fix the three tutorials (pyro-ppl#1571)

DanWaxman · Mar 30, 2023 · 0589859 · 0589859
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diff --git a/examples/mortality.py b/examples/mortality.py
@@ -33,11 +33,11 @@
 .. math:: :nowrap:
 
     \\begin{align}
-        \\alpha_{1s_1} & \\sim \\mathcal{N}(0,\\sigma_{\\alpha_{s_1}}^2) \\\\
-        \\alpha_{1s} & \\sim \\mathcal{N}(\\alpha_{1s_1(s_2)},\\sigma_{\\alpha_{s_2}}^2) \\\\
-        \\alpha_{2a} & \\sim \\mathcal{N}(\\alpha_{2,a-1},\\sigma_{\\alpha_a}^2) \\quad \\alpha_{2,0} = \\alpha_0 \\\\
-        \\beta_{2a} & \\sim \\mathcal{N}(\\beta_{2,a-1},\\sigma_{\\beta_a}^2) \\quad \\beta_{2,0} = \\beta_0 \\\\
-        \\pi_{t} & \\sim \\mathcal{N}(\\pi_{t-1},\\sigma_{\\pi}^2), \\quad \\pi_{0} = 0 \\\\
+        \\alpha_{1s_1} & \\sim \\text{Normal}(0,\\sigma_{\\alpha_{s_1}}^2) \\\\
+        \\alpha_{1s} & \\sim \\text{Normal}(\\alpha_{1s_1(s_2)},\\sigma_{\\alpha_{s_2}}^2) \\\\
+        \\alpha_{2a} & \\sim \\text{Normal}(\\alpha_{2,a-1},\\sigma_{\\alpha_a}^2) \\quad \\alpha_{2,0} = \\alpha_0 \\\\
+        \\beta_{2a} & \\sim \\text{Normal}(\\beta_{2,a-1},\\sigma_{\\beta_a}^2) \\quad \\beta_{2,0} = \\beta_0 \\\\
+        \\pi_{t} & \\sim \\text{Normal}(\\pi_{t-1},\\sigma_{\\pi}^2), \\quad \\pi_{0} = 0 \\\\
         \\text{logit}(m_{ast}) & = \\alpha_{1s} + \\alpha_{2a} + \\beta_{2a} t + \\pi_{t}
     \\end{align}
 
@@ -46,9 +46,9 @@
 .. math:: :nowrap:
 
     \\begin{align}
-        \\alpha_0 & \\sim \\mathcal{N}(0,10), \\\\
-        \\beta_0 & \\sim \\mathcal{N}(0,10), \\\\
-        \\sigma_i & \\sim \\mathcal{N}^{+}(1)
+        \\alpha_0 & \\sim \\text{Normal}(0,10), \\\\
+        \\beta_0 & \\sim \\text{Normal}(0,10), \\\\
+        \\sigma_i & \\sim \\text{Half-Normal}(1)
     \\end{align}
 
 Further detail about the model terms can be found in [1].

diff --git a/notebooks/source/bayesian_hierarchical_linear_regression.ipynb b/notebooks/source/bayesian_hierarchical_linear_regression.ipynb
diff --git a/notebooks/source/tbip.ipynb b/notebooks/source/tbip.ipynb
@@ -240,6 +240,7 @@
    ]
   },
   {
+   "attachments": {},
    "cell_type": "markdown",
    "metadata": {
     "id": "n8SUSFpLuXRP"
@@ -256,8 +257,8 @@
     "We use lognormal factors for the positive variables and Gaussian factors for the real variables:\n",
     "$$q(\\theta_{dk}) = \\text{LogNormal}(\\mu_{\\theta_{dk}}\\sigma^2_{\\theta_{dk}})$$\n",
     "$$q(\\theta_{dv}) = \\text{LogNormal}(\\mu_{\\beta_{kv}}, \\sigma^2_{\\beta_{kv}})$$\n",
-    "$$q(\\eta_{kv}) = \\mathcal{N}(\\mu_{\\eta_{kv}}, \\sigma^2_{\\eta_{kv}})$$\n",
-    "$$q(x_s) = \\mathcal{N}(\\mu_{x_s}, \\sigma^2_{x_s}).$$\n",
+    "$$q(\\eta_{kv}) = \\text{Normal}(\\mu_{\\eta_{kv}}, \\sigma^2_{\\eta_{kv}})$$\n",
+    "$$q(x_s) = \\text{Normal}(\\mu_{x_s}, \\sigma^2_{x_s}).$$\n",
     "\n",
     "Thus, our goal is to maximize the ELBO with respect to $\\phi = \\{\\mu_\\theta, \\sigma_\\theta, \\mu_\\beta, \\sigma_\\beta,\\mu_\\eta, \\sigma_\\eta, \\mu_x, \\sigma_x\\}$. \n",
     "\n",