SCIENCE · INVESTIGATE AND EXPLAIN

Interpret volcanic unrest without reversing a conditional probability

Volcanic monitoring combines seismic activity, deformation, gas chemistry and other evidence with a volcano’s history. Unrest can arise without a subsequent eruption, and the meaning of a signal depends on background behavior and the event definition. A statement about how often a signal precedes an event is not automatically the probability of an event after observing that signal.

Learning outcome: Use natural frequencies to reconstruct numerator and denominator. Change prior and false-positive probability separately. Explain why two correlated monitoring signals should not automatically count as independent confirmations.

Starting recap

Keep map geometry, relative displacement, source magnitude and conditional hazard evidence distinct. A model probability is not a deterministic forecast.

All lessons are open directly. Your saved experiments remain when you leave and return.

Try

With prior 0.02 and false-positive probability 0.10, 10000 windows contain 120 expected evidence-positive events and 980 evidence-positive non-events. Posterior is 120/1100≈0.109091, not the sensitivity 0.6.

Open the experiment

Predict

Can a signal present before many eruptions still have a modest event probability when it occurs?

Your prediction and reason

Experiment

Use natural frequencies to reconstruct numerator and denominator. Change prior and false-positive probability separately. Explain why two correlated monitoring signals should not automatically count as independent confirmations.

Update an invented eruption probability without reversing conditionals

Worked teaching model · synthetic values · Fictional event and evidence categories: P(E|event)=0.6, P(E|no event)=b, prior=a. Posterior 0.6a/[0.6a+b(1−a)]. Natural frequencies use a hypothetical 10000-window reference ensemble. No actual volcano, calibrated warning threshold or independence of multiple signals is assumed.

Prior event probability in a fixed 30-day window: 0.02 fraction Probability of evidence without event: 0.1 fraction

Reset keeps your prediction, captures and practice history.

A signal common before eruption is not necessarily specific to eruption.

Prior probability and false-positive frequency both affect the posterior. Multiple correlated unrest signals cannot be multiplied as independent evidence without justification. Hazard probability is distinct from exposure, vulnerability and an operational warning decision.

Complete conditional quantities; mixed units are labeled per row
Quantity	Value	Unit
Prior event windows in reference ensemble	200	expected windows
Evidence with event	120	expected windows
Evidence without event	980	expected windows
Total evidence-positive windows	1100	expected windows
Posterior event probability	0.109090909	fraction
Evidence likelihood ratio	6	ratio

A signal common before eruption is not necessarily specific to eruption.

Observation to attach to a capture

Captures preserve recipes and replay their calculated results. They are synthetic model evidence, not physical measurements.

Understand

1. Define the evidence and convention

2. Connect mechanism and model

The fictional event is eruption in a specified 30-day window. The supplied sensitivity is P(E|event)=0.6, false-positive probability is P(E|no event)=b and prior event probability is a. Among 10000 reference windows, expected evidence-positive event windows are 6000a and evidence-positive non-event windows are 10000b(1−a). Their ratio gives the posterior event probability.

At a low base rate, many evidence-positive windows can still be non-events. Multiple signals may share a causal process or measurement dependence; multiplying separate likelihood ratios as if independent can overstate evidence. A joint calibrated model, documented observation history and uncertainty are needed for actual forecasting.

Operational warnings are decisions informed by evidence and potential consequences, not merely a classroom posterior crossing an arbitrary line. Hazard probability differs from the distribution of eruption size/style and from risk to exposed communities. This fictional calculation is not an alert assessment, personal safety advice or a prediction for any named volcano.

3. Reconstruct the worked packet

4. Predict and investigate

Predict first: Can a signal present before many eruptions still have a modest event probability when it occurs?

5. Test a changed case

Apply the evidence to a changed case

At prior 0.10 and false-positive probability 0.05, find the two evidence-positive counts and posterior.

Retain the evidence frame, calculations and assumptions before opening public feedback.

Compare a worked response

There are 600 expected event-positive and 450 non-event-positive windows. Posterior is 600/1050=4/7≈0.571429. These stipulated frequencies do not calibrate a real volcano.

6. Retain a defensible evidence notebook

Preserve first predictions, map orientation, intermediate calculations, units, assumptions and alternatives. These maps, numerical packets and diagrams are original invented instructional cases, not surveyed sites or current hazard forecasts. Independent practical review and genuinely unfamiliar evidence remain separate learner gates.

Mechanism reference, checked 30 October 2026. Original prose, diagrams and numerical exercises. No physical loading, pressurization or field hazard exposure is requested.

Apply

Public practice checks a specific claim. It does not establish independent mastery.

At prior 0.10 and false-positive probability 0.05, find the two evidence-positive counts and posterior.

Your explanation and limitations

Continue

Completion requires a saved prediction, at least one capture and a reflection. Presence checks do not grade your reasoning.

Skipping retains experiments and awards no mastery.

Previous: Balance volatile inventory without inventing an eruption threshold Next: Integrate an actual discharge archive without inventing an instantaneous peak

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