Model structure
The Bayesian pairwise workflow uses study effects y_i and standard errors sigma_i derived from the selected pairwise or generic analysis. A normal-normal random-effects model can be written as y_i ~ Normal(theta_i, sigma_i^2), theta_i ~ Normal(mu, tau^2).
The posterior combines the likelihood from the study estimates with priors on mu and tau. Coventra's pairwise Bayesian service uses bayesmeta exact numerical integration rather than MCMC for this workflow.
Default priors
- Overall effect prior: mu ~ Normal(0, 2^2) by default on the analysis scale.
- Heterogeneity prior: tau uses a half-normal prior with scale 0.5 by default.
- Prior sensitivity is enabled by default in the client options.
- The tau prior family can be changed to half-normal, half-Cauchy, uniform, or exponential where supported by the prior configuration.
- The tau prior scale, upper bound, or rate is changeable depending on selected prior family.
Diagnostics that apply
Because the pairwise Bayesian workflow uses exact numerical integration, MCMC diagnostics such as R-hat and effective sample size are not applicable to that endpoint. Instead, reviewers should inspect prior settings, prior sensitivity, posterior location, posterior interval width, posterior tau, and whether sparse data make the posterior prior-sensitive.
Bayesian network models that use MCMC, such as gemtc/JAGS workflows, require MCMC convergence diagnostics. That is a separate diagnostic responsibility from the exact pairwise bayesmeta endpoint.
Posterior summaries
The posterior mean, median, credible interval, and posterior tail probabilities are conditional on the model, priors, data, and extraction choices. A 95 percent credible interval should not be described as a frequentist confidence interval.
For ratio measures, the posterior is computed on the log scale and can be back-transformed for display. Reviewers must still report the analysis scale and prior scale.
Reporting checklist
- Report the likelihood scale and effect measure.
- Report the mu prior and tau prior exactly.
- Report whether prior sensitivity was run and what changed.
- State that exact numerical integration was used for Bayesian pairwise output, so MCMC R-hat/ESS do not apply.
- Avoid interpreting Bayesian output without checking whether the posterior is prior-sensitive.