Chapter map

1. 1. Case definition
2. 2. Time index
3. 3. Historical window
4. 4. Simple check
5. 5. Mean model
6. 6. Trend term
7. 7. Seasonality
8. 8. Dispersion
9. 9. Reweighting
10. 10. Expected count
11. 11. Predictive threshold
12. 12. Exceedance score
13. 13. Alarm rule
14. 14. Backtest
15. 15. Operational review
16. 16. Investigation

Visit the How Mathematics Works hub for the wider series and its connections to education, reasoning, science, computing, design and careers.

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1. Case definition

This is where modelling choices begin to affect evidence. Fix what one count represents.

A concrete situation

Weekly laboratory confirmations use one definition.

What the mathematics does not license

Definition changes mimic outbreaks. That distinction matters because a correct formula can still answer the wrong operational question.

Try it, check it, transfer it

Version the definition. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

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2. Time index

The central mathematical idea is concrete. Align complete reporting weeks.

A concrete situation

Week t has current count 9.

What the mathematics does not license

Partial weeks bias comparisons. The habit of checking assumptions is one of the practical benefits of learning mathematics.

Try it, check it, transfer it

Mark data completeness. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

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3. Historical window

Here the geometry becomes operational. Select comparable earlier weeks.

A concrete situation

Five checks are 3,4,5,4,6.

What the mathematics does not license

Too little history is unstable. The same reasoning helps students move from an exercise to a real dataset.

Try it, check it, transfer it

Publish every included date. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

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4. Simple check

This step deserves a careful pause. Calculate mean and ratio before modelling.

A concrete situation

Mean 4.4; 9/4.4≈2.05.

What the mathematics does not license

This is not the predictive threshold. That distinction matters because a correct formula can still answer the wrong operational question.

Try it, check it, transfer it

Keep it as an audit. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

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5. Mean model

The useful question is not only how to calculate, but what the calculation assumes. Use a log link for expected counts.

A concrete situation

log μ includes intercept and trend.

What the mathematics does not license

Bad functional form distorts expectation. The habit of checking assumptions is one of the practical benefits of learning mathematics.

Try it, check it, transfer it

Inspect residuals. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

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6. Trend term

A small example makes the mechanism visible. Allow declared long-run change.

A concrete situation

Reporting grows gradually over years.

What the mathematics does not license

Trend can absorb an emerging event. The same reasoning helps students move from an exercise to a real dataset.

Try it, check it, transfer it

Apply guarded rules. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

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7. Seasonality

This is where modelling choices begin to affect evidence. Represent recurring annual position.

A concrete situation

Comparable weeks share a seasonal factor.

What the mathematics does not license

Broad windows may mix regimes. That distinction matters because a correct formula can still answer the wrong operational question.

Try it, check it, transfer it

Test seasonal fit. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

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8. Dispersion

The central mathematical idea is concrete. Estimate variance relative to the mean.

A concrete situation

Var(Y)≈φμ with φ above one.

What the mathematics does not license

Few points make φ uncertain. The habit of checking assumptions is one of the practical benefits of learning mathematics.

Try it, check it, transfer it

Use conservative checks. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

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9. Reweighting

Here the geometry becomes operational. Downweight large historical residuals.

A concrete situation

One old outbreak contributes less.

What the mathematics does not license

Real baseline change may be discarded. The same reasoning helps students move from an exercise to a real dataset.

Try it, check it, transfer it

Archive weights. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

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10. Expected count

This step deserves a careful pause. Predict μ0 for the current week.

A concrete situation

The fitted value is near the historical level.

What the mathematics does not license

Prediction inherits model uncertainty. That distinction matters because a correct formula can still answer the wrong operational question.

Try it, check it, transfer it

Report it. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

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11. Predictive threshold

The useful question is not only how to calculate, but what the calculation assumes. Calculate an upper quantile for Y0.

A concrete situation

A count above U is flagged.

