Interpret recurrence as a conditional probability model

1. Define the evidence and convention

A mean recurrence interval summarizes a statistical model or record; it is not a schedule. Under a stationary homogeneous Poisson model with rate λ, the expected number of events in a window T is λT and the probability of at least one is 1−exp(−λT). Expected count and probability are different quantities.

2. Connect mechanism and model

The fictional rate is the inverse of a supplied 100–500 year mean interval. Independent increments and a constant rate are explicit assumptions. In this model a long quiet period does not make the next equally long window more probable: the model has no memory of elapsed time since the last event.

Real earthquake sequences include clustering, aftershocks, faults with uncertain recurrence histories and possible time-dependent renewal behavior. A different supported model can therefore produce different conditional probabilities. Even an accurately estimated window probability would not specify the date, location and magnitude of a particular next event.

Hazard describes potentially damaging phenomena and their likelihood or intensity. Risk also depends on exposed people/assets and vulnerability. Neither a model probability nor absence of a recent event establishes that a site is safe. This fictional exercise is not a forecast for a real fault or a replacement for official hazard information.

3. Reconstruct the worked packet

With mean interval 200 years and window 30 years, expected count is 0.15 and probability at least one is 1−e^−0.15≈0.139292. Reporting 15% as exact conflates a small-rate approximation with the exponential model.

4. Predict and investigate

Predict first: Does a 200-year mean interval promise an event exactly every 200 years?

Compare expected counts and probabilities over several windows. State the assumptions under which elapsed quiet time does not change the answer, then name evidence that would motivate a renewal or clustered model.

5. Test a changed case

Apply the evidence to a changed case

At mean interval 100 years and window 50 years, find expected count and at-least-one probability.

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

Compare a worked response

Expected count is 0.5 events, while probability is 1−e^−0.5≈0.393469. A possible fractional expected count does not mean half an earthquake occurs.

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.