The Gold Standard of Archaeology | Expected Information Gain, Stop Rules and Choosing the Next Radiocarbon Sample

1. Define the decision before measuring information

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Information is valuable only relative to a question. A dating programme may need to decide whether two phases overlap, whether a destruction horizon belongs before or after a historical event, whether an occupation lasted one generation or several, or whether two competing stratigraphic models remain plausible. Translate that purpose into a quantity or decision: boundary width, probability of overlap, support for model A versus model B, or probability that a phase falls inside a policy-relevant interval. Without this target, the phrase information gain can reward a narrow date that does not answer the excavation’s real question.

Specify the current evidence before selecting the next sample. This includes existing radiocarbon determinations, calibration curve and version, stratigraphic relationships, sample-event associations, other scientific dates, typology and documentary constraints. Distinguish uncertainty about calendar time from uncertainty about the archaeological model. A date can reduce the first while leaving the second untouched. If the critical doubt is whether a deposit is residual, another determination from the same ambiguous deposit may create a denser but not more credible chronology.

Choose a decision threshold that is demanding enough to matter and modest enough to be achievable. For example, the aim might be to estimate a transition within an 80-year interval at 95% probability, or to reduce the posterior probability of one model below 0.1. Simulate whether any available sampling strategy can plausibly meet that requirement. If the calibration curve and surviving material cannot do so, revise the question openly rather than collecting dates until the budget ends.

Translate the research objective into a chronological contrast before selecting material. “Date the site” is not operational. A useful objective might be to decide whether a boundary was established before or after a burial phase, whether two rebuilding events overlap, or whether occupation ended within a fifty-year interval. For each candidate sample, write which model parameter it informs and which competing interpretation could change. A sample that merely repeats a well-constrained phase may add little, even if it is excellent material. A less glamorous sample from a secure transition may carry more expected information because it separates the alternatives that matter. This objective-to-parameter map is the foundation for both simulation and stopping.

2. Understand expected information gain in practical terms

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Expected information gain compares what is known now with what might be known after a candidate result, averaging across the possible results that could occur. In a formal Bayesian design it may be expressed through expected reduction in entropy, expected utility or change in a decision loss. An archaeological project does not always need a sophisticated formula. It can simulate plausible outcomes for each candidate and compare expected reductions in boundary width, model uncertainty or risk of a wrong decision. The essential point is prospective comparison: evaluate the sample before seeing its result.

A candidate with high potential precision is not necessarily highly informative. If every plausible result falls in a period already established, the date adds confirmation but little discrimination. A sample with a broader individual calibration may be valuable if its stratigraphic position separates competing sequences. Conversely, a date at the edge of a plateau may provide far more calendar information than one in the plateau’s centre. Information depends on the curve, prior constraints and the question, not on material quality alone.

Expected value should be reduced by failure and misassociation risks. A short-lived seed may have excellent event proximity but too little carbon; a human bone may be datable but carry an uncertain reservoir offset; a beautiful charcoal fragment may be old wood. Model technical failure, contamination, residuality and intrusion as outcomes, not afterthoughts. A simple decision table can multiply potential learning by the probability the sample actually records the target event. This prevents a theoretically powerful but archaeologically fragile sample from outranking a more dependable one.

Build the candidate pool independently of the laboratory submission list. Include context, material, short-life assessment, residuality risk, intrusive risk, quantity, pretreatment concerns and destructive-sampling constraints. Mark dependencies: two seeds from one deposit may share the same contextual uncertainty, and fragments from one object are not independent events. Then score each candidate against explicit exclusion rules. A high expected information gain cannot rescue a poor association with the target event. Conversely, excluding all imperfect candidates may make the objective unanswerable; that limitation should appear in the research design rather than being discovered after money is spent.

3. Build a candidate pool with explicit sample-event links

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Create the candidate pool before ranking it. For each object or entity, record material, taxon, life span, context, stratigraphic position, preservation, pretreatment needs, carbon yield, reservoir risk, suspected residuality or intrusion, destructive-sampling cost and the event it is supposed to date. Photograph and label the exact entity. Radiocarbon dates samples, not contexts, so the chain from organism to death, deposition, recovery and target event must be stated.

