### Bayesian Statistics: In a layman terms

What is Bayesian Statistics: (I will try to explain in easy terms)

Often researchers
investigating an unknown population parameter have information available from
other sources in advance of the study that provides a strong indication of what
values the parameter is likely to take. This additional information might be in
a form that cannot be incorporated directly in the current study. The classical
statistical approach offers no scope for the researchers to take this additional
information into account. However, the Bayesian statistics is the approach
which allows to take this additional information into account while estimating
a population parameter.

Let me explain you with
the help of an example:

4 championship races had been done between Mr. A and Mr. B.

Out of which A has won 3 races and B has won
1 race. So, on whom are you going to bet your money in the next race?

You will Say Mr. A because
P(A) = 0.75 and P(B) = 0.25

So your initial estimate about B is P(B) = 0.25

Now I will give you
additional information say, there was a rain when Mr. B won and there was rain
once when Mr. A won. And in the next match there will definitely be a rain.

So now I ask you again on
whom will you bet your money?

Let’s decode the answer:

1. P(R) = 0.50
(Because rain happened twice out of 4 matches)

2. P(R|B) = 1 (Because
whenever Mr. B won there was a rain)

So I want to find out that
what is probability that in the next race Mr. B will won if it is given that
there will be a rain:

P(B|R) = P(R|B)*P(B)/P(R)
= 0.50

I hope you know how this
formula comes up otherwise you can mention me in comments I will tell you how.

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Conclusion: Initially we
comes up with an answer that P(B) = 0.25 which is my prior estimate and then I
give additional information about rain which we incorporated in the form of
conditional probability i.e. P(R|B) = 1 and then ultimately we find P(B|R)
which is my posterior probability.

So you see how with the
help of Bayesian statistics I incorporated additional information into my
current study and how my value changes from 0.25 to 0.50.

Statistics seems easy
now. 😊

Its an art and you are an
artist.

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