Chapter map

1. 1. Series stream
2. 2. Current regime
3. 3. Cut-off length l
4. 4. Probability level p
5. 5. Variance estimate
6. 6. Critical t
7. 7. Critical difference
8. 8. Candidate crossing
9. 9. Shift direction
10. 10. RSI start
11. 11. Confirmation window
12. 12. Candidate rejection
13. 13. Confirmed regime
14. 14. Autocorrelation
15. 15. Parameter sensitivity
16. 16. Independent explanation

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. Series stream

The useful question is not only how to calculate, but what the calculation assumes. Order complete observations through time.

A concrete situation

New values arrive yearly.

What the mathematics does not license

Backfilled data changes earlier decisions. The same reasoning helps students move from an exercise to a real dataset.

Try it, check it, transfer it

Version releases. 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. Current regime

A small example makes the mechanism visible. Estimate the active regime mean.

A concrete situation

The old mean is zero after standardization.

What the mathematics does not license

A changing mean is not stable. That distinction matters because a correct formula can still answer the wrong operational question.

Try it, check it, transfer it

Monitor 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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3. Cut-off length l

This is where modelling choices begin to affect evidence. Set the minimum regime horizon.

A concrete situation

l=10.

What the mathematics does not license

Long l delays detection. The habit of checking assumptions is one of the practical benefits of learning mathematics.

Try it, check it, transfer it

Match the question. 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. Probability level p

The central mathematical idea is concrete. Choose the candidate confidence rule.

A concrete situation

p=.05.

What the mathematics does not license

Repeated sequential testing changes error rates. The same reasoning helps students move from an exercise to a real dataset.

Try it, check it, transfer it

Evaluate operation. 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. Variance estimate

Here the geometry becomes operational. Estimate variability for the t comparison.

A concrete situation

Standard deviation is one.

What the mathematics does not license

Outliers inflate it. That distinction matters because a correct formula can still answer the wrong operational question.

Try it, check it, transfer it

Use declared weighting. 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. Critical t

This step deserves a careful pause. Use the degrees of freedom implied by l.

A concrete situation

At 2l-2=18, t≈2.1.

What the mathematics does not license

Dependence reduces effective information. The habit of checking assumptions is one of the practical benefits of learning mathematics.

Try it, check it, transfer it

Adjust carefully. 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. Critical difference

The useful question is not only how to calculate, but what the calculation assumes. Translate t and variance into mean separation.

A concrete situation

diff≈.94 in the paper example.

What the mathematics does not license

Different l changes diff. The same reasoning helps students move from an exercise to a real dataset.

Try it, check it, transfer it

Publish the calculation. 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. Candidate crossing

A small example makes the mechanism visible. Compare the new point with regime mean plus diff.

A concrete situation

A value 1.2 crosses by .26.

What the mathematics does not license

One point can be an outlier. That distinction matters because a correct formula can still answer the wrong operational question.

Try it, check it, transfer it

Begin confirmation only. 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. Shift direction

This is where modelling choices begin to affect evidence. Lock the candidate direction.

A concrete situation

The proposed shift is upward.

What the mathematics does not license

Mixed signs weaken the case. The habit of checking assumptions is one of the practical benefits of learning mathematics.

Try it, check it, transfer it

Track each value. 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. RSI start

The central mathematical idea is concrete. Initialize cumulative normalized evidence.

A concrete situation

The first supporting value gives positive RSI.

What the mathematics does not license

Formula conventions must match software. The same reasoning helps students move from an exercise to a real dataset.

Try it, check it, transfer it

Archive every term. 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. Confirmation window

Here the geometry becomes operational. Read up to l supporting observations.

A concrete situation

Later values remain above the boundary.

What the mathematics does not license

Missing values reduce evidence. That distinction matters because a correct formula can still answer the wrong operational question.

Try it, check it, transfer it

Declare handling. 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. Candidate rejection

This step deserves a careful pause. Cancel when evidence reverses under the rule.

A concrete situation

A low value can end the candidate.

What the mathematics does not license

Aggressive rejection may miss noisy shifts. The habit of checking assumptions is one of the practical benefits of learning mathematics.

Try it, check it, transfer it

Backtest. 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. Confirmed regime

The useful question is not only how to calculate, but what the calculation assumes. Update the regime mean after confirmation.

A concrete situation

The new segment becomes active.

