Approximate Bayesian Computation — Likelihood-Free Inference
Approximate Bayesian Computation (ABC) · Also known as: ABC, likelihood-free inference, simulation-based inference, Yaklaşık Bayesçi Hesaplama (ABC)
Approximate Bayesian Computation (ABC) is a family of simulation-based inference methods that estimate posterior distributions without requiring an analytically tractable likelihood function. Introduced by Beaumont, Zhang and Balding (2002) in the context of population genetics, ABC replaced the intractable likelihood with repeated model simulation and a comparison of summary statistics between simulated and observed data.
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When to use it
ABC is the right choice when the model can be simulated forward but its likelihood function cannot be evaluated analytically — a situation that arises frequently in population genetics, epidemiology, ecology, and agent-based economic modelling. It handles continuous, binary, and count outcome variables and places no normality requirement on the data. There is no hard minimum sample size, but the summary statistics must carry adequate information about the parameters. When the simulation budget is large and tolerance can be set low, ABC approximates the true posterior closely; when simulations are expensive, SMC-ABC or neural posterior estimation variants are preferable. If the likelihood is tractable, standard MCMC is more efficient.
Strengths & limitations
- Operates without a closed-form likelihood, opening Bayesian inference to complex generative models that are easy to simulate but hard to evaluate analytically.
- Flexible enough to handle continuous, binary, and count outcomes under any structural model the analyst can encode as a simulator.
- Variants such as SMC-ABC and ABC-MCMC substantially reduce the number of simulations needed compared to naive rejection sampling.
- The posterior approximation converges to the true posterior as the tolerance threshold approaches zero.
- Naive rejection ABC requires an enormous number of simulations to achieve a low tolerance threshold and meaningful acceptance rate, making it computationally expensive for high-dimensional parameter spaces.
- The quality of the posterior approximation depends critically on the choice of summary statistics; poorly chosen summaries can produce a biased or high-variance posterior.
- There is no analytic guarantee that the chosen summary statistics are sufficient, so information is generally lost relative to the full likelihood.
- Fewer than roughly 1 000 total accepted proposals typically yields an unreliable posterior approximation; when the simulation budget is limited, standard MCMC should be considered.
Frequently asked
How is ABC different from standard MCMC?
Both methods produce samples from a posterior distribution, but MCMC evaluates the likelihood at each proposed parameter value, whereas ABC replaces that evaluation with a forward simulation and a summary-statistic comparison. Use ABC when the likelihood is intractable; use MCMC when it can be computed.
How do I choose summary statistics?
Summary statistics should capture as much information about the parameters of interest as possible. Common practice is to use domain knowledge (e.g., mean, variance, allele frequencies) and to validate choices by checking whether the statistics change when the true parameter changes. Sufficient statistics exist only for exponential-family models; for other models, some information loss is unavoidable.
How small does the tolerance epsilon need to be?
There is no universal rule. A practical approach is to tighten epsilon incrementally and check whether the posterior shape stabilises. The posterior approximation improves as epsilon decreases, but the acceptance rate falls accordingly and more simulations are needed. SMC-ABC automates this trade-off by adaptively reducing epsilon across populations.
When should I use SMC-ABC instead of rejection ABC?
When simulation is expensive, naive rejection ABC wastes most simulations because the acceptance rate can be extremely low at a tight tolerance. SMC-ABC uses a sequence of intermediate tolerance thresholds and importance-weighted populations to concentrate simulations near the posterior, making it far more efficient for the same final epsilon.
Sources
- Beaumont, M.A., Zhang, W. & Balding, D.J. (2002). Approximate Bayesian Computation in Population Genetics. Genetics, 162(4), 2025-2035. DOI: 10.1093/genetics/162.4.2025 ↗
- Sisson, S.A., Fan, Y. & Beaumont, M.A. (Eds.) (2018). Handbook of Approximate Bayesian Computation. Chapman & Hall/CRC. DOI: 10.1201/9781315117195 ↗
How to cite this page
ScholarGate. (2026, June 1). Approximate Bayesian Computation (ABC). ScholarGate. https://scholargate.app/en/simulation/approximate-bayesian-computation
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.
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