What the mathematics does not license

Approximation can fail at tiny counts. The habit of checking assumptions is one of the practical benefits of learning mathematics.

Try it, check it, transfer it

Validate by simulation. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

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12. Exceedance score

A small example makes the mechanism visible. Scale how far the observation passes expectation.

A concrete situation

Y0=9 is compared with μ0 and U.

What the mathematics does not license

Scores from different settings differ. The same reasoning helps students move from an exercise to a real dataset.

Try it, check it, transfer it

State the formula. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

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13. Alarm rule

This is where modelling choices begin to affect evidence. Freeze the decision before viewing outcomes.

A concrete situation

Flag when count exceeds U.

What the mathematics does not license

Repeated testing creates alarms. That distinction matters because a correct formula can still answer the wrong operational question.

Try it, check it, transfer it

Track the full stream. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

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14. Backtest

The central mathematical idea is concrete. Replay old data without peeking forward.

A concrete situation

Historical outbreaks and quiet weeks are scored.

What the mathematics does not license

Labels may be incomplete. The habit of checking assumptions is one of the practical benefits of learning mathematics.

Try it, check it, transfer it

Report multiple metrics. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

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15. Operational review

Here the geometry becomes operational. Check delay and false-alert burden.

A concrete situation

Analysts can investigate the alarm volume.

What the mathematics does not license

Perfect sensitivity may be unusable. The same reasoning helps students move from an exercise to a real dataset.

Try it, check it, transfer it

Match resources. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

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16. Investigation

This step deserves a careful pause. Combine the signal with field evidence.

A concrete situation

Reporting changes are checked first.

What the mathematics does not license

The algorithm cannot identify cause. That distinction matters because a correct formula can still answer the wrong operational question.

Try it, check it, transfer it

Document resolution. Then explain the result to someone who has not seen the formula. If the explanation needs a hidden assumption, add that assumption to the model record.

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A seven-day practice lab

1. Day 1: define the decision, observation unit, X variables and Y or reference condition.
2. Day 2: reproduce the smallest worked example and check every dimension, unit and sign.
3. Day 3: build a transparent baseline and write what it assumes.
4. Day 4: fit the main method inside a training-only pipeline; record every parameter.
5. Day 5: challenge one assumption with a deliberately difficult dataset or operating regime.
6. Day 6: compare validation metrics with the practical workload created by errors.
7. Day 7: present one supported conclusion, one unresolved uncertainty and one safe next experiment.

Questions for a student, parent or mentor

• Which part of the model is a mathematical definition, and which part is a choice?
• What small calculation would catch a sign, scale or dimension error?
• What evidence comes from training, validation and the untouched test?
• What benign condition could look like a fault or prediction failure?
• How would the answer change for another response, asset, school project or time period?
• What should a human review before acting on the score?

A method-specific audit before deployment

The Farrington outbreak-detection algorithm asks a disciplined question: how surprising is the newest count after allowing for the ordinary level, long-term trend, seasonal position and extra-Poisson variation seen in comparable historical weeks? The answer is a predictive threshold. A count above that threshold becomes an alarm for investigation, not a diagnosis that an outbreak certainly exists.

The original method fits a log-linear regression to historical surveillance counts and uses robust reweighting so past outbreaks do not pull the baseline upward. Later flexible versions use a quasi-Poisson mean–variance relationship, selected historical windows, trend rules and seasonal factors. Every choice changes what “expected” means, so the baseline must be described as carefully as the current count.

Suppose comparable historical counts are 3, 4, 5, 4 and 6. Their simple mean is 4.4, while the current count is 9. The raw excess is 4.6 and the ratio is about 2.05. Those arithmetic summaries are useful checks, but they are not a Farrington alarm by themselves: a valid threshold also needs the fitted regression, dispersion, historical-window design, reweighting and predictive quantile.