What the mathematics does not license

Early mean estimates are uncertain. The same reasoning helps students move from an exercise to a real dataset.

Try it, check it, transfer it

Show revisions. 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. Autocorrelation

A small example makes the mechanism visible. Adjust or prewhiten only with a plan.

A concrete situation

AR(1) reduces effective sample size.

What the mathematics does not license

Poor prewhitening creates artefacts. That distinction matters because a correct formula can still answer the wrong operational question.

Try it, check it, transfer it

Compare raw and adjusted. 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. Parameter sensitivity

This is where modelling choices begin to affect evidence. Repeat plausible l and p choices.

A concrete situation

Major shifts persist across a grid.

What the mathematics does not license

Selecting one convenient result is biased. The habit of checking assumptions is one of the practical benefits of learning mathematics.

Try it, check it, transfer it

Report all declared settings. 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. Independent explanation

The central mathematical idea is concrete. Compare shifts with external evidence.

A concrete situation

A system redesign occurs nearby.

What the mathematics does not license

Timing alone is not causation. The same reasoning helps students move from an exercise to a real dataset.

Try it, check it, transfer it

Investigate mechanisms. 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

Rodionov’s sequential regime-shift algorithm was designed to detect a persistent change near the end of a growing time series instead of waiting until many later observations have accumulated. It proposes a candidate new regime when a value crosses a critical difference from the current regime mean, then uses a regime shift index to test whether subsequent values support persistence.

The method declares a cut-off length l, a significance level p and a variance estimate. These determine a critical difference between regime means through a Student t construction. A candidate shift must maintain the same direction during the confirmation window; contradictory observations can reject the candidate and return monitoring to the previous regime.

In the paper’s standardized illustration, l=10 and p=.05 give a critical difference of about .94 when the relevant standard deviation is one. A new value 1.2 above the current regime mean crosses that candidate threshold by .26. It is still only the first step: the following observations must build a positive regime shift index rather than reverse direction.

The algorithm’s sensitivity depends on l, p, variance estimation, autocorrelation treatment, outliers and missing data. A regime is a statistical level segment, not proof of a physical state change. Responsible use publishes the full RSI path, candidate rejections, parameter sensitivity and independent evidence about mechanisms.

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Frequently asked questions

What is a statistical regime?

It is a segment treated as having a relatively stable level under the chosen algorithm and parameters.

What does cut-off length l mean?

It is the minimum persistence horizon used to define and confirm a candidate regime.

What is the critical difference?

It is the mean separation required by the declared variance, l and probability level.

What is the RSI?

The regime shift index accumulates normalized evidence from observations after a candidate shift.

Can a candidate be rejected?

Yes. Opposite-direction observations during confirmation can cancel the evidence and return monitoring to the old regime.

Does a confirmed regime prove a physical mechanism?

No. It is a statistical segmentation that requires independent scientific or operational explanation.

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Primary source and fact-check note

Sergei N. Rodionov, “A Sequential Algorithm for Testing Climate Regime Shifts,” Geophysical Research Letters 31, L09204 (2004), DOI 10.1029/2004GL019448. 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

• Page–Hinkley change detection
• Buishand range test
• 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

Stream audit

Version observations and revisions.

Parameter audit

Publish l, p, variance and degrees of freedom.

Difference audit

Reproduce the critical mean separation.

Candidate audit

Archive every crossing and direction.

RSI audit

Show cumulative confirmation values.

Rejection audit

Record failed candidates as well as confirmed shifts.

Sensitivity audit

Report plausible parameter grids.

Final claim

Describe a regime segment without causal certainty.

Mechanism workshop: calculate, challenge and transfer

Workshop 1: Series stream

Begin with this mechanism: Order complete observations through time. Recreate the concrete case: New values arrive yearly. Write observations, regime means, cut-off lengths, probability levels, variance estimates, degrees of freedom, critical t values, critical differences, candidate directions, RSI terms, confirmation windows and regime labels 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: Backfilled data changes earlier decisions. Complete the transfer step: Version releases. Change exactly one observation, date, analysis window, reference station, reference weight, mean, standard deviation, split point, segment length, cumulative deviation, range, tie rule, pair sign, cut-off length, probability level, critical value, autocorrelation estimate, null model, simulation seed, seasonal grouping, metadata event or validation period. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep observation, preprocessing, statistic, complete-search calibration, uncertainty, interpretation and independent validation on separate notebook lines. Reserve complete periods or reference series outside tuning when testing transfer.

