    "- level_2_to_level_1\n",
+    "\n",
+    "Then you would define priors like this:\n",
+    "\n",
+    "- level_0_effect\n",
+    "- level_1_effect, centered on level_0_effect[level_1_to_level_0]\n",
+    "- level_2_effect, centered on level_1_effect[level_2_to_level_1]\n",
+    "\n",
+    "Each additional level only requires one more factorized index and one more mapping array.  \n",
+    "Nothing else about the PyMC model needs to change.\n",
+    "\n",
+    "This is what people sometimes call a telescoping hierarchy: every group is centered on the group above it, and the indexing arrays connect the levels together.\n"
+   ]
+  },
   {
    "cell_type": "markdown",
    "id": "39c4c0af",