A surveillance signal can arise from an outbreak, a reporting backlog, a laboratory change, a revised case definition or random variation. Good use therefore keeps detection and investigation separate, monitors false alarms and detection delay, checks residuals and backtests frozen settings on periods that were not used for tuning.

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Frequently asked questions

What does the Farrington algorithm estimate?

It estimates an expected count and an upper predictive threshold from comparable historical surveillance data.

Why use quasi-Poisson variation?

Surveillance counts often vary more than an ordinary Poisson model allows, so a dispersion factor is estimated.

What does robust reweighting do?

It reduces the influence of historical observations that look like past outbreaks while fitting the baseline.

Does an exceedance prove an outbreak?

No. It is an investigation signal and may reflect reporting, coding, laboratory or random changes.

Why do seasonal windows matter?

They compare the current period with historically similar parts of the year rather than unrelated seasons.

How should settings be chosen?

They should be frozen from the operational aim and evaluated by false alarms, sensitivity and delay on realistic held-out data.

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Primary source and fact-check note

C. P. Farrington, Nicholas J. Andrews, A. D. Beale and M. A. Catchpole, “A Statistical Algorithm for the Early Detection of Outbreaks of Infectious Disease,” Journal of the Royal Statistical Society Series A 159(3), 547–563 (1996), DOI 10.2307/2983331. Definitions and core claims in this article were checked against this primary publication. Calculations shown here were independently recomputed. Examples are educational illustrations; they are not reported industrial performance results.

Useful next reading

• Clayton–Kaldor empirical Bayes disease maps
• Epidemic modelling and reproduction numbers
• How Mathematics Works

Keep the options open. Mathematics education supports clearer questions, transferable problem-solving skills and informed choices across science, engineering, computing, AI, statistics, design and many other careers. It does not guarantee intelligence, income, admission or employment; those outcomes depend on far more than one subject or model.

Extended laboratory: topic-specific validation and responsible use

Definition audit

Freeze case definition and reporting week.

History audit

Publish comparable weeks and exclusions.

Model audit

Reproduce trend, seasonality, dispersion and weights.

Threshold audit

Recalculate the predictive upper limit.

Backtest audit

Report alarms, misses and delay.

Data audit

Check completeness, backlog and laboratory changes.

Transfer audit

Run frozen settings on later periods.

Final claim

Describe an investigation signal, never automatic proof.

Mechanism workshop: calculate, challenge and transfer

Workshop 1: Case definition

Begin with this mechanism: Fix what one count represents. Recreate the concrete case: Weekly laboratory confirmations use one definition. Write case counts, reporting weeks, historical windows, fitted means, trend coefficients, seasonal factors, dispersion factors, residual weights, predictive limits, exceedance scores, alarm flags and investigation outcomes with units, denominators and assumptions. Calculate the smallest non-trivial example by hand and reproduce it in a spreadsheet or short program. Challenge this limitation: Definition changes mimic outbreaks. Complete the transfer step: Version the definition. Change exactly one observed count, reporting date, historical window, baseline mean, standard deviation, guard-band length, dispersion factor, trend term, seasonal factor, robust weight, predictive quantile, baseline rate, target rate, likelihood score, reset value, decision limit, EWMA weight, starting value, variance model, calendar effect, exposure denominator, random seed, monitoring horizon or validation period. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep observation, preprocessing, baseline design, model, computation, threshold, uncertainty, interpretation and independent investigation on separate notebook lines. Reserve complete periods outside tuning when testing transfer.

