probit_bayesian_MCMC

MS in Data Science

Implementation & theory of a Metropolis Hastings and a Gibbs Algorithm to estimate the parameters of a Probit linear model on simulated and real data.

Authors

• Chiavarino Federico
• Giancola Simone Linkedin | webpage | e-mail
• Liscai Dario
• Marchetti Simone

Main Files:

• compt_stat_script.ipynb: Jupyter notebook with main functions' calls and plots
• report.pdf: theoretical introduction to the topic, analysis of the results, explanation of the procedures to implement the two algorithms

Theoretical Knowledge and Techniques used

• Linear Algebra
• Probability & Statistics
• Generalized Linear Models
  • Fisher Information
  • MLE
  • OLS
• Bayesian Probability
• Markov Chain Monte Carlo Algorithms
  • Metropolis Hastings Algorithm
  • Gibbs Sampling Algorithm
  • Markov Chain convergence diagnostic checks
• Python Programming
  • Numpy
  • Matplotlib
  • Scipy
  • prototyping
  • parameter exploration

Structure of the Repository

Assignment_files folder: material provided for the assignment describing requirements

• Computation Statistics Project.pdf : assignment description and desired outcomes
• Albert and Chib 1993.pdf : main paper to reference
• Bayesian Probit.pdf : slides with further description and hints about the problem

Report auxiliary Files: all .py scripts. These are splits of the original code to tidy up the notebook.