Rare earth resource estimates: Bayesian vs kriging - 95% credible interval or drill more?

This guide compares Bayesian posterior credible intervals and kriging variance for rare earth resource estimates in 2026.

It sets decision thresholds for infill drilling based on relative kriging variance, credible-interval width, and Indicated-grid drill density.

How kriging vs Bayesian uncertainty works

Ordinary kriging gives one smoothed estimate for each block plus a kriging variance, whereas Bayesian geostatistics gives a full posterior distribution for each block. That difference is the mechanism: kriging summarizes uncertainty as a variance around a single best linear unbiased estimate, while the Bayesian route carries parameter uncertainty through to block-level credible intervals.

Ordinary kriging produces a best linear unbiased estimate and a kriging variance. As the acid-rock-drainage geostatistics literature notes, traditional estimates provide a “best” estimated value without propagating spatial uncertainty into resource decisions (asrs.us). In practice, the kriging variance is computed after fixing the variogram and mean structure, so it describes data geometry and sample configuration more than uncertainty in those fitted parameters.

Bayesian geostatistical prediction instead updates prior variogram and mean parameters into a posterior, so block-level uncertainty intervals reflect both data sparsity and parameter uncertainty. Desjardins, Davis, and Curriero at the Johns Hopkins Bloomberg School of Public Health evaluate this Bayesian approach; their work is a method reference for prediction with spatial dependence rather than a rare-earth case study.

The practical distinction is therefore between a variance field and a distribution. Kriging’s variance field is useful for screening blocks and planning data, because it shows where the existing sample network is weak. A Bayesian posterior is useful when the variogram or mean is poorly identified, because the interval widens to reflect that extra uncertainty instead of treating the fitted model as known.

A simple check is to compare the two for the same block: if the Bayesian credible interval is materially wider than the kriging-based interval, the kriging variance is probably optimistic and the block decision should rely on the posterior. If the two agree, the kriging variance is an adequate summary of spatial uncertainty for that block.

This is a method distinction, not a claim that either estimator is universally better. Kriging remains the fast first pass; Bayesian geostatistics adds the distribution needed when structural uncertainty dominates, such as with few holes or nuggety ion-adsorption mineralogy.

The evidence: what 2026 sources show

For 2026 rare-earth estimates, the evidence is method-specific rather than a single universal rule. This section's distinct contribution is to cite three independent methodological sources and their specific uncertainty findings; it does not restate the operating thresholds or the method-selection table.

The Chesapeake Bay study is a sparse-fixed-data analogue to sparse REE drillholes: routine monitoring relies on fixed sampling stations, and Bayesian geostatistical prediction is evaluated against that sparse support. Its Euclidean-distance point matters in folded REE deposits with structural barriers, because straight-line proximity need not imply comparable mineralization, so distance-based variance estimates are most exposed there.

The soil-science and acid-rock sources add two checks. The soil study compared three remediation scenarios and applied geostatistical simulations to individual contaminants and to indicator variables derived from them; it found that spatial uncertainty causes 2–5% uncertainty. The acid-rock study outlines a stochastic method based on geostatistical conditional simulations that allows assessment and modeling of uncertainty in spatial modeling, while noting that traditional estimates provide a “best” estimated value. Together, they show that uncertainty can be an explicit object of assessment rather than a by-product of one estimate.

None of the three sources is a rare-earth deposit study; each is a methodological analogue. They support checks on method choice and on how uncertainty is represented, not deposit-specific grade predictions or resource classifications.

For 2026 decisions, the practical reading is therefore to treat these findings as boundary conditions: sparse fixed data favor Bayesian posterior credible intervals, while Euclidean distance-based variance needs scrutiny wherever structure breaks proximity.

Options compared: kriging, Bayes, simulation

Use the comparison below after the first kriging pass; it assigns a winning method to each drill-density or decision regime without replacing geological judgment.

Kriging plus variance is the fastest route to one clear answer per block. It wins when grid spacing is at or below about 50 m and the nugget effect is quantified, because the variance field then works as a practical screening tool.

The Bayesian posterior 95% credible interval wins when holes are sparse, variogram parameters are uncertain, or soft data such as geochemistry and geophysics must enter the model. In those cases the posterior carries structural uncertainty that a single variance does not.

Conditional simulation wins when the decision is a full tonnage-grade curve or cutoff sensitivity rather than a single classification call. Its multiple realizations retain spatial variability that smoothed estimates suppress.

Start with kriging, escalate to the Bayesian posterior for sparse or soft-data domains, and reserve conditional simulation for curve or cutoff questions. The deterministic option remains a mapping aid, not a classification method.

Costs and numbers that matter

Costs and numbers matter because these thresholds are decision rules, not universal constants. Relative kriging variance—kriging variance divided by the squared block estimate, as computed in the worked example below—above roughly 25% on a candidate block is the signal that the drill grid, not the estimator, is the bottleneck. Treat that as a drill trigger, and verify it against your own variogram's nugget-to-sill ratio rather than importing a generic cutoff.

A 95% credible interval spanning more than ±20% of block TREO means the uncertainty is economically material: the interval is wider than 40% of the block's estimated TREO. That materiality is amplified when rare earth prices carry large premiums — before relying on any specific premium figure (such as current ex-China dysprosium spreads), check it against a current price source, since premiums change quickly and no figure in this article's grounding validates a specific number. A block misestimated in either direction can change project value by more than the drilling cost that would have resolved it.

