Statistics and Data Science Seminar
Keli Liu
Stanford University
Stat Wars Episode VI: Return of the Fiducialist
Abstract: Priors are the path to the dark side. Fisher developed the Fiducial argument to obtain prior free "posterior" inferences but at the
seeming cost of violating basic probability laws. Was Fisher crazy or did madness mask innovation? Fiducial calculations can be
easily understood through the missing-data perspective which illuminates for us that the Fiducial "posterior" is in fact a prior updated
not with the full data likelihood, but a partial likelihood in the spirit of Cox regression. Just as Cox regression arose from a
need to render inferences robust to an unknown hazard function, so Fiducial inferences are insensitive to the prior. While Statistics has
fixated two extremes---fully conditional (but fragile) Bayesian inferences or unconditional (but robust) Frequentist inferences---a
compromise via partial conditioning has gone ignored. Surely, the middle ground is more fiducial than either extreme.
Wednesday September 3, 2014 at 4:00 PM in SEO 636