Question

what is Bayesian statistics?

Answer 1

From the given question we are asked to explain the Bayesian statistics. So, for solving this question we will use the probability concept and also we will use the definition of Bayesian statistics. Using this we will explain the concept and solve the given question.

Complete step-by-step solution:
Let us first state the concept. “The concept of Bayesian statistics is a mathematical procedure that applies probabilities to statistical problems in mathematics. It provides people the tools to update their beliefs in the evidence of new data.”
We are aware that the classical statistics uses techniques like the Ordinary Least Squares and Maximum Likelihood and these are the conventional type of statistics that we usually find in most textbooks covering topics like estimation, regression, etc... We can thus say that in fact, Bayesian statistics is all about probability calculations.
Now, let us understand more about it. So, the Bayesian model is a statistical model where we use probability to represent all uncertainty within the model. Now, this can include both the uncertainty regarding the output and also the uncertainty regarding the input to the model.
The Bayes theorem describes the probability of an event based on the prior knowledge of the conditions that might be related to the event. If we know the conditional probability, we can use the bayes rule to find out the reverse probabilities.
We can now look at an example. The comparison of two data sets is a good one.
Let us suppose that out of all the 4 matches of chess between P and Q, P won 3 times while Q managed only 1. So, if we were to bet on the winner of the next match, who would that be? We know that it would be P.
Now, let us consider that, what if we are told that it snowed once when Q won and once when P won and it is definite that it will snow on the next date. So, who would we bet our money on now? By intuition, we can easily see that chances of winning for Q have increased. But here, we have the question as to how much. We can use the Bayesian statistics and we will get the required answer.

Note: Students should have good knowledge in the concept of probability and its applications. Bayesian theorem is a result in conditional probability, stating that for two random quantities y and $\theta$,
$\Rightarrow p\left( \dfrac{\theta }{y} \right)=p\left( \dfrac{y}{\theta } \right)\times \dfrac{p\left( \theta \right)}{p\left( y \right)}$ .