# 1. INTRODUCTION

Bayesian statistics is a way of reasoning about uncertainty in a systematic and mathematically rigorous way. It is named after the 18th-century mathematician and philosopher Thomas Bayes, who developed **a theorem that provides a way to update our beliefs about a hypothesis as we collect new data.**

In Bayesian statistics, we start with a prior probability distribution, which represents our beliefs about a hypothesis before we have seen any data. **As we collect new data, we update this prior distribution using Bayes’ theorem to obtain a posterior probability distribution, which represents our beliefs about the hypothesis after taking into account the data we have observed.**

# 2. EXAMPLE

To give an example, suppose we are interested in estimating the proportion of voters who will vote for a certain candidate in an upcoming election.

We start with a prior belief that the proportion of voters who will vote for the candidate is uniformly distributed between 0 and 1. As we collect new data, such as the results of a poll, we can update this prior distribution using Bayes’ theorem to obtain a posterior distribution that takes into account the new information we have.