Is it a valid approach, when estimating a bayesian model, to build a 3-dimensional graph which plots the bayesian model estimates of the coefficient (y-axis) dependent on different assumed prior values for the standard deviation (z-axis) and mean (x-axis) of the prior?
Is this what is meant by superpriors?
If yes, can someone point me towards some relevant papers/books?
Thanks in advance.
https://stats.stackexchange.com/questions/91344/advice-on-sensitivity-analysis-for-priors-in-bayesian-statistics
https://stats.stackexchange.com/questions/91344/advice-on-sensitivity-analysis-for-priors-in-bayesian-statistics
A super prior is a distribution imposed on the unknown parameters of a prior distribution when the real prior distribution is unknown - also called a hyperprior (probably the more common term). You can find more information by looking into hierarchical Bayes modeling.
Yes, manipulating the prior is a typical example of model checking/sensitivity analysis in Bayesian Statistics.
This way you can then see to what extent the posterior inference changes with different models/priors. If there is very little change in the results you could argue that the results are mostly driven by the data as they are rather robust towards different prior specifications. Which is a usefull thing to do since you'll want to show people that your results are not just the consequene of some partical set of priors.
To show the results of the sensitivity analysis you have a bunch of options really, you could compare posterior means, you could make a table with key posterior values under the different priors, you could make plots of posteriors with the priors as different groups etc.
Some books that discuss this further are are: "Bayesian Biostatistics" by Lesaffre and "Bayesian Data Analysis" by Gelman
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