From 29c1fe5a49a948d4bd8b76c5da4069332dfde201 Mon Sep 17 00:00:00 2001
From: Asad Hussain <asadh@utexas.edu>
Date: Mon, 28 Oct 2024 13:46:03 -0500
Subject: [PATCH] tutorial changes

---
 docs/Examples/gravpop_tutorial.ipynb | 72 +++++++++++++++-------------
 1 file changed, 39 insertions(+), 33 deletions(-)

diff --git a/docs/Examples/gravpop_tutorial.ipynb b/docs/Examples/gravpop_tutorial.ipynb
index 5a91069..a0ba0f3 100644
--- a/docs/Examples/gravpop_tutorial.ipynb
+++ b/docs/Examples/gravpop_tutorial.ipynb
@@ -2,11 +2,17 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "b76f782c",
+   "id": "32ac9285",
    "metadata": {},
    "source": [
     "# Gravpop tutorial\n",
     "\n",
+    "\n",
+    "\n",
+    "\n",
+    "\n",
+    "\n",
+    "\n",
     "This is a library that allows you to perform a population analysis, ala [Thrane et. al](https://arxiv.org/abs/1809.02293), but using a trick described in [Hussain et. al](...) that allows one to be able to probe population features even when they get very narrow, and get close to the edges of a bounded domain. \n",
     "\n",
     "The trick essentially relies on dividing the parameter space into a sector (which we call the __analytic__ sector $\\theta^a$) where our population model is made out of some weighted sum of multivariate truncated normals - where we can analytically compute the population likelihood, and another where the model is general and we can compute it using the monte-carlo estimate of the population likelihood (we call this sector the __sampled__ sector $\\theta^s$). \n",
@@ -71,7 +77,7 @@
   {
    "cell_type": "code",
    "execution_count": 3,
-   "id": "b1a23da0",
+   "id": "3400f274",
    "metadata": {},
    "outputs": [
     {
@@ -275,7 +281,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c3b69488",
+   "id": "af24f0c3",
    "metadata": {},
    "source": [
     "We can then fit the events we want to TGMMs. Note that the `.dataproduct()` method of the TGMM class provides the fitted data in the format that is required by `gravpop`."
@@ -284,7 +290,7 @@
   {
    "cell_type": "code",
    "execution_count": 4,
-   "id": "8926b86d",
+   "id": "605cd216",
    "metadata": {},
    "outputs": [
     {
@@ -337,7 +343,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "15496b80",
+   "id": "9ece8b92",
    "metadata": {},
    "source": [
     "We can now construct the data product we need:\n",
@@ -347,7 +353,7 @@
   {
    "cell_type": "code",
    "execution_count": 5,
-   "id": "af61ce61",
+   "id": "f97e716f",
    "metadata": {},
    "outputs": [
     {
@@ -388,7 +394,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "71db1530",
+   "id": "0cf13137",
    "metadata": {},
    "source": [
     "we now have our data in the correct format. \n",
@@ -431,7 +437,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5c02d0b1",
+   "id": "3554d94c",
    "metadata": {},
    "source": [
     "# Models"
@@ -439,7 +445,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fcc567e4",
+   "id": "a92b56fa",
    "metadata": {},
    "source": [
     "One can specify population models using a set of building block models. Each population model is defined as a distributions over some parameters $\\theta$, defined below by `var_names`, and some hyper-parameters $\\Lambda$, defined below by `hyper_var_names`. \n",
@@ -486,7 +492,7 @@
   {
    "cell_type": "code",
    "execution_count": 1,
-   "id": "fa13cbe8",
+   "id": "d79b6aff",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -512,7 +518,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c10fb445",
+   "id": "9abb71b8",
    "metadata": {},
    "source": [
     "We can combine these building blocks however we like. Using the following operations:\n",
@@ -532,7 +538,7 @@
   {
    "cell_type": "code",
    "execution_count": 2,
-   "id": "3846c608",
