Approximate Bayesian Computation with Missing Data
Also known as: ABC with missing data, likelihood-free inference with missing data, simulation-based inference for incomplete data, ABC-MD
Approximate Bayesian Computation with missing data extends the likelihood-free ABC framework to settings where observations are incomplete or partially recorded. By simulating data under a posited model and accepting parameter draws whose simulated summary statistics are close to the observed ones, it bypasses the need to evaluate an intractable likelihood — even when some data values are absent.
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When to use it
Use ABC with missing data when the likelihood is analytically intractable (e.g. complex genetic, ecological, or agent-based models) and the dataset has missing values that cannot be trivially imputed. It is particularly valuable when the missingness mechanism itself is of scientific interest (MNAR models) or when multiple imputation under a parametric model is not credible. Do not use it as a first resort when the likelihood is available and tractable — standard Bayesian inference with data-augmentation MCMC will be more efficient. Also avoid it when the proportion of missing data is very high and informative summary statistics capturing the observed patterns are difficult to construct.
Strengths & limitations
- Avoids evaluation of an intractable likelihood, enabling inference for complex generative models with missing data.
- Handles both ignorable (MAR) and non-ignorable (MNAR) missingness by incorporating the missing-data mechanism directly into the simulation.
- Provides a full approximate posterior distribution, quantifying parameter uncertainty even under missingness.
- Easily extended with SMC or regression adjustment to improve posterior approximation quality.
- Flexible: works with any data type (counts, survival times, genetic sequences) as long as a simulator can be written.
- Computationally expensive: thousands to millions of simulations are required, and cost scales with data complexity.
- Choice of summary statistics is critical and problem-specific; poor summaries yield an uninformative or biased approximate posterior.
- The tolerance threshold epsilon trades bias for variance — too small reduces sample size, too large inflates approximation error.
- When the fraction of missing data is large, the simulated observed portion may carry little information, further degrading inference.
Frequently asked
How is ABC with missing data different from multiple imputation?
Multiple imputation fills in missing values under a parametric imputation model, then analyses each completed dataset separately. ABC with missing data integrates over the missing values implicitly through simulation, enabling inference for complex models where no tractable likelihood exists — it is not limited to parametric imputation assumptions.
What summary statistics should I use when data are missing?
Summaries should be computed on the observed portion only and should be approximately sufficient for the parameters of interest. Missingness-specific summaries (e.g. rates of missingness by covariate level) should be included when the mechanism is MNAR. Sensitivity analysis comparing different summary sets is essential.
Can I combine ABC with sequential Monte Carlo to handle missing data?
Yes. SMC-ABC (also called ABC-SMC) adaptively lowers the tolerance threshold across a sequence of target distributions, producing a more accurate posterior. It is especially useful for high-dimensional missing-data problems because it is more sample-efficient than plain rejection ABC.
How do I check that my ABC posterior is reliable when data are missing?
Run posterior predictive checks: simulate complete datasets from accepted posterior draws, discard the simulated counterparts of missing entries, and verify that the simulated observed summaries match the real observed summaries. Also inspect sensitivity to epsilon and to the assumed missingness mechanism.
When is data-augmentation MCMC preferable to ABC for missing data?
When the likelihood is available in closed form, data-augmentation MCMC (treating missing values as additional parameters) is far more efficient and produces an exact rather than approximate posterior. Use ABC only when the likelihood is genuinely intractable.
Sources
- Beaumont, M. A., Zhang, W. & Balding, D. J. (2002). Approximate Bayesian computation in population genetics. Genetics, 162(4), 2025–2035. link ↗
- Rubin, D. B. (1987). Multiple Imputation for Nonresponse in Surveys. John Wiley & Sons. ISBN: 978-0471655749
How to cite this page
ScholarGate. (2026, June 3). Approximate Bayesian Computation with Missing Data. ScholarGate. https://scholargate.app/en/bayesian/approximate-bayesian-computation-with-missing-data
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- Approximate Bayesian ComputationSimulation↔ compare
- Bayesian Inference with Missing DataBayesian↔ compare
- MCMC with missing dataBayesian↔ compare
- Multiple ImputationStatistics↔ compare
- Particle FilterBayesian↔ compare
- Sequential Monte CarloBayesian↔ compare