add clarifition on what is R in BYM

20_areal_data.ipynb

@@ -538,7 +538,7 @@
    "source": [
     "## Models of areal data\n",
     "\n",
-    "In models for areal data, the geographic units are denoted by $B_i$, and the data are typically sums or averages of variables over these blocks. To introduce spatial association, we define a neighborhood structure based on the arrangement of the blocks in the map. Once the neighborhood structure is defined, one can construct models models resembling autoregressive time series models, such as the intrinsic conditionally autoregressive model (ICAR, also called Besag) and conditionally autoregressive model (CAR).\n",
+    "In models for areal data, the geographic units are denoted by $B_i$, and the data are typically sums or averages of variables over these blocks. To introduce spatial association, we define a neighborhood structure based on the arrangement of the blocks in the map. Once the neighborhood structure is defined, one can construct models resembling autoregressive time series models, such as the intrinsic conditionally autoregressive model (ICAR, also called Besag) and conditionally autoregressive model (CAR).\n",
     "\n",
     "All of the classical have the same functional form\n",
     "\n",
@@ -715,9 +715,11 @@
     "The Besag, York, and Mollié (BYM) decomposes the spatial random effect $f$ into the sum of an i.i.d. component $v$ and spatiallly structured component $w$. Each of these two components has its own precision parameter $\\tau_v$ and $\\tau_w$, respectively:\n",
     "\n",
     "$$\n",
-    "f \\sim \\mathcal{N}(0, \\tau_v^{-1}I + \\tau_w^{-1}R^-).\n",
+    "f \\sim \\mathcal{N}(0, \\tau_v^{-1}I + \\tau_w^{-1}R^-),\n",
     "$$\n",
     "\n",
+    "where the $R$ is responsible for the ICAR components, i.e. $R = D - A$.\n",
+    "\n",
     "This model provides more flexibility than the CAR formulation. "
    ]
   },