another version of the corrected harmonic mean estimator

A few days ago I came across a short paper in the Central European Journal of Economic Modelling and Econometrics by Pajor and Osiewalski that proposes a correction to the infamous harmonic mean estimator that is essentially the one Darren and I made in 2009, namely to restrict the evaluations of the likelihood function to a subset A of the simulations from the posterior. Paper that relates to an earlier 2009 paper by Peter Lenk, which investigates the same object with this same proposal and that we had missed for all that time. The difference is that, while we examine an arbitrary HPD region at level 50% or 80% as the subset A, Lenk proposes to derive a minimum likelihood value from the MCMC run and to use the associated HPD region, which means using all simulations, hence producing the same object as the original harmonic mean estimator, except that it is corrected by a multiplicative factor P(A). Or rather an approximation. This correction thus maintains the infinite variance of the original, a point apparently missed in the paper.

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