Workshop 2: Time index

Begin with this mechanism: Align complete reporting weeks. Recreate the concrete case: Week t has current count 9. Write case counts, reporting weeks, historical windows, fitted means, trend coefficients, seasonal factors, dispersion factors, residual weights, predictive limits, exceedance scores, alarm flags and investigation outcomes with units, denominators and assumptions. Calculate the smallest non-trivial example by hand and reproduce it in a spreadsheet or short program. Challenge this limitation: Partial weeks bias comparisons. Complete the transfer step: Mark data completeness. Change exactly one observed count, reporting date, historical window, baseline mean, standard deviation, guard-band length, dispersion factor, trend term, seasonal factor, robust weight, predictive quantile, baseline rate, target rate, likelihood score, reset value, decision limit, EWMA weight, starting value, variance model, calendar effect, exposure denominator, random seed, monitoring horizon or validation period. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep observation, preprocessing, baseline design, model, computation, threshold, uncertainty, interpretation and independent investigation on separate notebook lines. Reserve complete periods outside tuning when testing transfer.

Workshop 3: Historical window

Begin with this mechanism: Select comparable earlier weeks. Recreate the concrete case: Five checks are 3,4,5,4,6. Write case counts, reporting weeks, historical windows, fitted means, trend coefficients, seasonal factors, dispersion factors, residual weights, predictive limits, exceedance scores, alarm flags and investigation outcomes with units, denominators and assumptions. Calculate the smallest non-trivial example by hand and reproduce it in a spreadsheet or short program. Challenge this limitation: Too little history is unstable. Complete the transfer step: Publish every included date. Change exactly one observed count, reporting date, historical window, baseline mean, standard deviation, guard-band length, dispersion factor, trend term, seasonal factor, robust weight, predictive quantile, baseline rate, target rate, likelihood score, reset value, decision limit, EWMA weight, starting value, variance model, calendar effect, exposure denominator, random seed, monitoring horizon or validation period. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep observation, preprocessing, baseline design, model, computation, threshold, uncertainty, interpretation and independent investigation on separate notebook lines. Reserve complete periods outside tuning when testing transfer.

Workshop 4: Simple check

Begin with this mechanism: Calculate mean and ratio before modelling. Recreate the concrete case: Mean 4.4; 9/4.4≈2.05. Write case counts, reporting weeks, historical windows, fitted means, trend coefficients, seasonal factors, dispersion factors, residual weights, predictive limits, exceedance scores, alarm flags and investigation outcomes with units, denominators and assumptions. Calculate the smallest non-trivial example by hand and reproduce it in a spreadsheet or short program. Challenge this limitation: This is not the predictive threshold. Complete the transfer step: Keep it as an audit. Change exactly one observed count, reporting date, historical window, baseline mean, standard deviation, guard-band length, dispersion factor, trend term, seasonal factor, robust weight, predictive quantile, baseline rate, target rate, likelihood score, reset value, decision limit, EWMA weight, starting value, variance model, calendar effect, exposure denominator, random seed, monitoring horizon or validation period. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep observation, preprocessing, baseline design, model, computation, threshold, uncertainty, interpretation and independent investigation on separate notebook lines. Reserve complete periods outside tuning when testing transfer.

Workshop 5: Mean model

Begin with this mechanism: Use a log link for expected counts. Recreate the concrete case: log μ includes intercept and trend. Write case counts, reporting weeks, historical windows, fitted means, trend coefficients, seasonal factors, dispersion factors, residual weights, predictive limits, exceedance scores, alarm flags and investigation outcomes with units, denominators and assumptions. Calculate the smallest non-trivial example by hand and reproduce it in a spreadsheet or short program. Challenge this limitation: Bad functional form distorts expectation. Complete the transfer step: Inspect residuals. Change exactly one observed count, reporting date, historical window, baseline mean, standard deviation, guard-band length, dispersion factor, trend term, seasonal factor, robust weight, predictive quantile, baseline rate, target rate, likelihood score, reset value, decision limit, EWMA weight, starting value, variance model, calendar effect, exposure denominator, random seed, monitoring horizon or validation period. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep observation, preprocessing, baseline design, model, computation, threshold, uncertainty, interpretation and independent investigation on separate notebook lines. Reserve complete periods outside tuning when testing transfer.

