Exact Markov chains Monte Carlo methods for the normalised power prior

In statistical modeling with historical data, a central challenge is effectively integrating information from past studies with current data. This is particularly relevant in clinical trials and medical research, where leveraging historical data can improve the efficiency and robustness of statistical inferences. A natural approach in this setting is the use of informative priors, which incorporate prior knowledge into the analysis, thereby enhancing parameter estimation and decision-making.

Among the various methods for constructing informative priors, power priors have gained significant attention. They allow for controlled borrowing of information from historical data by adjusting a power parameter, η, which typically ranges between 0 and 1. When η = 0, no historical information is incorporated, whereas η = 1 fully integrates the historical data into the current analysis.

Despite their advantages, the posterior distribution in these models is often doubly intractable, making standard Markov Chain Monte Carlo (MCMC) methods challenging to apply. Current approaches rely on approximate methods, which lack theoretical guarantees and explicit convergence bounds. This work addresses this gap by developing an exact MCMC algorithm capable of efficiently sampling from these complex posterior distributions.