update minor text details

Author: rusty-electron

examples/Intro_Amortized_Posterior_Estimation.ipynb

@@ -969,7 +969,7 @@
     "\n",
     "SBC is a technique used to assess whether a probabilistic model correctly infers parameters from data. The basic idea is to simulate a large number of datasets from the model's prior distribution and then perform posterior inference on these simulated datasets. The goal is to check if the inferred posterior distributions are consistent with the priors. Essentially, SBC tests if the model can accurately recover the parameters it used to generate the data in the first place. This process helps identify any systematic biases or inaccuracies in the model's inference process.\n",
     "\n",
-    "To perform SBC, we first need to obtain a number of `L` posterior draws from `M` simulated data sets. While the procedure is typically intractable, amortized inference allows us to perform SBC instantly."
+    "To perform SBC, we first need to obtain `L` number of posterior draws from `M` simulated data sets. While the procedure is typically intractable, amortized inference allows us to perform SBC instantly."
    ]
   },
   {
@@ -1050,12 +1050,18 @@
    "metadata": {},
    "source": [
     "#### Posterior z-score and contraction\n",
+    "\n",
+    "* Posterior z-score: It measures how many standard deviations away the mean of the posterior distribution is from the true value of the parameter. A z-score of 0 indicates the mean perfectly aligns with the true value (no bias) while positive/negative z-scores indicate positive/negative bias, respectively.\n",
+    "* Posterior contraction: It measures how much the posterior distribution contracts around the true value of the parameter as more data is observed. A higher contraction indicates that the data provides strong evidence, narrowing the uncertainty range.\n",
+    "\n",
+    "Ideally, we should obtain high contraction and a z-score near 0. This means the model accurately captures the true value with little bias and high confidence.\n",
+    "\n",
     "A quick and dirty way to gain an understanding of how good point estimates and uncertainty estimates capture the \"true\" parameters, assuming the generative model is well-specified. For this, we will draw more samples from the posteriors in order to get smaller Monte Carlo error."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 32,
+   "execution_count": null,
    "id": "descending-election",
    "metadata": {},
    "outputs": [],
@@ -1091,7 +1097,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 34,
+   "execution_count": null,
    "id": "virtual-incidence",
    "metadata": {},
    "outputs": [