parameterization

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parameterization

Dave C
I have been reading through your book and am anxious to use more Bayes in my work. Finding the correct parameters for my priors is a challenge. For example, on page 275 of your book it says that 95% of nail tosses turned up tails (laying down) and that there were 20 tosses. The beta parameters are therefore 2 and 20 (for a and b respectively). How did you get these parameters from 95% and 20 tosses? I tried applying the equations on page 83 to no avail. Any help would be appreciated.

Thanks!
Dave
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Re: parameterization

John K. Kruschke
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Sorry if that passage of the book was a bit cryptic. Here's the idea.

Suppose we start with a generic beta( theta | a=1 , b=1 ) "proto-prior".

Then, suppose we have some fictional data that express our prior beliefs, in this case getting 95% tails in 20 tosses. That is, we fictionally observe z=1 head in N=20 flips. If we update the proto-prior with these fictional data, we get
beta( theta | a+z , b+N-z ) = beta( theta | 1+1 , 1+19 ) = beta( theta | 2 , 20 )
as our new prior based on the fictional data.

It's the same process as if we had real previous data with z=1 and N=20, but here we have fictional data to express our prior beliefs. In general, it's often easier to express prior beliefs in terms of idealized data than in terms of parameter values...

Hope that helps.

And thanks for reading the book!

--John

John K. Kruschke, Professor
Doing Bayesian Data Analysis
The book: http://www.indiana.edu/~kruschke/DoingBayesianDataAnalysis/

The blog: http://doingbayesiandataanalysis.blogspot.com/





On Tue, Sep 24, 2013 at 6:13 PM, Dave C [via Doing Bayesian Data Analysis] <[hidden email]> wrote:
I have been reading through your book and am anxious to use more Bayes in my work. Finding the correct parameters for my priors is a challenge. For example, on page 275 of your book it says that 95% of nail tosses turned up tails (laying down) and that there were 20 tosses. The beta parameters are therefore 2 and 20 (for a and b respectively). How did you get these parameters from 95% and 20 tosses? I tried applying the equations on page 83 to no avail. Any help would be appreciated.

Thanks!
Dave


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