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QuantEcon · Dec 13, 2023 · cc9d4ee · cc9d4ee
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diff --git a/_sources/ar1_bayes.ipynb b/_sources/ar1_bayes.ipynb
@@ -2,7 +2,7 @@
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     "# Posterior Distributions for  AR(1) Parameters\n",
@@ -13,7 +13,7 @@
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@@ -27,7 +27,7 @@
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@@ -51,7 +51,7 @@
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     "This lecture uses Bayesian methods offered by [pymc](https://www.pymc.io/projects/docs/en/stable/) and [numpyro](https://num.pyro.ai/en/stable/) to make statistical inferences about two parameters of a univariate first-order autoregression.\n",
@@ -151,7 +151,7 @@
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@@ -179,7 +179,7 @@
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@@ -189,7 +189,7 @@
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     "Now we shall use Bayes' law to construct a posterior distribution, conditioning on the initial value of $y_0$.\n",
@@ -207,7 +207,7 @@
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@@ -228,7 +228,7 @@
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     "[pmc.sample](https://www.pymc.io/projects/docs/en/latest/api/generated/pymc.sample.html?highlight=sample#pymc.sample) by default uses the NUTS samplers to generate samples as shown in the below cell:"
@@ -237,7 +237,7 @@
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@@ -252,7 +252,7 @@
   {
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@@ -262,7 +262,7 @@
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     "Evidently, the posteriors aren't centered on the true values of $.5, 1$ that we used to generate the data.\n",
@@ -278,7 +278,7 @@
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@@ -290,7 +290,7 @@
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     "Now we shall compute a posterior distribution after seeing the same data but instead assuming that $y_0$ is drawn from the stationary distribution.\n",
@@ -307,7 +307,7 @@
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@@ -331,7 +331,7 @@
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@@ -348,7 +348,7 @@
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@@ -359,7 +359,7 @@
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@@ -371,7 +371,7 @@
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     "Please note how the posterior for $\\rho$ has shifted to the right relative to when we conditioned on $y_0$ instead of assuming that $y_0$ is drawn from the stationary distribution.\n",
@@ -393,7 +393,7 @@
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@@ -427,7 +427,7 @@
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@@ -446,7 +446,7 @@
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@@ -478,7 +478,7 @@
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@@ -487,7 +487,7 @@
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     "Next, we again compute the posterior under the assumption that $y_0$ is drawn from the stationary distribution, so that\n",
@@ -502,7 +502,7 @@
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@@ -525,7 +525,7 @@
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@@ -557,7 +557,7 @@
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@@ -566,7 +566,7 @@
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     "Look what happened to the posterior!\n",