Workshop 2: Current regime

Begin with this mechanism: Estimate the active regime mean. Recreate the concrete case: The old mean is zero after standardization. Write observations, regime means, cut-off lengths, probability levels, variance estimates, degrees of freedom, critical t values, critical differences, candidate directions, RSI terms, confirmation windows and regime labels 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: A changing mean is not stable. Complete the transfer step: Monitor residuals. Change exactly one observation, date, analysis window, reference station, reference weight, mean, standard deviation, split point, segment length, cumulative deviation, range, tie rule, pair sign, cut-off length, probability level, critical value, autocorrelation estimate, null model, simulation seed, seasonal grouping, metadata event or validation period. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep observation, preprocessing, statistic, complete-search calibration, uncertainty, interpretation and independent validation on separate notebook lines. Reserve complete periods or reference series outside tuning when testing transfer.

Workshop 3: Cut-off length l

Begin with this mechanism: Set the minimum regime horizon. Recreate the concrete case: l=10. Write observations, regime means, cut-off lengths, probability levels, variance estimates, degrees of freedom, critical t values, critical differences, candidate directions, RSI terms, confirmation windows and regime labels 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: Long l delays detection. Complete the transfer step: Match the question. Change exactly one observation, date, analysis window, reference station, reference weight, mean, standard deviation, split point, segment length, cumulative deviation, range, tie rule, pair sign, cut-off length, probability level, critical value, autocorrelation estimate, null model, simulation seed, seasonal grouping, metadata event or validation period. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep observation, preprocessing, statistic, complete-search calibration, uncertainty, interpretation and independent validation on separate notebook lines. Reserve complete periods or reference series outside tuning when testing transfer.

Workshop 4: Probability level p

Begin with this mechanism: Choose the candidate confidence rule. Recreate the concrete case: p=.05. Write observations, regime means, cut-off lengths, probability levels, variance estimates, degrees of freedom, critical t values, critical differences, candidate directions, RSI terms, confirmation windows and regime labels 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 sequential testing changes error rates. Complete the transfer step: Evaluate operation. Change exactly one observation, date, analysis window, reference station, reference weight, mean, standard deviation, split point, segment length, cumulative deviation, range, tie rule, pair sign, cut-off length, probability level, critical value, autocorrelation estimate, null model, simulation seed, seasonal grouping, metadata event or validation period. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep observation, preprocessing, statistic, complete-search calibration, uncertainty, interpretation and independent validation on separate notebook lines. Reserve complete periods or reference series outside tuning when testing transfer.

Workshop 5: Variance estimate

Begin with this mechanism: Estimate variability for the t comparison. Recreate the concrete case: Standard deviation is one. Write observations, regime means, cut-off lengths, probability levels, variance estimates, degrees of freedom, critical t values, critical differences, candidate directions, RSI terms, confirmation windows and regime labels 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: Outliers inflate it. Complete the transfer step: Use declared weighting. Change exactly one observation, date, analysis window, reference station, reference weight, mean, standard deviation, split point, segment length, cumulative deviation, range, tie rule, pair sign, cut-off length, probability level, critical value, autocorrelation estimate, null model, simulation seed, seasonal grouping, metadata event or validation period. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep observation, preprocessing, statistic, complete-search calibration, uncertainty, interpretation and independent validation on separate notebook lines. Reserve complete periods or reference series outside tuning when testing transfer.

Workshop 6: Critical t

Begin with this mechanism: Use the degrees of freedom implied by l. Recreate the concrete case: At 2l-2=18, t≈2.1. Write observations, regime means, cut-off lengths, probability levels, variance estimates, degrees of freedom, critical t values, critical differences, candidate directions, RSI terms, confirmation windows and regime labels 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: Dependence reduces effective information. Complete the transfer step: Adjust carefully. Change exactly one observation, date, analysis window, reference station, reference weight, mean, standard deviation, split point, segment length, cumulative deviation, range, tie rule, pair sign, cut-off length, probability level, critical value, autocorrelation estimate, null model, simulation seed, seasonal grouping, metadata event or validation period. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep observation, preprocessing, statistic, complete-search calibration, uncertainty, interpretation and independent validation on separate notebook lines. Reserve complete periods or reference series outside tuning when testing transfer.

