Cosmology Parameter Estimation – MCMC & Fisher Matrix

This repository contains my Jupyter notebooks where I explore parameter estimation in cosmology using two main approaches:

1. Markov Chain Monte Carlo (MCMC) sampling, and
2. Fisher Matrix forecasting techniques.

The notebooks document both the code implementations and the underlying concepts step by step, with explanations, derivations, and analysis. The goal is not just to run the code but to understand how cosmological parameters are extracted from data and how uncertainties are quantified.

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Contents

• 📓 Jupyter Notebooks:

  • Walkthroughs of parameter estimation techniques.
  • Implementation of MCMC algorithms (e.g., Metropolis-Hastings).
  • Example likelihood functions relevant to cosmology.
  • Playing with the Fisher Matrix as a tool for forecasting constraints.

• 🧠 Conceptual Notes:

  • How likelihoods are constructed in cosmology.
  • Role of priors in Bayesian inference.
  • Comparison between Fisher Matrix approximations and full MCMC results.
  • Visualization of posteriors, confidence contours, and parameter degeneracies.

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Major Ideas

• MCMC in Cosmology:

  • Sampling the posterior distribution of cosmological parameters.
  • Estimating uncertainties and correlations.
  • Understanding convergence and mixing of chains.

• Fisher Matrix:

  • Using derivatives of the likelihood to estimate expected constraints.
  • Advantages (fast, approximate) and limitations (valid only near Gaussian likelihoods).
  • Exploring how Fisher forecasts compare with MCMC posteriors.

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Requirements

The notebooks are written in Python 3 and make use of common scientific libraries:

• numpy
• scipy
• matplotlib
• pandas
• emcee (for MCMC)
• corner
• camb
• getdist
• pyactlike

You can install dependencies with:

pip install -r requirements.txt

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How to Use

1. Clone the repo:

   git clone https://github.com/PhysicsiPhile/Cosmology.git
   cd Cosmology

2. Launch Jupyter:

   jupyter notebook

3. Open the notebooks and follow along with the explanations and code cells.

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Notes

• These notebooks are exploratory and educational — not meant as production-ready pipelines.
• I am still experimenting with different likelihood forms, samplers, and Fisher matrix toy models.
• Expect some rough edges, but the main aim is to document the learning process.

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Future Directions

• Adding examples with real cosmological data (CMB / LSS).
• Exploring more advanced MCMC samplers (e.g. Hamiltonian Monte Carlo).
• Extending Fisher Matrix analysis to multi-parameter, correlated cases.

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License

MIT License – feel free to use, modify, and share with attribution.