Workshop 6: Trend term

Begin with this mechanism: Allow declared long-run change. Recreate the concrete case: Reporting grows gradually over years. Write case counts, reporting weeks, historical windows, fitted means, trend coefficients, seasonal factors, dispersion factors, residual weights, predictive limits, exceedance scores, alarm flags and investigation outcomes with units, denominators and assumptions. Calculate the smallest non-trivial example by hand and reproduce it in a spreadsheet or short program. Challenge this limitation: Trend can absorb an emerging event. Complete the transfer step: Apply guarded rules. Change exactly one observed count, reporting date, historical window, baseline mean, standard deviation, guard-band length, dispersion factor, trend term, seasonal factor, robust weight, predictive quantile, baseline rate, target rate, likelihood score, reset value, decision limit, EWMA weight, starting value, variance model, calendar effect, exposure denominator, random seed, monitoring horizon or validation period. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep observation, preprocessing, baseline design, model, computation, threshold, uncertainty, interpretation and independent investigation on separate notebook lines. Reserve complete periods outside tuning when testing transfer.

Workshop 7: Seasonality

Begin with this mechanism: Represent recurring annual position. Recreate the concrete case: Comparable weeks share a seasonal factor. Write case counts, reporting weeks, historical windows, fitted means, trend coefficients, seasonal factors, dispersion factors, residual weights, predictive limits, exceedance scores, alarm flags and investigation outcomes with units, denominators and assumptions. Calculate the smallest non-trivial example by hand and reproduce it in a spreadsheet or short program. Challenge this limitation: Broad windows may mix regimes. Complete the transfer step: Test seasonal fit. Change exactly one observed count, reporting date, historical window, baseline mean, standard deviation, guard-band length, dispersion factor, trend term, seasonal factor, robust weight, predictive quantile, baseline rate, target rate, likelihood score, reset value, decision limit, EWMA weight, starting value, variance model, calendar effect, exposure denominator, random seed, monitoring horizon or validation period. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep observation, preprocessing, baseline design, model, computation, threshold, uncertainty, interpretation and independent investigation on separate notebook lines. Reserve complete periods outside tuning when testing transfer.

Workshop 8: Dispersion

Begin with this mechanism: Estimate variance relative to the mean. Recreate the concrete case: Var(Y)≈φμ with φ above one. Write case counts, reporting weeks, historical windows, fitted means, trend coefficients, seasonal factors, dispersion factors, residual weights, predictive limits, exceedance scores, alarm flags and investigation outcomes with units, denominators and assumptions. Calculate the smallest non-trivial example by hand and reproduce it in a spreadsheet or short program. Challenge this limitation: Few points make φ uncertain. Complete the transfer step: Use conservative checks. Change exactly one observed count, reporting date, historical window, baseline mean, standard deviation, guard-band length, dispersion factor, trend term, seasonal factor, robust weight, predictive quantile, baseline rate, target rate, likelihood score, reset value, decision limit, EWMA weight, starting value, variance model, calendar effect, exposure denominator, random seed, monitoring horizon or validation period. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep observation, preprocessing, baseline design, model, computation, threshold, uncertainty, interpretation and independent investigation on separate notebook lines. Reserve complete periods outside tuning when testing transfer.

Workshop 9: Reweighting

Begin with this mechanism: Downweight large historical residuals. Recreate the concrete case: One old outbreak contributes less. Write case counts, reporting weeks, historical windows, fitted means, trend coefficients, seasonal factors, dispersion factors, residual weights, predictive limits, exceedance scores, alarm flags and investigation outcomes with units, denominators and assumptions. Calculate the smallest non-trivial example by hand and reproduce it in a spreadsheet or short program. Challenge this limitation: Real baseline change may be discarded. Complete the transfer step: Archive weights. Change exactly one observed count, reporting date, historical window, baseline mean, standard deviation, guard-band length, dispersion factor, trend term, seasonal factor, robust weight, predictive quantile, baseline rate, target rate, likelihood score, reset value, decision limit, EWMA weight, starting value, variance model, calendar effect, exposure denominator, random seed, monitoring horizon or validation period. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep observation, preprocessing, baseline design, model, computation, threshold, uncertainty, interpretation and independent investigation on separate notebook lines. Reserve complete periods outside tuning when testing transfer.