Separate candidates that answer different kinds of uncertainty. A sample immediately below a boundary may constrain its earliest date; one above may constrain its latest date; paired entities may test a reservoir offset; a replicate may test whether one context is mixed; a sample in a poorly represented structure may improve archaeological coverage. Ranking them on one scale can hide these different jobs. Group candidates by decision contribution, then compare within and across groups.

Representation matters as well as precision. Selecting only the best-preserved hearths may build an excellent chronology for one building while leaving the site sequence biased. A statistically efficient set should still cover the features, phases and activities relevant to the interpretation. Historic England’s guidance emphasises balancing the risk of dating a sample against the probability of meeting the programme’s objectives and recommends simulation, staged dating and replication. The candidate register turns that principle into an auditable object rather than an informal discussion among specialists.

Use prior predictive simulation as a design check, not as a promise of the final date. Generate plausible determinations from the current chronological model, calibrate them and examine how candidate placements affect posterior estimates. Repeat across plausible true calendar positions, measurement errors and outlier states. A sample may be highly informative in one simulated history and redundant in another. Summarise the distribution of improvement—such as change in interval width or probability of resolving an order—not only the best case. If the apparent value depends on a narrow prior assumption, label it as model-dependent.

4. Simulate the next date across the calibration curve

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For each plausible candidate, simulate a range of true calendar ages consistent with the current model, generate radiocarbon measurements using realistic laboratory uncertainty, calibrate them with the chosen curve and insert them into the chronological model. Repeat the process enough times to see the distribution of possible outcomes. Summarise how often the candidate meets the decision threshold, how much it reduces uncertainty on average, and how often it creates little change or exposes a model conflict.

The calibration curve can reverse intuitive rankings. A candidate close to a steep curve section may sharply constrain time, while an equally precise measurement on a plateau can remain broad. A sample that seems redundant in calendar position may help if its place in a stratigraphic sequence allows the model to exploit curve wiggles. Run scenarios across the plausible calendar window rather than simulating from one convenient year. Include curve uncertainty and appropriate reservoir corrections.

Simulation is conditional, not prophecy. It inherits the phase structure, prior distributions, sample association and error assumptions. Test alternative models and uncertain stratigraphic links. If a candidate appears highly informative only under one disputed ordering, report that dependence. Also compare a no-new-date option. Sometimes the expected gain is so small that field re-examination, refitting, material identification or another dating method has greater value than the next radiocarbon measurement.

Define information gain in the units of the decision. Entropy reduction is general, but a project may care about the probability that Phase B began before AD 900, the width of an end-date interval or the chance of separating two episodes by at least thirty years. Different utilities can rank samples differently. Prespecify the principal utility and retain secondary diagnostics. Avoid a composite score whose weights were chosen after seeing which candidate wins. When community, conservation or destructive-sampling values matter, place them beside chronological gain rather than disguising them as statistical terms.

5. Rank candidates by utility, risk and irreversibility

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A practical ranking combines expected archaeological learning with reliability, cost, schedule and destruction. One option is a transparent utility score with separate components: probability of answering the decision, expected change in the key parameter, probability of technical success, confidence in event association, destructive cost and time to result. Avoid hiding value judgements inside one unexplained number. Show the component scores and let stakeholders see why a rare artefact is not automatically sacrificed for a small statistical gain.

Destructive sampling creates an option cost. Once a unique object is consumed, future methods cannot use that material. Prefer surplus material or minimally destructive subsampling when information is similar. Consult curators, descendant communities and relevant authorities before ranking restricted material. Scientific value does not override consent, ownership or cultural significance. A lower-information sample may be the correct choice when the higher-ranked one carries unacceptable harm.

Risk also has asymmetry. A failed date may cost money and material, while a misleading date from poorly associated material can distort the entire model. Penalise misassociation more strongly than ordinary analytical imprecision. Include paired or replicate dates when they test a specific risk. The goal is not to maximise the number of calendar years removed from an interval; it is to improve a trustworthy archaeological inference with proportionate use of finite evidence.

A staged batch should include diagnostic diversity. If all first-round samples come from one material type, pretreatment route or contextual class, a shared problem can remain invisible. Include material that tests the model’s vulnerable links: a short-lived specimen from a boundary, a replicate from a critical context, or an independent phase indicator. The aim is not equal representation of every context. It is to learn whether the assumptions that give high-value samples their leverage are credible before the remaining budget is committed.

