Printed in Great Britain Approximate predictive pivots and densities

This paper suggests two predictive likelihoods that can be applied in almost any parametric model setting. The first can sometimes be interpreted as an approximate predictive pivot (Barnard, 1986) while the second is often an approximation to a Bayesian predictive density with a flat prior. The issue of calibrating various predictive likelihoods in terms of long run predictive coverage is also discussed and a specific criterion by which these likelihoods can be compared is proposed