# Cosmological parameter inference with Bayesian statistics

## TL;DR

This paper reviews Bayesian statistical methods and MCMC algorithms for cosmological parameter inference, demonstrating their application to the standard and alternative cosmological models using observational data.

## Contribution

It provides a comprehensive overview of Bayesian techniques and introduces an MCMC implementation for testing cosmological models against observational data.

## Key findings

- Identified best-fit parameters for the $\\Lambda$CDM model.
- Compared alternative cosmological models using MCMC.
- Demonstrated the effectiveness of Bayesian methods in cosmology.

## Abstract

Bayesian statistics and Markov Chain Monte Carlo (MCMC) algorithms have found their place in the field of Cosmology. They have become important mathematical and numerical tools, especially in parameter estimation and model comparison. In this paper, we review some fundamental concepts to understand Bayesian statistics and then introduce MCMC algorithms and samplers that allow us to perform the parameter inference procedure. We also introduce a general description of the standard cosmological model, known as the $\Lambda$CDM model, along with several alternatives, and current datasets coming from astrophysical and cosmological observations. Finally, with the tools acquired, we use an MCMC algorithm implemented in python to test several cosmological models and find out the combination of parameters that best describes the Universe.