Who is Bayes? What is Bayes?

Bayesian Data Analysis in Python

Michal Oleszak

Machine Learning Engineer

Who is Bayes?

Thomas Bayes

¹ Public Domain, https://commons.wikimedia.org/w/index.php?curid=14532025

A weatherperson forecasting 50% or rain.

Heavy, dark clouds and a thunder.

Bayesian inference means updating one's belief about something as the new information becomes available.

Bayesian inference means updating one's belief about something as the new information becomes available.
It is quite different from the classical approach.

	Frequentist (classical) approach	Bayesian approach
probability
parameters

Bayesian inference means updating one's belief about something as the new information becomes available.
It is quite different from the classical approach.

	Frequentist (classical) approach	Bayesian approach
probability	proportion of outcomes	degree of belief
parameters

Bayesian inference means updating one's belief about something as the new information becomes available.
It is quite different from the classical approach.

	Frequentist (classical) approach	Bayesian approach
probability	proportion of outcomes	degree of belief
parameters	fixed values	random variables

Natural handling of uncertainty (because parameters have distributions!).
Possibility to include expert opinion or domain knowledge in the model (because probability means the degree of belief!).
No need to rely on fixed constants such as p-values.
Statistically correct even with little data.
Often coincides with frequentist results, but offers more flexibility to build custom models.

A distribution of a random variable specifies what values this variable can take, and with what probabilities.
Can be discrete (finite set of possible values) or continuous (infinitely many possible values)
Continuous distributions can be visualized on a density plot.

A symmetric, bell-shaped curve peaking around the X-axis value of 165.

print(draws)

[146.58686154393, 159.40688614250, ..., ]

print(len(draws))

import matplotlib.pyplot as plt
import seaborn as sns
sns.kdeplot(draws, shade=True)
plt.show()

A symmetric, bell-shaped curve peaking around the X-axis value of 165.

Bayesian Data Analysis in Python