Bayesian Inference of Cosmological Parameters and Hubble's Constant

In this project, we will use bayesian inference to estimate the matter density parameter, the dark energy density parameter and the Hubble constant using Supernova luminosity data.

Table of contents

• Introduction
• Repository Structure
• Reading
• Authors

Introduction

This project is done as part of the Data Science for Science course (PHY 250) at UC Davis in Spring 2020. The goal of this project is to use bayesian inference to estimate cosmological parameters using Supernovae luminosity data. More specifically, we estimate the matter density parameter, the dark energy density parameter and the Hubble constant using the $\Lambda$ CDM + $\Omega_K$ model of the universe. We estimate the parameters by inferring posterior probability densities of cosmological parameters from distance vs. redshift data with the use of Markov Chain Monte Carlo. The data used is described in Scolnic et al. (2018) and can be found here.

Repository Structure

Here is what each file in the repository contains:

presentation.ipynb - This notebook contains all the top level calls to produce the bayesian inference results and do the testing.

core_mcmc_functions.py - This file contains all the core mcmc chain functions.

prior_likelihood.py - This file contains the prior and likelihood functions used during bayesian inference.

theoretical_mag.py - This file contains the apparent magnitude calculator function using the cosmological model.

test_function.py - This file contains all the test functions.

lambda_cdm_functions.py - This file contains all the functions needed to run the mcmc chain test for the Lambda CDM model.

lcparam_DS17f.txt, sys_DS17f.txt - These are the data files.

Reading

Refer to the resources provided below to better your understanding of the cosmological concepts and the bayesian inference model used in this project.

Cosmology:

1. https://phys.libretexts.org/Courses/University_of_California_Davis/UCD%3A_Physics_156_-_A_Cosmology_Workbook/A_Cosmology_Workbook/16%3A_Distance_and_Magnitude

2. https://phys.libretexts.org/Courses/University_of_California_Davis/UCD%3A_Physics_156_-_A_Cosmology_Workbook/A_Cosmology_Workbook/17%3A_Parallax%2C_Cepheid_Variables%2C_Supernovae%2C_and_Distance_Measurement

Monte Carlo Markov Chain:

1. https://machinelearningmastery.com/markov-chain-monte-carlo-for-probability/

2. https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&cad=rja&uact=8&ved=2ahUKEwiVk9ml3MruAhWNvp4KHUP6CkMQFjABegQIAhAC&url=https%3A%2F%2Ftowardsdatascience.com%2Ffrom-scratch-bayesian-inference-markov-chain-monte-carlo-and-metropolis-hastings-in-python-ef21a29e25a&usg=AOvVaw3DPIB2woz5amzOtKgCyhx4

Authors

Avinash (aavinash@ucdavis.edu), Kyle (kjray@ucdavis.edu), Pratik (pjgandhi@ucdavis.edu), Sudheer (ssreedhar@ucdavis.edu)