6. Worked example: choosing the third date in a harbour sequence

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A fictional harbour excavation contains an early quay, a repair phase and a final abandonment layer. Two pilot dates on short-lived seeds place the sequence broadly between AD 540 and 690, but the calibration curve produces two possible boundary regions. Model A interprets a compact silt as a brief repair; Model B treats it as a long hiatus. The team can date one of three candidates: charcoal beneath the repair, a barley grain sealed in the repair surface, or a fish bone from the abandonment layer.

Simulations show that the charcoal often calibrates broadly and carries old-wood risk. The fish bone could constrain abandonment, but a marine reservoir correction is uncertain and both models already place the endpoint similarly. The barley grain sits exactly where the models diverge. Even though some simulated results remain multimodal, the grain has a high probability of changing the model comparison. Botanical review confirms a single short-lived entity and the context appears sealed. It ranks first.

The result supports a short repair interval and reduces the probability of Model B below the predeclared threshold. The next-sample plan says to stop if the boundary interval is then narrower than 90 years and no agreement or outlier diagnostics fail. Those conditions are met. The team does not date the fish bone merely because one budget line remains. It preserves the material, reports the unresolved reservoir question and explains that an additional endpoint date was unlikely to change the decision.

When a result arrives, classify the surprise before updating the sampling plan. It may be a laboratory quality issue, a sample-identity problem, residual or intrusive material, a mistaken stratigraphic relation, an underestimated outlier process or genuine chronological complexity. Each diagnosis suggests a different next sample. Automatically dating an adjacent specimen can waste material if the real problem is a context record or calibration plateau. Record the competing explanations and choose the next sample for its ability to discriminate among them.

7. Write stop rules before the programme becomes attached to precision

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A stop rule states when no further radiocarbon sampling is justified. It can be based on a decision threshold, expected marginal information, futility, exhaustion of reliable candidates, unacceptable destruction, budget or timetable. Scientific and operational rules should be distinguished. Reaching the desired boundary precision is a scientific stop. Reaching the end of a grant is an operational stop and should not be described as evidence that the chronology is complete.

Define success and futility. Success might mean the posterior probability of phase overlap is below 0.05 or a transition interval is narrower than the resolution required for interpretation. Futility might mean that every remaining sample has less than a specified chance of changing the conclusion, that the calibration plateau prevents the desired resolution, or that context uncertainty dominates. The threshold should be chosen with the research question, not after the preferred model appears.

Allow safety stops and model-repair pauses. Unexpected reservoir effects, incompatible replicates or poor agreement may require investigation before more samples are submitted. Continuing automatically can compound a wrong model. A stop rule is not a ban on learning: it directs the team to the most useful next action, which might be field archive review, another scientific method or transparent acknowledgement of uncertainty. Record who applies the rule and whether departure needs independent approval.

Write stop rules in both positive and negative form. Stop because the decision target has been met—for example, the relevant boundary has a ninety-five per cent interval narrower than the prespecified width and the ordering probability exceeds its target. Also stop when additional available samples are unlikely to change the answer, the remaining pool is contextually weak, model conflict is unresolved, or destructive cost exceeds expected gain. “The budget is exhausted” is an administrative stop, not an evidence-based one; it may still happen, but should be distinguished in the report.

8. Changed-context transfer check: a cemetery without secure ordering

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A harbour sequence can have strong physical stratigraphy. A cemetery may have graves that are spatially organised but lack reliable temporal order. The transfer is not to copy the sequence model. It is to define a decision, build a candidate pool, simulate possible results and choose the sample most likely to discriminate the defensible models. Candidate graves might differ by artefact style, kin group, location or suspected phase, but these relations should not be turned into exact prior order without evidence.

Human bone introduces dietary reservoir risk, and destructive sampling may require specific permissions. A paired terrestrial animal from the same grave can test an offset, but only when association is secure. If the research question concerns whether two burial clusters overlap, a date from the centre of each cluster may be less informative than a grave whose attributes link or separate them. Simulate cluster models with and without disputed seriation.

The stopping rule may focus on model discrimination rather than a narrow boundary. If dates show both clusters were used contemporaneously, more evenly spaced dates may add description but not change that conclusion. If no remaining graves can distinguish the models without assuming the very chronology being tested, stop and report the structural limit. Sequential design remains useful because it prevents the cemetery from becoming a collection of dates detached from a clear inferential purpose.

