Beta Function used in Beta distribution

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Discussion Overview

The discussion revolves around the beta function and its application in the beta distribution, particularly in the context of Bayesian statistics. Participants seek to understand the beta function's role and how normalization occurs within the beta distribution, while also addressing the prerequisites for studying the Dirichlet distribution.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested
  • Homework-related

Main Points Raised

  • One participant requests a layman's explanation of the beta function and its relationship to the beta distribution, expressing difficulty with the concepts involved.
  • Another participant suggests a resource for understanding the beta distribution in a Bayesian context.
  • A participant expresses confusion specifically about the normalization process in the beta distribution and questions whether the beta function is solely responsible for this normalization.
  • Some participants note that the beta distribution can serve as the posterior distribution under a uniform prior in Bayesian analysis, but this is seen as complex for novices.
  • One participant recommends looking into the Beta Integral to understand how the beta function is derived in the context of the beta distribution.

Areas of Agreement / Disagreement

Participants express varying levels of understanding regarding the beta function and its applications. There is no consensus on the best way to explain these concepts, and some participants feel that the existing explanations are too complex for beginners.

Contextual Notes

Participants highlight the need for simpler explanations and examples, particularly regarding the normalization aspect of the beta distribution. There is an acknowledgment of the prerequisites needed to fully grasp the Dirichlet distribution, which may complicate the discussion.

Who May Find This Useful

This discussion may be useful for individuals interested in Bayesian statistics, the beta function, and the beta distribution, particularly those seeking foundational understanding or clarification of these concepts.

justin001
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Could anyone explain in laymen terms what really the beta function does as said in Beta Function:https://en.wikipedia.org/wiki/Beta_function .I know that gamma function is used to find the factorial of real numbers but when it comes to beta function I can't get what really beta function does.I am reading an article: Empirical Analysis:http://1drv.ms/1GUqmdO:and it explains about Dirichlet distribution:https://en.wikipedia.org/wiki/Dirichlet_distribution

After looking for the prerequisites needed to study Dirichlet distribution as said in Prerequisites for Dirichlet distribution:http://www.metacademy.org/graphs/concepts/dirichlet_distribution#focus=5zwsgm7z&mode=explore I have reached up to Beta distribution:https://en.wikipedia.org/wiki/Beta_distribution in the tree.This is where the beta function comes in beta distribution and that's where I'm stuck.Could anyone help me.

I would like an answer that doesn't uses too much symbols,concepts and jargon terms.I would like a simple explanation for Beta function and how it is used in Beta distribution.
 
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Stephen Tashi said:
Since you're reading Bayesian material, try this explanation: http://www.statlect.com/beta_distribution.htm
I have went through all of these many times before but the concept that get my head stuck is normalization in beta distribution.I would like to know how normalization takes place in beta distribution.Is it(normalization) done by the beta function alone or is there any other factor involved?Also I can't see anything related to Bayesian here.Did you mean to say about conditional probability?
 
justin001 said:
I can't see anything related to Bayesian here.

The explanation gives an example where the beta distribution is the posterior distribution when a uniform prior on [0,1] is assumed ( a Bayesian approach) and particular data is observed.
 
Stephen Tashi said:
The explanation gives an example where the beta distribution is the posterior distribution when a uniform prior on [0,1] is assumed ( a Bayesian approach) and particular data is observed.

I think that's too heavy for an novice in Bayesian statistics.Could you show an example by plugging the values α and β that might give an intuition into how beta distribution works.
 
Look up the Beta Integral and by taking out the constant not related to the integral you will see that you get a Beta function back as a result.

Hence the name Beta distribution.
 

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