During my MSc Data Science course, I completed a software exercise as the main assignment for the Data Analysis Techniques (890F3) module.

The exercise, written in Python, mostly focuses on key data analysis techniques and their application in Physics. Of course, these methods also apply across numerous other domains. This was a challenging module, but really helped me revisit the fundamentals in a very rigorous way. I was able to gain a much greater understanding of the theoretical basis of these techniques and how to correctly interpret and apply them.

This exercise consisted of 3 parts:

1. Monte Carlo parameter estimation for muon decay
   • Use the transformation/inversion method to find an expression for the inverse CDF.
   • Generate 1,000 \(x\) values, where \(x \sim p(x)\) and \(\alpha\) = -0.33. Plot histogram.
   • Use maximum likelihood and method of moments to estimate \(\alpha\) from the simulated data.
2. Polynomial regression model selection
   • Determine which order of polynomial best fits the data.
   • Tabulate \(\chi^{2}\), \(\chi^{2}\) confidence level, AIC and BIC for each order of polynomial.
   • Plot best fit model with the data.
3. Markov chain Monte Carlo parameter recovery with the galaxy stellar mass function
   • Use the transformation/inversion method to generate 1000 synthetic stellar masses, distributed according to the Schechter function.
   • Plot histogram of generates stellar masses.
   • Use the Affine Invariant Ensemble Sampler algorithm to recover model parameters.