George Kahrimanis | Searcharxiv

arXiv2004

Direct pivotal predictive inference

Without assuming any pdf for some measured parameter, we derive a predictive pdf for the outcome of a second measurement, given the outcome of the first measurement and two common assumptions about the noise. These are that (1) it is additive, and (2) it is of some known pdf. The argument is based on a Bayesian analysis of the noise when no pdf is provided for the value of the parameter. In this way we avoid assuming an ad-hoc prior. We clarify how this method of direct predictive inference is distinct from fiducial prediction. We specify the distinct flaw in the fiducial argument, and outline the importance of this development in the foundations of probability and statistics. Keywords: nonparametric predictive inference, direct pivotal argument, pivotal argument, fiducial argument, fiducial prediction, Bayesian inference, reference prior, reference class.

math.ST↗

arXiv2003

Single or combined location measurements of the same parameter without prior probability. (Altern. title, Parametric inference as useful illusion; Part 1)

Motivation. This version is based solely on the calculus of probability, excluding any statistical principle. "Location measurement" means the pdf of the error is known. When the datum is obtained, intuition suggests something like a pdf for the parameter; here we attempt a critical examination of its meaning. Summary. In default of prior probability the parameter is not defined as a random variable, hence there can be no genuine prior-free parametric inference. Nevertheless prior-free predictive inference regarding any future datum is generated directly from the datum of a location measurement. Such inference turns out as if obtained from a certain pdf ("fiducial") indirectly associated with the parameter. This false pdf can expedite predictive inference, but is inappropriate in the analysis of combined measurements (unless they all are location measurements of the same parameter). Also it has the same distribution as the ostensible Bayesian posterior from a uniform "prior". However, if any of these spurious entities is admitted in the analysis, inconsistent results follow. When we combine measurements, we find that the quantisation errors, inevitable in data recording, must be taken into consideration. These errors cannot be folded into predictive inference in an exact sense; that is, we cannot render a predictive distribution of a future datum except as an approximation. Keywords: location measurement; combination of observations; parametric inference; predictive inference; prior-free inference; quantisation error; digitisation; frequentist interpretation; the fiducial argument; fiducial probability; pivotal inference; intuitive assessment; prior-free assessment

physics.data-an↗

arXiv1997

Pion-nucleus elastic scattering on 12C, 40Ca, 90Zr, and 208Pb at 400 and 500 MeV

Pion-nucleus elastic scattering at energies above the Delta(1232) resonance is studied using both pi+ and pi- beams on 12C, 40Ca, 90Zr, and 208Pb. The present data provide an opportunity to study the interaction of pions with nuclei at energies where second-order corrections to impulse approximation calculations should be small. The results are compared with other data sets at similar energies, and with four different first-order impulse approximation calculations. Significant disagreement exists between the calculations and the data from this experiment.

nucl-ex↗