Since Kim Pearce's question provoked such interest, let me air this
sentence adapted from a paper I was asked to comment on. The author
used MCMC# to test a logistic model and stated in the results section:
"The posterior probability that [the effect I was looking for exists] is
very high: P(f>0|D)=0.97."
The only output shown was a table of logistic parameters: mean, sd, 5th
percentile, median and 95th percentile for each.
I opined that the author had probably mis-quoted the output from
Winbugs, and assume he has calculated 1-significance, though the
parameter mean and SD do not equate with a significance of .03.
Do Bayes experts recognise the use of posterior probability to provide
evidence in favour of H1, and do you consider it valid?
Allan
# The exact wording is "Posterior inferences were conducted by MCMC
sampling techniques using the Winbugs software." I suspect the passive
voice conceals third party computing.
PS Fitting a logistic model directly produced similar parameter
estimates, and the paper was condemned more for the inappropriate form
of the model and invalid inferences drawn about causality.
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