Workshop 7: Critical difference

Begin with this mechanism: Translate t and variance into mean separation. Recreate the concrete case: diff≈.94 in the paper example. Write observations, regime means, cut-off lengths, probability levels, variance estimates, degrees of freedom, critical t values, critical differences, candidate directions, RSI terms, confirmation windows and regime labels 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: Different l changes diff. Complete the transfer step: Publish the calculation. Change exactly one observation, date, analysis window, reference station, reference weight, mean, standard deviation, split point, segment length, cumulative deviation, range, tie rule, pair sign, cut-off length, probability level, critical value, autocorrelation estimate, null model, simulation seed, seasonal grouping, metadata event or validation period. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep observation, preprocessing, statistic, complete-search calibration, uncertainty, interpretation and independent validation on separate notebook lines. Reserve complete periods or reference series outside tuning when testing transfer.

Workshop 8: Candidate crossing

Begin with this mechanism: Compare the new point with regime mean plus diff. Recreate the concrete case: A value 1.2 crosses by .26. Write observations, regime means, cut-off lengths, probability levels, variance estimates, degrees of freedom, critical t values, critical differences, candidate directions, RSI terms, confirmation windows and regime labels 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: One point can be an outlier. Complete the transfer step: Begin confirmation only. Change exactly one observation, date, analysis window, reference station, reference weight, mean, standard deviation, split point, segment length, cumulative deviation, range, tie rule, pair sign, cut-off length, probability level, critical value, autocorrelation estimate, null model, simulation seed, seasonal grouping, metadata event or validation period. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep observation, preprocessing, statistic, complete-search calibration, uncertainty, interpretation and independent validation on separate notebook lines. Reserve complete periods or reference series outside tuning when testing transfer.

Workshop 9: Shift direction

Begin with this mechanism: Lock the candidate direction. Recreate the concrete case: The proposed shift is upward. Write observations, regime means, cut-off lengths, probability levels, variance estimates, degrees of freedom, critical t values, critical differences, candidate directions, RSI terms, confirmation windows and regime labels 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: Mixed signs weaken the case. Complete the transfer step: Track each value. Change exactly one observation, date, analysis window, reference station, reference weight, mean, standard deviation, split point, segment length, cumulative deviation, range, tie rule, pair sign, cut-off length, probability level, critical value, autocorrelation estimate, null model, simulation seed, seasonal grouping, metadata event or validation period. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep observation, preprocessing, statistic, complete-search calibration, uncertainty, interpretation and independent validation on separate notebook lines. Reserve complete periods or reference series outside tuning when testing transfer.

Workshop 10: RSI start

Begin with this mechanism: Initialize cumulative normalized evidence. Recreate the concrete case: The first supporting value gives positive RSI. Write observations, regime means, cut-off lengths, probability levels, variance estimates, degrees of freedom, critical t values, critical differences, candidate directions, RSI terms, confirmation windows and regime labels 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: Formula conventions must match software. Complete the transfer step: Archive every term. Change exactly one observation, date, analysis window, reference station, reference weight, mean, standard deviation, split point, segment length, cumulative deviation, range, tie rule, pair sign, cut-off length, probability level, critical value, autocorrelation estimate, null model, simulation seed, seasonal grouping, metadata event or validation period. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep observation, preprocessing, statistic, complete-search calibration, uncertainty, interpretation and independent validation on separate notebook lines. Reserve complete periods or reference series outside tuning when testing transfer.

Workshop 11: Confirmation window

Begin with this mechanism: Read up to l supporting observations. Recreate the concrete case: Later values remain above the boundary. Write observations, regime means, cut-off lengths, probability levels, variance estimates, degrees of freedom, critical t values, critical differences, candidate directions, RSI terms, confirmation windows and regime labels 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: Missing values reduce evidence. Complete the transfer step: Declare handling. Change exactly one observation, date, analysis window, reference station, reference weight, mean, standard deviation, split point, segment length, cumulative deviation, range, tie rule, pair sign, cut-off length, probability level, critical value, autocorrelation estimate, null model, simulation seed, seasonal grouping, metadata event or validation period. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep observation, preprocessing, statistic, complete-search calibration, uncertainty, interpretation and independent validation on separate notebook lines. Reserve complete periods or reference series outside tuning when testing transfer.

