Spatial Approximate Bayesian Computation
Also known as: Spatial ABC, ABC for spatial data, likelihood-free Bayesian spatial inference, simulation-based spatial inference
Spatial Approximate Bayesian Computation (Spatial ABC) is a likelihood-free Bayesian inference framework for spatial data models whose likelihood function is intractable or too expensive to evaluate. It draws candidate parameters from a prior, simulates spatially structured datasets under those parameters, and accepts only the draws whose simulated spatial summary statistics closely match the observed data, thereby building an approximate posterior over model parameters.
Read the full method
Sign in with a free account to read this section.
Method map
The neighbourhood of related methods — select a node to explore.
When to use it
Use Spatial ABC when the spatial model of interest has an intractable or computationally prohibitive likelihood — common for spatial point processes (Strauss, Neyman-Scott, log-Gaussian Cox), spatial epidemic models, or complex geostatistical models with non-Gaussian dependence. It is appropriate when informative spatial summary statistics can be identified and when simulation of the process is feasible. Do not use it when a standard spatial likelihood (e.g. Gaussian process) is available and MCMC is computationally affordable — standard Bayesian MCMC will give exact (up to MCMC error) posterior inference more efficiently. Also avoid it when no good summary statistics exist for the spatial structure of interest, as the resulting posterior approximation may be poor.
Strengths & limitations
- Enables Bayesian inference for spatial models with intractable likelihoods, greatly expanding the class of models that can be fitted.
- Naturally incorporates spatial structure through purpose-built spatial summary statistics.
- Parallelises trivially — simulations are independent and can be distributed across cores or machines.
- Can be combined with Sequential Monte Carlo (ABC-SMC) to handle high-dimensional parameter spaces more efficiently.
- Model choice between competing spatial models is straightforward via posterior model probabilities estimated from the same ABC runs.
- Accuracy depends critically on the choice of summary statistics; insufficient statistics lead to information loss and a biased posterior.
- The tolerance epsilon introduces an approximation error that decreases slowly: halving epsilon typically requires an order-of-magnitude more simulations.
- Scales poorly to high-dimensional parameter spaces without enhancements such as ABC-SMC or regression adjustment.
- Selecting epsilon and summary statistics requires expertise and often preliminary tuning runs.
Frequently asked
How do I choose summary statistics for spatial ABC?
Prefer statistics that are sensitive to the parameters of interest and capture the spatial dependence structure of the model. For point processes, Ripley's K, the L-function, or nearest-neighbour distance distributions are common. For geostatistical models, the empirical variogram at several lags works well. Simulation studies comparing posterior accuracy under different summary choices are strongly recommended.
How large should epsilon be?
Start with a tolerance that yields an acceptance rate of around 1–5% and check that the posterior is substantially narrower than the prior. If the posterior is still close to the prior, tighten epsilon and increase the number of simulations. ABC-SMC reduces this tension by adapting epsilon over sequential populations of particles.
Can Spatial ABC handle very large spatial datasets?
Large datasets increase simulation time per draw and may make naive ABC impractical. Solutions include using spatial summary statistics computed on subregions, coupling ABC with emulators (surrogate models for the simulator), or using ABC-SMC to concentrate simulations in high-posterior regions rather than sampling the full prior.
Is Spatial ABC the same as regular ABC applied to spatial data?
The algorithmic skeleton is the same, but Spatial ABC specifically requires spatially informative summary statistics and a simulator that replicates the spatial dependence structure of the data. Using non-spatial summaries on spatial data would ignore the key information and produce unreliable posteriors.
How does Spatial ABC compare to INLA for spatial models?
INLA (Integrated Nested Laplace Approximation) is fast and accurate for latent Gaussian spatial models but cannot handle non-Gaussian likelihoods or complex spatial point processes where a tractable likelihood exists. Spatial ABC is slower but applies to a wider class of intractable spatial models.
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 ↗
- Diggle, P. J., & Gratton, R. J. (1984). Monte Carlo methods of inference for implicit statistical models. Journal of the Royal Statistical Society: Series B, 46(2), 193–212. DOI: 10.1111/j.2517-6161.1984.tb01290.x ↗
How to cite this page
ScholarGate. (2026, June 3). Spatial Approximate Bayesian Computation. ScholarGate. https://scholargate.app/en/bayesian/spatial-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.
- Approximate Bayesian ComputationSimulation↔ compare
- Sequential Monte CarloBayesian↔ compare
- Spatial Bayesian InferenceBayesian↔ compare
- Spatial MCMCBayesian↔ compare