Report the sampling path, including candidates not chosen. A final model containing twelve dates can look inevitable even when it emerged through sequential choices guided by interim results. Preserve the candidate register, simulation settings, utilities, batch decisions and reasons for stopping. This record lets readers assess selection effects and helps future projects learn which forecasts were accurate. It also prevents a negative or awkward determination from disappearing simply because it reduced the appeal of its context.

9. Know the limits and common misconceptions

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Expected information gain does not guarantee the most informative result in the realised study. It averages over possible outcomes under a model. A candidate can produce a surprising result that increases uncertainty, and that may be scientifically valuable. The calculation is only as good as the current model, curve, error terms and sample-event assessments. It should not be presented as an objective truth independent of archaeological judgement.

The narrowest individual calibrated range is not always the best next date. More dates are not automatically more credible. Replication can be highly informative when it tests residuality, contamination or offsets, even if it appears redundant in a simple calendar model. Conversely, repeatedly dating similar material on a plateau may add almost nothing. A low expected gain should not be used to suppress evidence that could challenge a favoured model; alternative-model simulations are essential.

Stop rules cannot remove all discretion. New discoveries, revised curve data or a failed sample can justify changes, but amendments must be recorded before the next result is known where possible. A formal utility score cannot override cultural permissions or conservation obligations. Some questions are better answered by dendrochronology, luminescence, archaeomagnetism, documentary evidence or renewed stratigraphic work. Sequential radiocarbon design is a framework for choosing within a broader evidence system, not a claim that radiocarbon should dominate it.

Expected information gain can be negative in practical terms even when a new date narrows a model parameter. A destructive sample may remove diagnostic material, consume curatorial time or create a false sense that chronological uncertainty is the only uncertainty that matters. Add a cost column for material loss, stakeholder significance and the possibility that future methods could extract more information. A candidate should advance the stated archaeological decision enough to justify those costs. Where destructive permission is conditional, treat the condition as part of the design rather than an administrative note.

10. Audit the forecast, choice and stopping decision

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Archive the research question, decision threshold, current model, calibration data, software and version, candidate register, sample-event assessments, laboratory-error assumptions, simulation code, random seeds, utility components, permissions and ranking. Retain candidates that were not selected and the reasons. Otherwise, readers cannot tell whether the chosen sample was prospectively informative or merely described that way after producing a convenient result.

For each round, freeze a decision note before submission: which sample is next, what outcomes are plausible, what change would trigger model repair, and which stop rule will be applied. When the result arrives, replace the simulated determination with the observed one, inspect laboratory and contextual diagnostics, rerun alternative models and document how the ranking changes. Do not delete failed or discordant outcomes from the history.

At the end, compare forecast and realised learning. Did the date reduce the target uncertainty? Did gain come from the measurement, stratigraphy or a strong prior? Were stopping conditions met, or did the programme end for operational reasons? Publish enough detail for another team to reconstruct the sequence. Audit transforms sequential choice from expert intuition into a transparent chain of archaeological decisions while still recognising where judgement entered.

Plateaus and multimodal calibrated distributions can make more precision in radiocarbon years translate into little calendar improvement. Simulate against the calibration curve before expecting a narrower laboratory error to solve the problem. In some periods, a stratigraphically placed sample or a sequence of dates provides more leverage than a single ultra-precise determination. Report when the curve, not laboratory performance, limits expected gain. This distinction protects laboratories from unrealistic requests and helps projects invest in context where context carries the information.

11. Frequently asked questions

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What is expected information gain? It is the anticipated reduction in decision-relevant uncertainty after averaging across plausible results for a candidate sample. Must it be calculated with entropy? No. A well-defined simulation using boundary width, model probability or decision loss can be more interpretable. Is the cleanest sample always next? No; it must also address the uncertainty that matters. Can a replicate have high information value? Yes, when it tests context integrity, a reservoir effect or laboratory reliability.

When should dating stop? When the decision threshold is met, further gain is negligible, reliable candidates are exhausted, destruction is unjustified, or another form of evidence is more useful. Does a budget limit count as a stop rule? It is an operational limit, not proof of scientific completeness. Should surprising results be discarded? No. Investigate sample association, measurement and model assumptions, then retain the outcome and the reasoning.

