Bayesian Inference

 

Statistical Inference

Statistical inference is the process of analyzing the result and making conclusions from data subject to random variation.

In Simple,

There is an unknown quantity that we would like to estimate. We get some data. From the data, we estimate the desired quantity. There are two major approaches to this problem:

Frequentist (classical) Inference

Bayesian Inference

Bayesian inference is a method of statistical inference  in which Bayes' theorem is used to update the probability for a hypothesis as more evidence or information becomes available.

In the Bayesian approach the unknown quantity Θ is assumed to be a random variable, and we assume that we have some initial guess about the distribution of Θ. After observing the data, we update the distribution of Θ using Bayes' Rule.

Bayesian Inference is an application of Bayes Theorem.