fix admonitions + add notebook reference to LKJ notebook

Author: drbenvincent

examples/generalized_linear_models/GLM-simpsons-paradox.ipynb

@@ -372,7 +372,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    ":::{info}\n",
+    ":::{note}\n",
     "We can also express Model 1 in Wilkinson notation as `y ~ 1 + x` which is equivalent to `y ~ x` as the intercept is included by default.\n",
     "\n",
     "* The `1` term corresponds to the intercept term $\\beta_0$.\n",
@@ -934,7 +934,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    ":::{info}\n",
+    ":::{note}\n",
     "We can also express this Model 2 in Wilkinson notation as `y ~ g + x:g`.\n",
     "\n",
     "* The `g` term captures the group specific intercept $\\beta_0[g_i]$ parameters.\n",
@@ -1451,7 +1451,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    ":::{info}\n",
+    ":::{note}\n",
     "We can also express this Model 3 in Wilkinson notation as `1 + x + (1 + x | g)`.\n",
     "\n",
     "* The `1` captures the global intercept, $\\mathrm{Normal}(p_{0\\mu}, p_{0\\sigma})$.\n",
@@ -1466,10 +1466,17 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    ":::{note}\n",
-    "The hierarchical model we are considering contains a simplification in that the population level slope and intercept are assumed to be independent. It is possible to relax this assumption and model any correlation between these parameters by using a multivariate normal distribution.\n",
-    "\n",
-    "In one sense this move from Model 2 to Model 3 can be seen as adding parameters, and therefore increasing model complexity. However, in another sense, adding this knowledge about the nested structure of the data actually provides a constraint over parameter space.\n",
+    ":::{seealso}\n",
+    "The hierarchical model we are considering contains a simplification in that the population level slope and intercept are assumed to be independent. It is possible to relax this assumption and model any correlation between these parameters by using a multivariate normal distribution. See the {ref}`lkj_prior_for_multivariate_normal` notebook for more details.\n",
+    ":::"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    ":::{seealso}\n",
+    "In one sense this move from Model 2 to Model 3 can be seen as adding parameters, and therefore increasing model complexity. However, in another sense, adding this knowledge about the nested structure of the data actually provides a constraint over parameter space. It would be possible to engage in model comparison to arbitrate between these models - see for example the {ref}`GLM-model-selection` notebook for more details.\n",
     ":::"
    ]
   },

examples/generalized_linear_models/GLM-simpsons-paradox.myst.md

@@ -119,7 +119,7 @@ $$
 
 +++
 
-:::{info}
+:::{note}
 We can also express Model 1 in Wilkinson notation as `y ~ 1 + x` which is equivalent to `y ~ x` as the intercept is included by default.
 
 * The `1` term corresponds to the intercept term $\beta_0$.
@@ -283,7 +283,7 @@ Where $g_i$ is the group index for observation $i$. So the parameters $\beta_0$
 
 +++
 
-:::{info}
+:::{note}
 We can also express this Model 2 in Wilkinson notation as `y ~ g + x:g`.
 
 * The `g` term captures the group specific intercept $\beta_0[g_i]$ parameters.
@@ -450,7 +450,7 @@ This model could also be called a partial pooling model.
 
 +++
 
-:::{info}
+:::{note}
 We can also express this Model 3 in Wilkinson notation as `1 + x + (1 + x | g)`.
 
 * The `1` captures the global intercept, $\mathrm{Normal}(p_{0\mu}, p_{0\sigma})$.
@@ -462,10 +462,14 @@ We can also express this Model 3 in Wilkinson notation as `1 + x + (1 + x | g)`.
 
 +++
 
-:::{note}
-The hierarchical model we are considering contains a simplification in that the population level slope and intercept are assumed to be independent. It is possible to relax this assumption and model any correlation between these parameters by using a multivariate normal distribution.
+:::{seealso}
+The hierarchical model we are considering contains a simplification in that the population level slope and intercept are assumed to be independent. It is possible to relax this assumption and model any correlation between these parameters by using a multivariate normal distribution. See the {ref}`lkj_prior_for_multivariate_normal` notebook for more details.
+:::
+
++++
 
-In one sense this move from Model 2 to Model 3 can be seen as adding parameters, and therefore increasing model complexity. However, in another sense, adding this knowledge about the nested structure of the data actually provides a constraint over parameter space.
+:::{seealso}
+In one sense this move from Model 2 to Model 3 can be seen as adding parameters, and therefore increasing model complexity. However, in another sense, adding this knowledge about the nested structure of the data actually provides a constraint over parameter space. It would be possible to engage in model comparison to arbitrate between these models - see for example the {ref}`GLM-model-selection` notebook for more details.
 :::
 
 +++

examples/howto/LKJ.ipynb

@@ -6,6 +6,7 @@
     "id": "XShKDkNir2PX"
    },
    "source": [
+    "(lkj_prior_for_multivariate_normal)=\n",
     "# LKJ Cholesky Covariance Priors for Multivariate Normal Models"
    ]
   },

examples/howto/LKJ.myst.md

@@ -12,6 +12,7 @@ kernelspec:
 
 +++ {"id": "XShKDkNir2PX"}
 
+(lkj_prior_for_multivariate_normal)=
 # LKJ Cholesky Covariance Priors for Multivariate Normal Models
 
 +++ {"id": "QxSKBbjKr2PZ"}