Can information gain choose culturally restricted material? It can describe potential learning, but permission, stewardship and harm remain separate constraints. How many rounds are needed? Historic England recommends staged programmes for all but the simplest applications; the number depends on risk and purpose. What if every candidate performs poorly in simulation? Reframe the question or use another method rather than consuming material for a result known in advance to be inadequate.

The audit should reproduce every selection decision from the evidence available at that time. Freeze model versions at each round and keep a chronology of when determinations, context revisions and external dates became known. Replaying decisions with the final model creates hindsight bias: a sample that now looks obviously redundant may have been the best discriminator before an unexpected result. Sequential transparency is therefore part of the archaeological interpretation, not merely project management.

12. The gold standard chooses the next sample for a reason

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A mature dating programme is not a queue of objects waiting for the laboratory. It is a sequence of decisions. The team states what the chronology must resolve, builds a pool of defensible sample-event links, simulates how each candidate could change the answer, and balances expected learning with failure, destruction, cost and cultural obligations. The selected sample is the one whose possible outcomes matter most to the defined decision.

After every result, the model and the candidate ranking are updated. Surprises can redirect the programme; failures remain evidence; replication is used when it tests a concrete risk. Stop rules prevent the pursuit of decorative precision and make clear whether the chronology is scientifically adequate, curve-limited, context-limited or simply constrained by operations.

The final report should let a reader replay the choices. Why this sample? Why at this stage? What would a different result have changed? Why did the team stop? When those answers are visible, sequential dating respects scarce material and produces a chronology designed around archaeological meaning rather than the accumulation of laboratory numbers.

A robust stopping decision should be communicated in ordinary archaeological language. State which historical alternatives have been separated, which remain possible, and why another available sample is unlikely to alter that conclusion. If stopping is driven by weak context, say so. If the target has been achieved, show the posterior quantity that met it. This prevents “enough dates” from becoming a convention detached from the research question and makes unfinished uncertainty visible to future excavators.

Before the final submission, hold a sampling review with the field archaeologist, finds or environmental specialist, chronologist, laboratory representative and curator where possible. Give each person the same candidate register and decision objective. Ask them to identify the highest-value sample, the most serious contextual risk and the evidence that would cause them to stop. Disagreement is useful: the modeller may value a boundary, the field archaeologist may know it was truncated, and the curator may identify destructive limits. Resolve the disagreement in the design record rather than after a surprising determination.

Use a sample dossier for every selected specimen. It should contain a unique identifier, photographs, plan and section references, material identification, sample mass, recovery and storage history, association argument, anticipated event, pretreatment concern and chain of custody. Link the dossier to the model parameter and expected-gain calculation. If the specimen changes during preparation or the laboratory selects a subsample, update the link. This prevents a sophisticated design from being applied to an object different from the one the design assumed.

After each batch, compare forecast and realised information. Record the predicted reduction in the decision metric, the actual change after model checking, and the reason for any gap. A date can be analytically precise yet add little because it falls on a calibration plateau; it can also add more than expected by exposing a false stratigraphic assumption. Forecast error is not a failure to hide. It is the evidence that improves the next selection.

Finally, publish enough negative information to keep the chronology honest. List failed samples, rejected determinations, unselected high-risk candidates and objectives that remained unresolved. Explain exclusions with rules fixed before interpretation where possible. A model containing only cooperative dates overstates control. The gold standard shows how material, context, calibration and sequential choice constrained what could be learned, and stops when another determination cannot responsibly close that gap.

The final report should distinguish a sample selected because it was expected to be informative from one added for replication, diagnosis or stakeholder value. These purposes have different success criteria. A replicate can be valuable even when it adds little chronological precision because it tests whether a critical result is reproducible. A diagnostic sample can widen a model by revealing mixing and still improve the truthfulness of interpretation. Expected information gain must therefore be read against the declared role of the sample, not reduced to narrower posterior intervals alone.

When the next sample remains genuinely uncertain, compare two or three candidates publicly in the project record. State what each could resolve, what assumption it depends on, and what result would change the following decision. This short comparison is often more useful than a single ranking score because it reveals the structure of the choice.