Bayesian Kriging (Model-Based Geostatistics)
Also known as: Bayesian geostatistics, model-based geostatistics, Bayesian spatial interpolation, stochastic kriging
Bayesian Kriging embeds classical geostatistical interpolation inside a full probabilistic framework. Instead of treating variogram parameters as fixed point estimates, it places prior distributions on them and updates these priors with observed spatial data to obtain a posterior distribution. Predictions at unsampled locations are then marginalised over this uncertainty, yielding honest predictive intervals that account for both spatial dependence and parameter uncertainty.
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When to use it
Use Bayesian Kriging when spatial interpolation is needed and honest quantification of prediction uncertainty is important — especially when the sample is small or irregularly distributed, leaving variogram parameters poorly determined. It is the preferred choice in environmental risk mapping, epidemiological disease mapping, and climate-data gap-filling where overconfident predictions are costly. Avoid it when computational resources are severely limited (MCMC can be slow for n > 2000 without approximations), when the spatial process is clearly non-stationary across a large domain, or when the study demands a simple, auditable workflow that non-specialists must replicate without specialist Bayesian software.
Strengths & limitations
- Propagates variogram parameter uncertainty into predictive intervals, avoiding overconfident plug-in estimates.
- Formally incorporates prior knowledge about spatial range, variance, or nugget from prior studies or physical constraints.
- Yields full posterior predictive distributions, enabling probabilistic exceedance maps and risk assessments.
- Robust to small sample sizes where classical variogram fitting is unstable.
- Easily extended to non-Gaussian likelihoods (e.g., Poisson for count data, binomial for prevalence) through the model-based geostatistics framework.
- Computationally expensive: MCMC scales poorly beyond a few thousand observations without sparse-matrix or approximation techniques (INLA, Vecchia approximation).
- Results are sensitive to prior choices for the spatial range and variance when data are sparse, requiring careful prior elicitation.
- Assumes stationarity and isotropy of the covariance function by default; non-stationary extensions add substantial complexity.
- Requires specialist statistical software (R packages: geoR, INLA, Stan, spBayes) and more expertise to implement correctly than plug-in kriging.
Frequently asked
How does Bayesian Kriging differ from ordinary kriging?
Ordinary kriging treats the fitted variogram parameters as known constants when predicting. Bayesian kriging treats them as uncertain and integrates over their posterior distribution, producing wider but more honest predictive intervals — particularly important when data are sparse.
What software can I use for Bayesian Kriging?
The R packages geoR (MCMC-based, Diggle & Ribeiro), spBayes (hierarchical Bayesian spatial models), and R-INLA (fast Laplace approximation via the SPDE approach) are the main options. Stan can also be used for fully custom Bayesian geostatistical models.
When should I use INLA instead of MCMC for Bayesian Kriging?
INLA is orders of magnitude faster than full MCMC for large spatial datasets (thousands to tens of thousands of observations) and is highly accurate for latent Gaussian models. Use MCMC when you need greater modelling flexibility or when INLA's Gaussian latent field assumption does not hold.
Can Bayesian Kriging handle non-Gaussian outcomes such as count data?
Yes. The model-based geostatistics framework replaces the Gaussian likelihood with a Poisson, binomial, or other exponential-family distribution linked to a Gaussian spatial latent field, enabling interpolation of disease counts, prevalence proportions, or similar outcomes.
How sensitive are results to the choice of prior on the spatial range?
The range parameter is often poorly identified in small datasets, making results sensitive to its prior. It is advisable to run sensitivity analyses with different priors and, where possible, to elicit informative priors from domain knowledge or pilot studies.
Sources
- Diggle, P. J., Tawn, J. A., & Moyeed, R. A. (1998). Model-based geostatistics. Journal of the Royal Statistical Society: Series C (Applied Statistics), 47(3), 299–350. DOI: 10.1111/1467-9876.00113 ↗
- Handcock, M. S., & Stein, M. L. (1993). A Bayesian analysis of kriging. Technometrics, 35(4), 403–410. DOI: 10.1080/00401706.1993.10485354 ↗
How to cite this page
ScholarGate. (2026, June 3). Bayesian Kriging (Model-Based Geostatistics). ScholarGate. https://scholargate.app/en/spatial-analysis/bayesian-kriging
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.
- Bayesian Spatial RegressionSpatial analysis↔ compare
- Co-krigingSpatial analysis↔ compare
- Ordinary KrigingSpatial analysis↔ compare
- Spatial AutocorrelationSpatial analysis↔ compare
- Universal KrigingSpatial analysis↔ compare