Xi'an's Og

Following our arXival on the new version of our HPD based Gelfand & Dey estimator of evidence, I got pointed at Wang et al. (2018), which I had forgotten I had read at the time (as testified by an ‘Og entry). Reading my own comments, I concur (with myself¹⁸!) that the method is not massively compelling since it requires a partition set that is strongly related with the targeted integral. The above illustration for a mixture, that is for a pseudo posterior that is a mixture with two Gaussian components with known variance, also shows (in reverse) the curse of dimension and the need for finely tuned partitions. Said partition corresponding to the myriad of sets on the rhs. With such a degree of partitioning, Riemann integration should also produce perfect estimate, as shown by the zero error in the resulting estimator (Table 4).

This entry was posted on November 21, 2025 at 12:25 am and is filed under Books, Statistics, University life with tags Bayesian Analysis, curse of dimensionality, estimating a constant, evidence, harmonic mean estimator, HPD region, importance sampling, marginal likelihood, Monte Carlo Statistical Methods. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.