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.