Workshop 12: Candidate rejection

Begin with this mechanism: Cancel when evidence reverses under the rule. Recreate the concrete case: A low value can end the candidate. Write observations, regime means, cut-off lengths, probability levels, variance estimates, degrees of freedom, critical t values, critical differences, candidate directions, RSI terms, confirmation windows and regime labels 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: Aggressive rejection may miss noisy shifts. Complete the transfer step: Backtest. Change exactly one observation, date, analysis window, reference station, reference weight, mean, standard deviation, split point, segment length, cumulative deviation, range, tie rule, pair sign, cut-off length, probability level, critical value, autocorrelation estimate, null model, simulation seed, seasonal grouping, metadata event or validation period. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep observation, preprocessing, statistic, complete-search calibration, uncertainty, interpretation and independent validation on separate notebook lines. Reserve complete periods or reference series outside tuning when testing transfer.

Workshop 13: Confirmed regime

Begin with this mechanism: Update the regime mean after confirmation. Recreate the concrete case: The new segment becomes active. Write observations, regime means, cut-off lengths, probability levels, variance estimates, degrees of freedom, critical t values, critical differences, candidate directions, RSI terms, confirmation windows and regime labels 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: Early mean estimates are uncertain. Complete the transfer step: Show revisions. Change exactly one observation, date, analysis window, reference station, reference weight, mean, standard deviation, split point, segment length, cumulative deviation, range, tie rule, pair sign, cut-off length, probability level, critical value, autocorrelation estimate, null model, simulation seed, seasonal grouping, metadata event or validation period. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep observation, preprocessing, statistic, complete-search calibration, uncertainty, interpretation and independent validation on separate notebook lines. Reserve complete periods or reference series outside tuning when testing transfer.

Workshop 14: Autocorrelation

Begin with this mechanism: Adjust or prewhiten only with a plan. Recreate the concrete case: AR(1) reduces effective sample size. Write observations, regime means, cut-off lengths, probability levels, variance estimates, degrees of freedom, critical t values, critical differences, candidate directions, RSI terms, confirmation windows and regime labels 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: Poor prewhitening creates artefacts. Complete the transfer step: Compare raw and adjusted. Change exactly one observation, date, analysis window, reference station, reference weight, mean, standard deviation, split point, segment length, cumulative deviation, range, tie rule, pair sign, cut-off length, probability level, critical value, autocorrelation estimate, null model, simulation seed, seasonal grouping, metadata event or validation period. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep observation, preprocessing, statistic, complete-search calibration, uncertainty, interpretation and independent validation on separate notebook lines. Reserve complete periods or reference series outside tuning when testing transfer.

Workshop 15: Parameter sensitivity

Begin with this mechanism: Repeat plausible l and p choices. Recreate the concrete case: Major shifts persist across a grid. Write observations, regime means, cut-off lengths, probability levels, variance estimates, degrees of freedom, critical t values, critical differences, candidate directions, RSI terms, confirmation windows and regime labels 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: Selecting one convenient result is biased. Complete the transfer step: Report all declared settings. Change exactly one observation, date, analysis window, reference station, reference weight, mean, standard deviation, split point, segment length, cumulative deviation, range, tie rule, pair sign, cut-off length, probability level, critical value, autocorrelation estimate, null model, simulation seed, seasonal grouping, metadata event or validation period. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep observation, preprocessing, statistic, complete-search calibration, uncertainty, interpretation and independent validation on separate notebook lines. Reserve complete periods or reference series outside tuning when testing transfer.

Workshop 16: Independent explanation

Begin with this mechanism: Compare shifts with external evidence. Recreate the concrete case: A system redesign occurs nearby. Write observations, regime means, cut-off lengths, probability levels, variance estimates, degrees of freedom, critical t values, critical differences, candidate directions, RSI terms, confirmation windows and regime labels 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: Timing alone is not causation. Complete the transfer step: Investigate mechanisms. Change exactly one observation, date, analysis window, reference station, reference weight, mean, standard deviation, split point, segment length, cumulative deviation, range, tie rule, pair sign, cut-off length, probability level, critical value, autocorrelation estimate, null model, simulation seed, seasonal grouping, metadata event or validation period. Explain which mathematical object changes, which conclusion survives and which claim must weaken. Keep observation, preprocessing, statistic, complete-search calibration, uncertainty, interpretation and independent validation on separate notebook lines. Reserve complete periods or reference series outside tuning when testing transfer.