+   "id": "455cd87a",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -562,7 +568,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8706088c",
+   "id": "fe8759a0",
    "metadata": {},
    "source": [
     "One can then evaluate this spin model on some set parameters"
@@ -571,7 +577,7 @@
   {
    "cell_type": "code",
    "execution_count": 9,
-   "id": "e880c5f9",
+   "id": "57e76904",
    "metadata": {},
    "outputs": [
     {
@@ -600,7 +606,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "941211a5",
+   "id": "24618218",
    "metadata": {},
    "source": [
     "## Sampled Models\n",
@@ -627,7 +633,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b473e5ad",
+   "id": "ffa7625f",
    "metadata": {},
    "source": [
     "# Population Likelihood\n",
@@ -648,7 +654,7 @@
   {
    "cell_type": "code",
    "execution_count": 15,
-   "id": "425accdc",
+   "id": "9490cfa7",
    "metadata": {},
    "outputs": [
     {
@@ -675,7 +681,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b51cdc38",
+   "id": "895e0eec",
    "metadata": {},
    "source": [
     "We can compute the loglikelihood for some hyper-parameters, and also confirm by computing the derivative that there are no nan derivatives.\n",
@@ -686,7 +692,7 @@
   {
    "cell_type": "code",
    "execution_count": 16,
-   "id": "b00b1586",
+   "id": "935f3404",
    "metadata": {},
    "outputs": [
     {
@@ -710,7 +716,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1d61327c",
+   "id": "cbf9cc31",
    "metadata": {},
    "source": [
     "All our models are auto-diff-able, so we can compute the gradient of the logpdf as below:"
@@ -719,7 +725,7 @@
   {
    "cell_type": "code",
    "execution_count": 18,
-   "id": "ba65cdd4",
+   "id": "a053808c",
    "metadata": {},
    "outputs": [
     {
@@ -745,7 +751,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7e11c500",
+   "id": "86c88b47",
    "metadata": {},
    "source": [
     "One can also load up the event and selection function data from a file:"
@@ -754,7 +760,7 @@
   {
    "cell_type": "code",
    "execution_count": 19,
-   "id": "96c86fd5",
+   "id": "9f1b8c10",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -770,7 +776,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a1be31ef",
+   "id": "7b98306c",
    "metadata": {},
    "source": [
     "# Sampling\n",
@@ -783,7 +789,7 @@
   {
    "cell_type": "code",
    "execution_count": 22,
-   "id": "83ce1f8d",
+   "id": "8cd350ea",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -801,7 +807,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3bd0c662",
+   "id": "4701fe32",
    "metadata": {},
    "source": [
     "Then, we can construct a `Sampler` object and put in our settings."
@@ -810,7 +816,7 @@
   {
    "cell_type": "code",
    "execution_count": 24,
-   "id": "23f28bb0",
+   "id": "e432d77c",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -824,7 +830,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5e388f7b",
+   "id": "08a66057",
    "metadata": {},
    "source": [
     "and we can begin sampling"
@@ -833,7 +839,7 @@
   {
    "cell_type": "code",
    "execution_count": 25,
-   "id": "b7de385f",
+   "id": "251e1512",
    "metadata": {},
    "outputs": [
     {
@@ -865,7 +871,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3c5a1549",
+   "id": "6d494a74",
    "metadata": {},
    "source": [
     "we can see the dataframe holding the hyper-posterior samples in:"
@@ -874,7 +880,7 @@
   {
    "cell_type": "code",
    "execution_count": 28,
-   "id": "b26d5de3",
+   "id": "6c1c5497",
    "metadata": {},
    "outputs": [
     {
@@ -1027,7 +1033,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1f40581d",
+   "id": "c0db874e",
    "metadata": {},
    "source": [
     "and here is a corner plot of our result"
@@ -1036,7 +1042,7 @@
   {
    "cell_type": "code",
    "execution_count": 31,
-   "id": "f11e5421",
+   "id": "bed347c9",
    "metadata": {},
    "outputs": [
     {