Bayesian Methods

Environment setup

import platform

print(f"Python version: {platform.python_version()}")
assert platform.python_version_tuple() >= ("3", "6")

import numpy as np

print(f"NumPy version: {np.__version__}")

from IPython.display import YouTubeVideo
Python version: 3.7.5
NumPy version: 1.18.1

Bayes’ theorem

Thomas Bayes (1701-1761)

English statistician, philosopher and presbyterian minister.

Thomas Bayes

Bayes’ legacy

  • Blaise Pascal (1623-1662) pioneered the study of probabilies of effects given causes.

  • On the contrary, Thomas Bayes proposed a formula, known as Bayes’s theorem, for computing the probability of a cause given an effect.

Intuitive explanation

YouTubeVideo("HZGCoVF3YvM")

Quick proof

YouTubeVideo("U_85TaXbeIo")

Naïve Bayes

Naïve Bayes in a nutshell

  • Set of (supervised) learning algorithms based on applying Bayes’ theorem.

  • “Naïve” assumption: conditional independence between every pair of features given the value of the class variable.