Add files via upload

docs/notebooks/cube_galaxy_sky.ipynb

@@ -2,10 +2,10 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "45dca41b",
+   "id": "5a5ae7c4",
    "metadata": {},
    "source": [
-    "# Toy model: infering the size of a cube galaxy from the inside\n",
+    "# :ice_cube: Toy model: infering the size of a cube galaxy from the inside\n",
     "\n",
     "written by Tristan Cantat-Gaudin - last edit 2023-10-27\n",
     "\n",
@@ -17,7 +17,7 @@
   {
    "cell_type": "code",
    "execution_count": 1,
-   "id": "350f4109",
+   "id": "9d422321",
    "metadata": {},
    "outputs": [
     {
@@ -68,7 +68,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b61e8c5a",
+   "id": "6832587f",
    "metadata": {},
    "source": [
     "Inside the box: the sky positions $(\\ell,b)$ are **observed quantities**: they are the pieces of information we have measured, and we will use to test our understanding of the Milky Way. The 3D positions $(X,Y,Z)$ are called **latent variables**: we don't know them for individual stars, and we are not even trying to calculate them.\n",
@@ -83,7 +83,7 @@
   {
    "cell_type": "code",
    "execution_count": 2,
-   "id": "6fe9d064",
+   "id": "293cdef4",
    "metadata": {},
    "outputs": [
     {
@@ -133,7 +133,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4dd1afd8",
+   "id": "65e451d7",
    "metadata": {},
    "source": [
     "This is what our cube Galaxy would look like on the sky:"
@@ -142,7 +142,7 @@
   {
    "cell_type": "code",
    "execution_count": 3,
-   "id": "326ad567",
+   "id": "77fef9ec",
    "metadata": {},
    "outputs": [
     {
@@ -178,7 +178,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f39efca1",
+   "id": "9e8e10d0",
    "metadata": {},
    "source": [
     "## Writing down the likelihood\n",
@@ -193,7 +193,7 @@
   {
    "cell_type": "code",
    "execution_count": 4,
-   "id": "4d8457b7",
+   "id": "36c2294f",
    "metadata": {
     "scrolled": true
    },
@@ -319,7 +319,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "29d2afce",
+   "id": "56f8718e",
    "metadata": {},
    "source": [
     "## Maximum likelihood estimation from positions $(\\ell,b)$\n",
@@ -345,7 +345,7 @@
   {
    "cell_type": "code",
    "execution_count": 5,
-   "id": "6885111f",
+   "id": "7d9cf2c2",
    "metadata": {},
    "outputs": [
     {
@@ -435,7 +435,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "879fd000",
+   "id": "40b98b23",
    "metadata": {},
    "source": [
     "## What if our data is incomplete?\n",
@@ -446,7 +446,7 @@
   {
    "cell_type": "code",
    "execution_count": 6,
-   "id": "3e8ae650",
+   "id": "7540a860",
    "metadata": {},
    "outputs": [
     {
@@ -508,7 +508,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b9a7a11a",
+   "id": "46356581",
    "metadata": {},
    "source": [
     "The incompleteness distorted the apparent distribution of stars on the sky. If we apply the same maximum likelihood method as above, we will get the wrong answer!"
@@ -517,7 +517,7 @@
   {
    "cell_type": "code",
    "execution_count": 7,
-   "id": "bdd7138d",
+   "id": "1073492e",
    "metadata": {},
    "outputs": [
     {
@@ -590,7 +590,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a8d8a78e",
+   "id": "93dd8482",
    "metadata": {},
    "source": [
     "The procedure is now returning incorrect results! We know the cube size is 40 kpc, but the incomplete data makes the stellar distribution more homogeneous on the sky (because it is more incomplete in the parts of the sky with a higher true density), which mimicks the effect of the cube being larger."
@@ -599,7 +599,7 @@
   {
    "cell_type": "code",
    "execution_count": 8,
-   "id": "104c05ad",
+   "id": "b802d9cd",
    "metadata": {},
    "outputs": [
     {
@@ -677,7 +677,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a36382c5",
+   "id": "f3172cfc",
    "metadata": {},
    "source": [
     "## Can I use the selection function to correct the data?\n",
@@ -690,7 +690,7 @@
   {
    "cell_type": "code",
    "execution_count": 9,
-   "id": "8a289976",
+   "id": "7906a720",
    "metadata": {},
    "outputs": [
     {
@@ -778,7 +778,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "caac99e0",
+   "id": "9b2f178a",
    "metadata": {},
    "source": [
     "The correct way to select the best-fit model is to compare panel C to panel E, for different choices of cube size.\n",
@@ -803,7 +803,7 @@
   {
    "cell_type": "code",
    "execution_count": 10,
-   "id": "e9a05c5e",
+   "id": "549c93d8",
    "metadata": {},
    "outputs": [
     {
@@ -878,7 +878,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bd1705df",
+   "id": "3d44d8f9",
    "metadata": {},
    "source": [
     "## Summary plot\n",
@@ -893,7 +893,7 @@
   {
    "cell_type": "code",
    "execution_count": 11,
-   "id": "a22d2891",
+   "id": "3308a52b",
    "metadata": {},
    "outputs": [
     {
@@ -1000,7 +1000,7 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Python 3 (ipykernel)",
+   "display_name": "Python 3",
    "language": "python",
    "name": "python3"
   },
@@ -1014,7 +1014,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.10.9"
+   "version": "3.7.6"
   }
  },
  "nbformat": 4,