IATBDP

Code repository for the Introduction to Bayesian Probability Theory course

Written together with Carlo Panu

Brief explanation of the codes

fit_pol_ran.py

Code that tries to fit the data contained in data.txt with a polynomial model looking for the optimal values ​​of the likelihood calculated in a set of parameters uniformly extracted in a range chosen by the user.

lupi.py

Exercise: Having seen M wolves, having tagged them and recognizing r tagged wolves out of n observed at a later time, estimate the total population N.

metropolis_hastings.py

Sampling a Gaussian using the metropolis-hastings algorithm

SIRD.py

Simulation of SIRD model

nested_sampling.py

Simple code that implements the nested sampling to compute the evidence D-dimensiona gaussian. The posterior distributions of the parameters are also calculated. It was always assumed that the a priori distribution was uniform according to the indifference principle.

fit_nested_sampling.jl

Code for fitting data using nested sampling. In this case, as an example, we wanted to use the same data for the fit_pol_ran.py code and also the same function as a theoretical model. Any changes for other models are not particularly complicated. The calculations of the average values ​​of the parameters are calculated starting from the various posterior distributions for the sole purpose of carrying out a posterior predictive check.