After multiple imputation (imputed dataset = 20), I would like to conduct Bayesian Model Estimation with Adaptive Metropolis Hastings Sampling (amh) -- using the MCMC method.

How can I pool the results together to obtain the following:

  • Parameter Summary (Marginal MAP estimation)
  • parameter MAP SD Q2.5 Q97.5 Rhat SERatio effSize accrate

  • MAP: Univariate marginal MAP estimation
  • mMAP: Multivariate MAP estimation (penalized likelihood estimate)
  • Mean: Mean of posterior distributions

I am wondering if I could extract and combine the estimates of the parameter (e.g., MAP) from each MCMC iteration from each imputed dataset -- giving me 10,000 iterations X 20 dataset = 200,000 estimates. I will then calculate the final/pooled estimates.


1 Answer 1


Combine the samples from all the individual fits to the imputed data and then use the pooled posterior samples as you would a single fit (e.g. to compute expectations, quantiles, ...).

As the number of imputed datasets grows, this would approach something close to the posterior of a model that does the imputation and fitting in a single big model. This is e.g. what the brms package does with its brm_multiple: https://paul-buerkner.github.io/brms/articles/brms_missings.html#imputation-before-model-fitting-1

  • $\begingroup$ Hi Martin, thank you very much! This is from the LAM::AMH package. Are you able to tell us what do the Rhat SERatio effSize and accrate mean? $\endgroup$
    – conner
    Jun 22, 2023 at 14:03

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