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@Potatoasad
Potatoasad committed Oct 28, 2024
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72 changes: 39 additions & 33 deletions docs/Examples/gravpop_tutorial.ipynb
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"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",
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{
"cell_type": "code",
"execution_count": 3,
"id": "b1a23da0",
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"metadata": {},
"outputs": [
{
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},
{
"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`."
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{
"cell_type": "code",
"execution_count": 4,
"id": "8926b86d",
"id": "605cd216",
"metadata": {},
"outputs": [
{
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},
{
"cell_type": "markdown",
"id": "15496b80",
"id": "9ece8b92",
"metadata": {},
"source": [
"We can now construct the data product we need:\n",
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{
"cell_type": "code",
"execution_count": 5,
"id": "af61ce61",
"id": "f97e716f",
"metadata": {},
"outputs": [
{
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},
{
"cell_type": "markdown",
"id": "71db1530",
"id": "0cf13137",
"metadata": {},
"source": [
"we now have our data in the correct format. \n",
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},
{
"cell_type": "markdown",
"id": "5c02d0b1",
"id": "3554d94c",
"metadata": {},
"source": [
"# Models"
]
},
{
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"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",
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{
"cell_type": "code",
"execution_count": 1,
"id": "fa13cbe8",
"id": "d79b6aff",
"metadata": {},
"outputs": [],
"source": [
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},
{
"cell_type": "markdown",
"id": "c10fb445",
"id": "9abb71b8",
"metadata": {},
"source": [
"We can combine these building blocks however we like. Using the following operations:\n",
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{
"cell_type": "code",
"execution_count": 2,
"id": "3846c608",
"id": "455cd87a",
"metadata": {},
"outputs": [],
"source": [
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},
{
"cell_type": "markdown",
"id": "8706088c",
"id": "fe8759a0",
"metadata": {},
"source": [
"One can then evaluate this spin model on some set parameters"
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{
"cell_type": "code",
"execution_count": 9,
"id": "e880c5f9",
"id": "57e76904",
"metadata": {},
"outputs": [
{
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},
{
"cell_type": "markdown",
"id": "941211a5",
"id": "24618218",
"metadata": {},
"source": [
"## Sampled Models\n",
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},
{
"cell_type": "markdown",
"id": "b473e5ad",
"id": "ffa7625f",
"metadata": {},
"source": [
"# Population Likelihood\n",
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{
"cell_type": "code",
"execution_count": 15,
"id": "425accdc",
"id": "9490cfa7",
"metadata": {},
"outputs": [
{
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},
{
"cell_type": "markdown",
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"We can compute the loglikelihood for some hyper-parameters, and also confirm by computing the derivative that there are no nan derivatives.\n",
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{
"cell_type": "code",
"execution_count": 16,
"id": "b00b1586",
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"metadata": {},
"outputs": [
{
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},
{
"cell_type": "markdown",
"id": "1d61327c",
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"source": [
"All our models are auto-diff-able, so we can compute the gradient of the logpdf as below:"
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{
"cell_type": "code",
"execution_count": 18,
"id": "ba65cdd4",
"id": "a053808c",
"metadata": {},
"outputs": [
{
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},
{
"cell_type": "markdown",
"id": "7e11c500",
"id": "86c88b47",
"metadata": {},
"source": [
"One can also load up the event and selection function data from a file:"
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{
"cell_type": "code",
"execution_count": 19,
"id": "96c86fd5",
"id": "9f1b8c10",
"metadata": {},
"outputs": [],
"source": [
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},
{
"cell_type": "markdown",
"id": "a1be31ef",
"id": "7b98306c",
"metadata": {},
"source": [
"# Sampling\n",
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{
"cell_type": "code",
"execution_count": 22,
"id": "83ce1f8d",
"id": "8cd350ea",
"metadata": {},
"outputs": [],
"source": [
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},
{
"cell_type": "markdown",
"id": "3bd0c662",
"id": "4701fe32",
"metadata": {},
"source": [
"Then, we can construct a `Sampler` object and put in our settings."
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{
"cell_type": "code",
"execution_count": 24,
"id": "23f28bb0",
"id": "e432d77c",
"metadata": {},
"outputs": [],
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},
{
"cell_type": "markdown",
"id": "5e388f7b",
"id": "08a66057",
"metadata": {},
"source": [
"and we can begin sampling"
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{
"cell_type": "code",
"execution_count": 25,
"id": "b7de385f",
"id": "251e1512",
"metadata": {},
"outputs": [
{
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},
{
"cell_type": "markdown",
"id": "3c5a1549",
"id": "6d494a74",
"metadata": {},
"source": [
"we can see the dataframe holding the hyper-posterior samples in:"
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{
"cell_type": "code",
"execution_count": 28,
"id": "b26d5de3",
"id": "6c1c5497",
"metadata": {},
"outputs": [
{
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},
{
"cell_type": "markdown",
"id": "1f40581d",
"id": "c0db874e",
"metadata": {},
"source": [
"and here is a corner plot of our result"
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{
"cell_type": "code",
"execution_count": 31,
"id": "f11e5421",
"id": "bed347c9",
"metadata": {},
"outputs": [
{
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