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The Optimal Discounting Parameter of the Power Prior under Predictive Log-Loss · arXivDesk

2608.12159Aug 12, 2026

The Optimal Discounting Parameter of the Power Prior under Predictive Log-Loss

Yuriy A. Reznik

Abstract

The power prior of Ibrahim and Chen incorporates historical data into a Bayesian analysis by raising the historical likelihood to a power $a_0 \in [0, 1]$ . The choice of the exponent has remained an open question. This paper gives a closed-form answer under the predictive log-loss. For a model with $d$ parameters, a historical sample of size $N_0$

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The power prior of Ibrahim and Chen incorporates historical data into a Bayesian analysis by raising the historical likelihood to a power a₀ ∈ [0, 1]. The choice of the exponent has remained an open question.

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The paper addresses: The Optimal Discounting Parameter of the Power Prior under Predictive Log-Loss.
The power prior of Ibrahim and Chen incorporates historical data into a Bayesian analysis by raising the historical likelihood to a power a₀ ∈ [0, 1].