Workshop 10: Expected count

Begin with this mechanism: Predict μ0 for the current week. Recreate the concrete case: The fitted value is near the historical level. Write case counts, reporting weeks, historical windows, fitted means, trend coefficients, seasonal factors, dispersion factors, residual weights, predictive limits, exceedance scores, alarm flags and investigation outcomes with units, denominators and assumptions. Calculate the smallest non-trivial example by hand and reproduce it in a spreadsheet or short program. Challenge this limitation: Prediction inherits model uncertainty. Complete the transfer step: Report it. Change exactly one observed count, reporting date, historical window, baseline mean, standard deviation, guard-band length, dispersion factor, trend term, seasonal factor, robust weight, predictive quantile, baseline rate, target rate, likelihood score, reset value, decision limit, EWMA weight, starting value, variance model, calendar effect, exposure denominator, random seed, monitoring horizon or validation period. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep observation, preprocessing, baseline design, model, computation, threshold, uncertainty, interpretation and independent investigation on separate notebook lines. Reserve complete periods outside tuning when testing transfer.

Workshop 11: Predictive threshold

Begin with this mechanism: Calculate an upper quantile for Y0. Recreate the concrete case: A count above U is flagged. Write case counts, reporting weeks, historical windows, fitted means, trend coefficients, seasonal factors, dispersion factors, residual weights, predictive limits, exceedance scores, alarm flags and investigation outcomes with units, denominators and assumptions. Calculate the smallest non-trivial example by hand and reproduce it in a spreadsheet or short program. Challenge this limitation: Approximation can fail at tiny counts. Complete the transfer step: Validate by simulation. Change exactly one observed count, reporting date, historical window, baseline mean, standard deviation, guard-band length, dispersion factor, trend term, seasonal factor, robust weight, predictive quantile, baseline rate, target rate, likelihood score, reset value, decision limit, EWMA weight, starting value, variance model, calendar effect, exposure denominator, random seed, monitoring horizon or validation period. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep observation, preprocessing, baseline design, model, computation, threshold, uncertainty, interpretation and independent investigation on separate notebook lines. Reserve complete periods outside tuning when testing transfer.

Workshop 12: Exceedance score

Begin with this mechanism: Scale how far the observation passes expectation. Recreate the concrete case: Y0=9 is compared with μ0 and U. Write case counts, reporting weeks, historical windows, fitted means, trend coefficients, seasonal factors, dispersion factors, residual weights, predictive limits, exceedance scores, alarm flags and investigation outcomes with units, denominators and assumptions. Calculate the smallest non-trivial example by hand and reproduce it in a spreadsheet or short program. Challenge this limitation: Scores from different settings differ. Complete the transfer step: State the formula. Change exactly one observed count, reporting date, historical window, baseline mean, standard deviation, guard-band length, dispersion factor, trend term, seasonal factor, robust weight, predictive quantile, baseline rate, target rate, likelihood score, reset value, decision limit, EWMA weight, starting value, variance model, calendar effect, exposure denominator, random seed, monitoring horizon or validation period. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep observation, preprocessing, baseline design, model, computation, threshold, uncertainty, interpretation and independent investigation on separate notebook lines. Reserve complete periods outside tuning when testing transfer.