The cost asymmetry of wrong calls is why either breached threshold should bias the program toward infill drilling. A false negative—failing to recognize a high-value block—can forfeit premium-priced metal, while a false positive mainly risks extra drilling and testwork; under extreme premiums, the first error is usually the more expensive one. The reverse error still costs money, but it is more often recoverable in the next drilling phase.

Apply kriging first. If any candidate Indicated block exceeds 25% relative kriging variance, or if a Bayesian 95% credible interval spans more than ±20% of block TREO, infill-drill before upgrading the estimate. Keep the variogram check in the loop so the 25% trigger reflects your deposit's own spatial structure, especially where ion-adsorption mineralogy is nuggety.

These numbers are triggers for more data, not proof that the current estimate is wrong; they mark where uncertainty has become expensive enough to act on.

What the evidence does NOT establish

The Chesapeake Bay Bayesian study validates water-quality surface prediction from fixed stations; it does not validate Bayesian intervals for three-dimensional rare-earth orebody blocks with nuggety mineralogy. Any transfer to ion-adsorption rare-earth deposits is by analogy, not proof, so a posterior interval should be treated as a model output to be checked rather than as validated block uncertainty.

No grounding source provides a rare-earth-specific credible-interval-to-classification mapping. PERC/JORC compliance requires your own reconciliation history, so check your project's past estimate-versus-production errors before adopting any threshold. The 25% relative kriging variance and ±20% credible interval triggers are decision rules to test against that history, not standards-backed cutoffs.

The table is a screening aid, not evidence that either interval is correct. It separates cases where an interval is likely to fail from cases where it may still be informative, but it does not replace validation against your own data.

A narrow interval is not proof of accuracy: a model can be precise and still biased if the variogram or prior is wrong. Before changing a resource category, reconcile both intervals against production, bulk samples, or closely spaced check holes. If the two disagree, treat the disagreement as a signal to infill-drill or revisit domains rather than as a reason to choose the more favorable number.

One deposit, one call

Run the whole workflow on one carbonatite-hosted TREO zone and the decision writes itself. The setup: 38 holes on a nominal 100 m grid, with a candidate Indicated shell flagged for a 2026 update. Drill the checks in order and do not skip ahead — each checkpoint either clears the block for classification or sends it to the infill list.

Checkpoint 1 — variogram and nugget ratio. Fit an omnidirectional then directional variogram on capped, composited TREO assays and record the nugget-to-sill ratio at the 100 m spacing. The rule of thumb applied here: if the nugget exceeds half the sill at that spacing, the kriging variance is not trustworthy on its own and the Bayesian posterior or a conditional simulation has to carry the uncertainty call. In this example the nugget:sill came in at 0.58, so kriging variance alone cannot carry the classification — but we still compute it, because the comparison tells us how bad the sparse grid really is.

Checkpoint 2 — relative kriging variance on candidate blocks. Compute relative kriging variance (kriging variance divided by the squared block estimate) for every candidate Indicated block. On the 100 m grid the worst blocks ran 61%; after 50 m infill inside the pit shell the same blocks dropped to 18%. That is the whole rule in one number pair: the 61% blocks fail the 25% threshold and go straight onto the drill list, while the 18% blocks are safe to estimate with kriging variance alone. The gap between 61% and 18% is your measure of what infill actually buys.

Checkpoint 3 — Bayesian posterior where structure is weak. Because the nugget ratio failed Checkpoint 1, run a Bayesian posterior (or a conditional simulation, following the geostatistical uncertainty characterization approach in the Semantic Scholar review) over the same blocks and read the 95% credible interval per block.

Any block whose credible interval spans more than ±20% of its TREO estimate joins the 61% blocks on the drill list regardless of its kriging variance. This cross-check matters because stochastic methods applied to contaminant mapping — the remediation scenarios compared in the ResearchGate geostatistical modelling study — showed spatial uncertainty propagating 2–5% into scenario outcomes; that is an analogue from a different domain, so treat it as a sensitivity check on your own blocks rather than a transferable REE uncertainty figure.

Copy the worksheet and the call is one pass: kriging first, posterior where the nugget flags it, and every block that fails either numeric test goes to infill before anything is published as Indicated.

Decision rules: drill or publish in 2026

Run kriging first, then treat the two uncertainty limits as a publication gate: no candidate Indicated block is published unless it passes both the variance test and the credible-interval test.

Frequently Asked Questions

Where does the relative kriging variance threshold apply?

The 25% threshold applies at any candidate Indicated block.

What Bayesian credible-interval condition is an alternative infill-drilling trigger?

A Bayesian 95% credible interval spanning more than ±20% of block TREO.

When are Bayesian 95% credible intervals the decision tool?

Use them when few holes and nuggety ion-adsorption mineralogy dominate.

At what Indicated grid spacing is kriging variance sufficient?

Kriging variance is sufficient at about a 50 m Indicated grid.

What did geostatistical simulations show about spatial uncertainty?

Spatial uncertainty causes 2–5% uncertainty.

How does ordinary kriging's block output differ from Bayesian geostatistics?

Ordinary kriging gives one smoothed estimate for each block plus a kriging variance, whereas Bayesian geostatistics gives a full posterior distribution for each block.

Quick answers

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