finished annotations on bonus nb

Author: ericmjl

notebooks/bonus-exploration-finches.ipynb

@@ -18,6 +18,13 @@
     "%config InlineBackend.figure_format = 'retina'"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "In this notebook, I would like to write an estimation model for beak shape. "
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,
@@ -52,6 +59,16 @@
     "scandens_idx = df[df['species'] == 'scandens'].index"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Model : Naive Division of Posteriors\n",
+    "\n",
+    "- Estimate posterior for depth and length independently.\n",
+    "- Use posterior samples to estimate distribution for shape."
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,
@@ -186,16 +203,6 @@
     "plt.tight_layout()"
    ]
   },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "plt.hist(samples['beak_depth'].flatten())\n",
-    "plt.hist(samples['beak_length'].flatten())"
-   ]
-  },
   {
    "cell_type": "code",
    "execution_count": null,
@@ -210,6 +217,15 @@
     "ax.plot(x, y)"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Ok, looks like this is not the right model. Dividing PPC samples is definitely not the right approach here.\n",
+    "\n",
+    "Maybe jointly modelling the observed beak and length distributions is the right thing to do?"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,
@@ -237,6 +253,8 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
+    "# Model: Joint Distribution\n",
+    "\n",
     "Going to try a new model: we explicity model depth and length jointly, as a multivariate gaussian."
    ]
   },
@@ -357,6 +375,8 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
+    "# Model: Regress Depth on Length\n",
+    "\n",
     "Maybe the right way to compute shape is to regress depth on length, and compute the slope. After all, that's all that depth/length really is.\n",
     "\n",
     "We will assume a model: $y=mx$, no intercept."
@@ -409,7 +429,9 @@
    "source": [
     "I have the model mis-specified - I get the posterior distribution over the slope, but not the distribution of shapes. I guess shapes and slopes are kind of different. \n",
     "\n",
-    "Let's try just estimating shape directly."
+    "Let's try just estimating shape directly.\n",
+    "\n",
+    "# Model: Estimate on Shape Parameter"
    ]
   },
   {