A numerically stable algorithm for integrating Bayesian models using Markov melding.

Area of Science:

• Statistics
• Bayesian inference
• Computational statistics

Background:

• Markov melding is a technique for combining Bayesian models from multiple data sources.
• A common quantity links submodels, but its prior density estimation can be challenging.
• Inaccurate prior density estimation leads to instability in Markov chain Monte Carlo (MCMC) samplers.

Purpose of the Study:

• To address the instability and unreliability of Markov melding due to errors in prior density estimation.
• To propose a robust two-stage algorithm for more accurate prior marginal self-density ratio estimation.
• To demonstrate the improved accuracy and reliability of the proposed method in evidence synthesis.

Main Methods:

• Developed a robust two-stage algorithm for Markov melding.
• Utilized weighted samples to estimate prior marginal self-density ratios.
• Applied the stabilized algorithm to evidence synthesis for HIV prevalence and A/H1N1 influenza.

Main Results:

• The proposed algorithm significantly improves accuracy, especially in the tails of the distribution.
• The stabilized Markov melding approach provides reliable inference.
• Demonstrated successful application in real-world evidence synthesis scenarios.

Conclusions:

• The robust two-stage algorithm enhances the accuracy and reliability of Markov melding.
• This method offers a pragmatic solution for complex statistical analyses involving multiple data sources.
• The approach is effective for evidence synthesis in public health applications.