This repo contains a proof of concept for Bayesian Inference in Python elaborated using both NumPy and a Fortran 95 engine to perform data generation and Markov Chain Monte Carlo (MCMC) simulation.
pip3 install numpy pandas matplotlib corner
The notebook generates a linear relationship between 2 variables x and y with a certain degree of uncertainty, given two input parameters m (gradient) and b (y-intercept).
Assuming a log-uniform distribution for the possible parameters m and b and a log-gaussian distribution for the likelihood of a value generated by these parameters, an MCMC random walk is performed using the Metropolis algorithm in order to maximise said likelihood and estimate m and b: this will allow us to visualize the posterior probability density function (PDF) for the two parameters.
An initial guess for the parameters is given as well as a step size for the variation of the parameters.
The random walk quickly equilibrates variable to oscillate around an estimate.
The estimates are extracted using the corner package:
The estimates are incredibly accurate as m = 0.72 plus-minus 0.05, compared to a true value of m = 0.736; and b = 31.50 (+1.98, -2.43), compared to a true value of b=30. Both are with estimated error range.
Similar results are obtained using the Fortran Engine:
