AS4PA final project

As a final project of the course, together with Paolo Zinesi, we implemented a Naive Bayes classifier for Fake News recognition, in the context of social media posts. More information can be found in the repository of the project: Fake News recognition. The resulting Shiny app is available here.

AS4PA exercises

Below you can find all the exercises carried out during the course. To download them in Rmd format, follow the link to the GitHub repository.

• Exercises R Laboratory 01
  First exercises in R to become familiar with the syntax and to start writing some basic instructions. In particular, the last one consists of a brief analysis of Covid-19 Vaccine data.

• Exercises R Laboratory 02
  • Review of basic probability concepts
  • Probability distributions in R
• Exercises R Laboratory 03
  • Random numbers generation
  • Markov’s inequality
  • Chebyshev’s inequality
  • The Six Boxes Toy Model: inference and simulation
• Exercises R Laboratory 04
  • Community Mobility Open Data (analysis of Covid-19 data sets)
  • Random number generation using the middle square algorithm
  • Bayesian Inference
• Exercises R Laboratory 05
  • Bayesian inference for a Poisson process
  • The Lighthouse problem
  • Signal over Background
• Exercises R Laboratory 06
  • Bayesian computation of posterior probability
  • Frequentist and Bayesian estimator
  • Hypotesis Testing
  • MCMC with JAGS (Just Another Gibbs Sampler)

Statistical Mechanics of Complex Systems projects

Application of the MaxEnt Principle
The MaxEnt principle can be used to find the less biased probability distribution compatible with a set of constraints, by maximizing the Shannon entropy subject to these constraints. In this project I apply the MaxEnt principle to some data, genered according to a known distribution, using the measured k-th moments as constraints. I consider only one simple discrete case, but in the future it would be interesting to apply this study on well-known continuous distributions such as the Gaussian and the Exponential.

Noise-induced schooling of fish
In this project we want to simulate the dynamics of schools of fish and compare the results with those shown in the article Noise-induced schooling of fish. In particular, we focus on a mean field model based on pairwise interactions.

The project was carried out together with Alberto Coppi.