C2 · Publication Volume 12

Competing Hypotheses

alternatives, predictions, falsification and stopping conditions

Learning goals

After this lesson, you should be able to generate genuinely distinct hypotheses, derive risky predictions before reviewing results, distinguish falsification from failure of an auxiliary assumption, update relative support and write stopping conditions that do not allow every result to rescue a preferred model.

Competing hypotheses are not cosmetic labels attached to the same target. They must imply different observations or actions. “Large system,” “medium system” and “small system” may be useful geometry scenarios but do not necessarily explain an anomaly differently. A stronger set might compare a bedrock mineral system, transported dispersion and an analytical or processing artefact.

Generating a complete-enough hypothesis set

Start from causal categories: primary geological process, remobilisation, weathering or transport, unrelated lithological contrast, cultural or environmental interference, sampling bias, analytical error and coordinate or processing artefact. The set need not contain every imaginable cause, but it should cover explanations with materially different predictions and consequences.

Avoid straw alternatives. An alternative must be stated at comparable detail and given a fair opportunity to predict evidence. Record who proposed it only as an accountable role if required; personal status or institutional identity does not affect its likelihood. Invite a reviewer to construct the strongest non-preferred explanation.

Hypotheses can be composite. A primary system may have a transported surface footprint; a geological anomaly and a coordinate error may coexist. State whether hypotheses are mutually exclusive, nested or combinable before assigning probabilities. If combinations matter, represent them explicitly rather than forcing a false either-or choice.

Prediction before accommodation

A prediction specifies observation, direction, location, scale, uncertainty and detection condition before the result is known. “Alteration may be present” is weak because absence can be excused and presence is undefined. A stronger prediction states which minerals or reactions, their spatial relationship to structure, the method and the footprint expected under each hypothesis.

Accommodation explains known evidence after the fact. It is valuable for model building but cannot be counted as an independent successful prediction. Preserve timestamps or versions so later review can distinguish the two. A model that changes after every observation may fit history while having little prospective power.

Seek risky predictions: outcomes expected under one hypothesis and unlikely under the others. Also predict negative space. If a pathway model is correct, where should the response diminish? If transport controls an anomaly, how should it relate to slope, drainage, particle size or regolith boundaries rather than bedrock contacts?

Falsification, auxiliaries and detection adequacy

Competing hypotheses make different predictions and face explicit revise or stop rules
Competing hypotheses make different predictions and face explicit revise or stop rules

Observations test a hypothesis together with auxiliary assumptions about geometry, preservation, method response, location and data quality. A negative hole may miss the predicted body because its geometry was wrong; this weakens that target model without necessarily refuting the regional mineral-system concept. State which level is being tested.

Falsification requires adequate power. If a survey could detect only a broad shallow footprint, failure cannot refute a narrow deep target. Conversely, endlessly invoking inadequate power makes a hypothesis immune to evidence. Predeclare minimum recovery, coverage, resolution and quality needed to interpret a negative result.

A contradiction log records the observation, affected prediction, adequacy, possible auxiliary failure and action. Contradictions should remain visible even when the model is revised. A model becomes less useful when revisions add unconstrained exceptions or move the target beyond every completed test.

Evidence matrix and stopping conditions

For each hypothesis, create rows for predicted positive, predicted negative and invariant observations. Assign qualitative likelihoods or calibrated ranges rather than arbitrary certainty. Record dependence: several pathfinder elements in one sample may reflect one dispersion process, not several independent confirmations.

Stopping conditions can apply to a target model, a process concept or the whole search space. Examples include: a necessary trap absent under adequate test; geometry moved outside the bounded target; an anomaly reproduced only in one failed analytical batch; no lawful low-disturbance test remaining; or posterior support below a declared threshold across reasonable priors.

Revision is justified when a failed auxiliary assumption has independent support and the revised model makes a new discriminating prediction. Revision is not justified merely because it preserves the preferred conclusion. Keep the retired version and compare predictive performance.

Worked synthetic example

A fictional surface anomaly has three alternatives: H_1, a local bedrock mineral system; H_2, transported material from outside the target; and H_3, preparation or analytical contamination. Priors are 0.45, 0.35 and 0.20. Three observations are evaluated sequentially with synthetic likelihoods.

First, field duplicates reproduce the anomaly. Likelihoods are 0.80, 0.80 and 0.20. Unnormalised weights are 0.36, 0.28 and 0.04, giving posteriors 0.529, 0.412 and 0.059. Reproducibility weakens contamination but does not distinguish bedrock from transport.

Second, anomaly strength follows a transported-sediment pathway and crosses interpreted bedrock boundaries. Likelihoods under the updated alternatives are 0.25, 0.75 and 0.40. Normalised posteriors become approximately 0.285, 0.665 and 0.051. Third, shallow observations find the response restricted to transported material with no predicted primary alteration at adequate exposure; likelihoods are 0.15, 0.80 and 0.50. Final relative support is about 0.071, 0.886 and 0.042.

The calculation does not prove transport, because likelihoods and priors are teaching assumptions and the source of transported material remains unknown. It does show that repeated anomaly values were not uniquely diagnostic of bedrock mineralisation. A next test should trace transport direction and source while retiring the current local-bedrock target geometry.

Interpretation workflow

  1. State the observation needing explanation without embedding a preferred cause.
  2. Generate geological, transported, unrelated and artefact alternatives.
  3. Define whether hypotheses are exclusive, nested or combinable.
  4. Derive predictions before inspecting the discriminating dataset.
  5. Specify location, scale, support, uncertainty and detection adequacy.
  6. Build an evidence matrix with dependence groups and negative space.
  7. Update relative support qualitatively or quantitatively without false precision.
  8. Log contradictions and identify the hypothesis level affected.
  9. Revise only when an auxiliary failure is independently supported and testable.
  10. Apply predeclared stopping or retirement conditions.

Practice and review

  1. Construct three alternatives for a magnetic anomaly, including a non-geological cause.
  2. Rewrite “geochemistry confirms the target” as a risky prediction under two competing hypotheses.
  3. Explain the difference between missing a target geometry and refuting a mineral-system concept.
  4. Recalculate the synthetic example using equal priors and compare the final ordering.
  5. Write one defensible revision and one ad hoc rescue for a failed alteration prediction.

Sources and further reading