Greetings,
I've been doing some exploratory work recently with quantile regressions
as a way of modeling certain types of insurance data. I have also been
reviewing the literature on Bayesian quantile regression and I am
working on developing a basic MCMC estimator.
One important dimension to this data is that results of the analysis
need to be regularly communicated to others in my company who are not
well-versed in statistics. I've found that when using traditional
(conditional mean) regression, the usual practice of presenting
estimated coefficients, their standard errors, p-values, prediction
confidence intervals, and an R-squared goodness-of-fit measure, usually
do a pretty good job of communicating the basic findings. In the case of
(frequentist) quantile regression, one can readily calculate an
analogous set of diagnostics, including a quantile-based R-squared. In
my experience, the basic idea that R-squared expresses how well a linear
model "fits" a scatter of data is intuitively appealing to
non-statisticians.
With a Bayesian estimator, however, I am unsure how to summarize and
discuss results in a way that a non-technical audience would grasp. I
was hoping that other Allstat subscribers might offer some ideas or
suggestions based upon their experiences of how one could effectively
articulate statistical findings in a compelling way. I suppose one can
calculate the Bayesian analogs to the usual frequentist statistics,
based upon the associated posterior distributions. These would at least
be familiar quantities to my usual audience. That said, I am unsure how
one might go about presenting a summary Bayesian goodness-of-fit
measure, or even if such a measure makes sense.
I would very much appreciate any ideas that other list members would be
will to share.
Thank you.
Best regards,
Mark
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