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BenS
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Bayes plot for effect screening

In the ''old" BayesPlotForFactors.jsl script there was an option to indicate the highest order interaction to consider when determining the posterior probability of a factor being active. Now that the Bayes plot has been included in Standard Least Squares under Effect Screening (hooray!) there is no place to indicate the highest order interactions to include in the calculation. Does anybody know what is the value used "by default", and why there is no longer that flexibility? 

 

Also, there is a change from Ridge Parameter Gamma to K contamination; what would the correspondence be among those two?

Thanks!

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Re: Bayes plot for effect screening

Confusion Alert! The Bayes plot provided in the Fit Least Squares platform and the one provided by the script are not the same method, although they are related.

 

First, the built-in plot was added to JMP a long time ago. (JMP 3?) It is based on the 1986 method by Box et. al. that only considers main effects. You cannot change that computation.

 

Second, the scripted plot was added to JMP sample files 10-15 years ago. It is based on the 1993 method by Box et. al. that was adapted to consider higher order terms.

 

So you have the chronology backwards.

 

The computations are completely different. The older method used K to define the ratio of the variance of the estimates with and without contamination (presence of non-null effects). You could specify individual prior probabilities for each parameter. The newer method uses a ridge parameter for shrinkage. It also uses a prior probability of 0.25 for all parameters. They both consider all potential terms within their respective scopes.

 

The papers behind each of these methods is very accessible. Box was a wonderful teacher and writer.

Learn it once, use it forever!
3 REPLIES 3
Highlighted

Re: Bayes plot for effect screening

Confusion Alert! The Bayes plot provided in the Fit Least Squares platform and the one provided by the script are not the same method, although they are related.

 

First, the built-in plot was added to JMP a long time ago. (JMP 3?) It is based on the 1986 method by Box et. al. that only considers main effects. You cannot change that computation.

 

Second, the scripted plot was added to JMP sample files 10-15 years ago. It is based on the 1993 method by Box et. al. that was adapted to consider higher order terms.

 

So you have the chronology backwards.

 

The computations are completely different. The older method used K to define the ratio of the variance of the estimates with and without contamination (presence of non-null effects). You could specify individual prior probabilities for each parameter. The newer method uses a ridge parameter for shrinkage. It also uses a prior probability of 0.25 for all parameters. They both consider all potential terms within their respective scopes.

 

The papers behind each of these methods is very accessible. Box was a wonderful teacher and writer.

Learn it once, use it forever!
BenS
New Contributor

Re: Bayes plot for effect screening

You're a wonderful writer as well, Mark! Thanks for the clarification. May I be curious: any technical reason as to why the Bayes Plot in Fit Least Squares has not been updated with the later version? Any reservations about that later method? Thanks!
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Re: Bayes plot for effect screening

It is not a technical matter, as far as I know. I believe that it is a matter of priority and direction. The Bayes Plot is a tool for model selection. Much effort is going to the new Generalized Regression platform in JMP Pro for the same purpose. You might request that the newer plot available as a script replace the older plot in the Fit Least Squares platform. See the JMP Wish List in the menu above. See if anyone else has requested this plot and vote for it or leave a new request otherwise.

 

I only use the Bayes Plot script. The earlier version (built-in) is not wrong, but as I said earlier, it only considers the main effect terms, so it is limited and I have seen many cases where an interaction was a big effect but neither factor exhibited a large posterior priority. The newer version of the plot represents a signficant improvement.

Learn it once, use it forever!
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