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How to Predict whats next ?


Overview :

  • What is Bayesian Statistics?

  • Difference between Bayesian statistics and Regular statistics


What is Bayesian Statistics?


Bayesian statistics is a particular approach of applying probability to statistical problems. It provides people with tools to update their beliefs in the evidence of new data.


The model of Bayesian statistics is :


Future information = prior information + data information



Formally :


Posterior = likelihood*prior

OR

P(θ|y) ∝ p(θ) p(y|θ)



where :


∝ is a symbol for proportionality .

θ is an unknown parameter .

y is data .

P(θ) is the density functions of the prior distributions .

p(θ|y) is the density functions of the posterior distributions .

p(y|θ) is the density functions of the sampling distributions .



Let’s understand this by an example :


Suppose there’s a cricket match to be played and there are two teams, team A and B, from prior information of recent 10 matches team A won 8 matches and team B only managed only 2.


So, on the basis of prior information what will be your answer for the next match?

I bet you would say team A.


Let’s add some twist to this problem, what if you’re told that the temperature was cold (<10 degrees) when team B won and hot (>10 degrees) on all the days when team A won. Now tell me what will be your answer?


For solving these kinds of problems, we need Bayesian statistics. We all somehow have used Bayesian statistics in our day to day life unintentionally.



Let’s discuss main difference between Bayesian statistics and Regular one :


Regular statistics (or Frequentist statistics) tests whether an event (hypothesis) will occur or not. It is helpful when the experiment is being repeated under the same conditions as it calculates the probability of an event in the long run of the experiment. The major flaw under the Regular statistics is that it is not practical that the experiment is conducted under the same situations repeatedly numerous other factors can also affect the outcome of the result but in Regular statistics these things are not taken in mind while calculating the results.


Whereas


In Bayesian statistics the outcome is dependent on the numerous factors which can affect our outcome or result. In Bayesian we include the dependence of other factors while calculating the probabilities (i.e. using conditional probabilities).

In Regular statistics the resultant probability depends on the number of times the experiment is repeated


Whereas


In the Bayesian statistics the outcome depends on the different factors which can make our outcome more robust and accurate.


Let’s test what you have just learned.

Written by Vivek Mittal ( Graduate in B.com (hons) from University of Delhi and 2 Actuarial Papers passed from IFOA )

Edited by Ayush Maskara ( Actuarial Management Trainee at WNS )

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