Workshop 13: Alarm rule

Begin with this mechanism: Freeze the decision before viewing outcomes. Recreate the concrete case: Flag when count exceeds U. Write case counts, reporting weeks, historical windows, fitted means, trend coefficients, seasonal factors, dispersion factors, residual weights, predictive limits, exceedance scores, alarm flags and investigation outcomes with units, denominators and assumptions. Calculate the smallest non-trivial example by hand and reproduce it in a spreadsheet or short program. Challenge this limitation: Repeated testing creates alarms. Complete the transfer step: Track the full stream. Change exactly one observed count, reporting date, historical window, baseline mean, standard deviation, guard-band length, dispersion factor, trend term, seasonal factor, robust weight, predictive quantile, baseline rate, target rate, likelihood score, reset value, decision limit, EWMA weight, starting value, variance model, calendar effect, exposure denominator, random seed, monitoring horizon or validation period. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep observation, preprocessing, baseline design, model, computation, threshold, uncertainty, interpretation and independent investigation on separate notebook lines. Reserve complete periods outside tuning when testing transfer.

Workshop 14: Backtest

Begin with this mechanism: Replay old data without peeking forward. Recreate the concrete case: Historical outbreaks and quiet weeks are scored. Write case counts, reporting weeks, historical windows, fitted means, trend coefficients, seasonal factors, dispersion factors, residual weights, predictive limits, exceedance scores, alarm flags and investigation outcomes with units, denominators and assumptions. Calculate the smallest non-trivial example by hand and reproduce it in a spreadsheet or short program. Challenge this limitation: Labels may be incomplete. Complete the transfer step: Report multiple metrics. Change exactly one observed count, reporting date, historical window, baseline mean, standard deviation, guard-band length, dispersion factor, trend term, seasonal factor, robust weight, predictive quantile, baseline rate, target rate, likelihood score, reset value, decision limit, EWMA weight, starting value, variance model, calendar effect, exposure denominator, random seed, monitoring horizon or validation period. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep observation, preprocessing, baseline design, model, computation, threshold, uncertainty, interpretation and independent investigation on separate notebook lines. Reserve complete periods outside tuning when testing transfer.

Workshop 15: Operational review

Begin with this mechanism: Check delay and false-alert burden. Recreate the concrete case: Analysts can investigate the alarm volume. Write case counts, reporting weeks, historical windows, fitted means, trend coefficients, seasonal factors, dispersion factors, residual weights, predictive limits, exceedance scores, alarm flags and investigation outcomes with units, denominators and assumptions. Calculate the smallest non-trivial example by hand and reproduce it in a spreadsheet or short program. Challenge this limitation: Perfect sensitivity may be unusable. Complete the transfer step: Match resources. Change exactly one observed count, reporting date, historical window, baseline mean, standard deviation, guard-band length, dispersion factor, trend term, seasonal factor, robust weight, predictive quantile, baseline rate, target rate, likelihood score, reset value, decision limit, EWMA weight, starting value, variance model, calendar effect, exposure denominator, random seed, monitoring horizon or validation period. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep observation, preprocessing, baseline design, model, computation, threshold, uncertainty, interpretation and independent investigation on separate notebook lines. Reserve complete periods outside tuning when testing transfer.

Workshop 16: Investigation

Begin with this mechanism: Combine the signal with field evidence. Recreate the concrete case: Reporting changes are checked first. Write case counts, reporting weeks, historical windows, fitted means, trend coefficients, seasonal factors, dispersion factors, residual weights, predictive limits, exceedance scores, alarm flags and investigation outcomes with units, denominators and assumptions. Calculate the smallest non-trivial example by hand and reproduce it in a spreadsheet or short program. Challenge this limitation: The algorithm cannot identify cause. Complete the transfer step: Document resolution. Change exactly one observed count, reporting date, historical window, baseline mean, standard deviation, guard-band length, dispersion factor, trend term, seasonal factor, robust weight, predictive quantile, baseline rate, target rate, likelihood score, reset value, decision limit, EWMA weight, starting value, variance model, calendar effect, exposure denominator, random seed, monitoring horizon or validation period. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep observation, preprocessing, baseline design, model, computation, threshold, uncertainty, interpretation and independent investigation on separate notebook lines. Reserve complete periods outside tuning when testing transfer.