Analyzing data is an interplay between modeling physical theories and using complex statistical inference to extract unbiased information from the data themselves. In the era of precision cosmology, data analysis has become a key tool for the falsification of cosmological theories and for the quest of finding new physical effects not predicted by our current modelization of the Universe.
Inevitably, many biases are introduced, willingly or not, in the procedure of extracting information from data since our theories are incomplete and our statistical inference is not perfect. Such biases could lead to wrong physical conclusions and particular care is required in deriving answers that are as free as possible from those biases.
In this series of two lectures, I will give an introduction to Monte Carlo Markov Chain (MCMC) and Machine Learning (ML) techniques for the inference of cosmological parameters. I will discuss their advantages and disadvantages and show how they can be used to gain accurate information about our Universe.
The first lecture will be dedicated to introducing the building blocks of statistical inference. Starting from the simplest example of fitting a linear model to data, I will introduce the main concepts behind the construction of MCMC and ML methods and show how to use them with real examples.
The second lecture will be dedicated to learning to use these methodologies to analyze real cosmological data and derive constraints on cosmological parameters. In particular, I will show the use of low-redshift (late-time) cosmological data to bound the Hubble parameter and discuss the results in view of the current literature on the Hubble tension.
