A Study on the Power Parameter in Power Prior Bayesian Analysis

Being Bayesian in the 2020s: opportunities and challenges in the practice of modern applied Bayesian statistics

“…Other approaches attempt to determine an appropriate value of by optimization. Different information criteria, from the standard deviance information criterion to more complex penalized likelihood-type criterion, have been used [ 113 ] including the marginal likelihood [ 114 ] and the pseudo-marginal likelihood [ 115 ] which are evaluated using only the target data.…”

On efficient posterior inference in normalized power prior Bayesian analysis

“…In principle, the use of the normalized power prior does not necessarily assume a proper initial prior on $$\bm \theta$$, whereas an improper initial prior often results in a similar normalized power prior after incorporating information from D 0 . Moreover, if $$\pi _0({\bm \theta })$$ is improper, the power prior may not be proper for all $$\delta > 0$$, even for the commonly used reference priors (Han et al., 2022). As a result, the starting point δ 1 may not be close to 0 and can vary case by case.…”

Correction

“…Reference 1 show that Remark 3 in the appendix of this paper is incorrect; the result needs further regularity conditions in order to hold. Please see Theorem 2 in Reference 1.…”

“…Reference 1 show that Remark 3 in the appendix of this paper is incorrect; the result needs further regularity conditions in order to hold. Please see Theorem 2 in Reference 1. The authors would like to note that this in no way impacts any of the other results, theoretical or empirical, presented herein.…”