Measuring Forecaster Performance

NATIONAL DEFENSE INTELLIGENCE COLLEGE

Measuring Forecaster Performance

Lt Col James E. Kajdasz, Ph.D., USAF

NATIONAL DEFENSE INTELLIGENCE COLLEGEScholarship of Intelligence Analysis

• “A comprehensive review of the literature indicates that while much has been written, largely there has not been a progression of thinking relative to the core aspect and competencies of doing intelligence analysis.” (Mangio & Wilkinson, 2008)

• “Do [they] teach structured methods because they are the best way to do analysis, or do they teach structured methods because that’s what they can teach?” (Marrin, 2009)

NATIONAL DEFENSE INTELLIGENCE COLLEGEGrade forecasters on % correct?

judgments• We could grade forecaster accuracy similar to a T/F test. (yes/no answers)– Will Qadhafi still be in Libya at this time next year? No– Will the government of Yemen fall in the next year?

No– Will I still be driving my 2001 Corolla in the year

2020? Yes• Wait until outcomes occur/don’t occur, and

calculate percent of correct forecasts. • Compare Forecaster A to Forecaster B by

seeing who has the higher % correct.

NATIONAL DEFENSE INTELLIGENCE COLLEGEWhat about probabilistic judgments?

• When there is a high level of uncertainty, laypeople and even experts often qualify judgments. – Will Qadhafi still be in Libya at this time next year? No

(70% confidence)– Will the government of Yemen fall in the next year?

No (60% confidence)– Will I still be driving my 2001 Corolla in the year

2020? Yes (95% confidence)

NATIONAL DEFENSE INTELLIGENCE COLLEGEWhat about probabilistic judgments?

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NATIONAL DEFENSE INTELLIGENCE COLLEGELet’s Compare analysts…

• So which analyst performed best?

• It’s hard to say… We need a summary statistic to summarize total performance.

Probability assignedEvent Occurred? Analyst 1 Analyst 2 Analyst 3

1 No (0) 0 0 0.12 Yes (1) 0.9 0.7 0.73 No (0) 0.1 0.3 04 Yes (1) 0.7 0.5 0.55 Yes (1) 0.9 1 1

NATIONAL DEFENSE INTELLIGENCE COLLEGEMean Probability Score

• Probability Score or Brier Score

– Estimate: • Probability provided by forecaster• .00 – 1.00

– Outcome: • 0 (if event did not occur)• 1 (if event did occur)

( )PS2( )PS Estimate Outcome


• Probability Score or Brier Score

– Forecaster says 70% probability X will occur.– X occurs.–

2( )PS Estimate Outcome

2 2(.70 1) ( .3) .09PS

( )PS


• Mean Probability Score or Mean Brier Score 2 2(.70 1) ( .3) .09PS

( )PS

2 2(.50 0) ( .5) .25PS 2 2(.10 0) (.10) .01PS

.12PS

NATIONAL DEFENSE INTELLIGENCE COLLEGELet’s Compare analysts…

Probability assignedEvent Occurred? Analyst 1 Analyst 2 Analyst 3

1 No (0) 0 0 0.12 Yes (1) 0.9 0.7 0.73 No (0) 0.1 0.3 04 Yes (1) 0.7 0.5 0.55 Yes (1) 0.9 1 1

0.02 0.09 0.07PS

NATIONAL DEFENSE INTELLIGENCE COLLEGEComponents of Total Forecaster Error

• Several things contribute to overall error, not all of which can be controlled by the forecaster.

Total Forecasting Error

Discrimination Errors

( )PS

CalibrationErrors

Variance of the Outcome

NATIONAL DEFENSE INTELLIGENCE COLLEGEDecomposing Mean Probability Score

PS

2Var(d) + (bias) [Var(d)(slope)](slope-2)+scatterPS

Bias Slope Scatter Var(d)


Decomposing PS: Bias

Bias f d Where:

= Mean estimate

= Mean outcome

Arkes, Dawson, Speroff & et.al. (1995)

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Outcome Index (d)


Decomposing PS: Slope

1 0Slope f f Where:

= Mean estimate when outcome was 1

= Mean estimate when outcome was 0


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Decomposing PS: Scatter

Where:

= Variance when outcome was 1 = Variance when outcome was 0


1( )Var f

0( )Var f

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Outcome Index (d)

NATIONAL DEFENSE INTELLIGENCE COLLEGETitle

• Body

Patients DoctorsPS=.23 Bias=0.13 Slope=.13 Scat.=.05 PS=.18 Bias=-0.11 Slope=.26 Scat.=.05

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Outcome Index (d) Outcome Index (d)


NATIONAL DEFENSE INTELLIGENCE COLLEGEPrediction Markets

NATIONAL DEFENSE INTELLIGENCE COLLEGEA-priori Hypotheses:

• H1: Discrimination will improve as the event nears

– Slope measure will increase over time.• H2: Scatter will decrease as the event nears

– Scatter measure will get smaller over time.• H3: Analysts will be biased toward predicting

the status quo– Bias measure will be negative

NATIONAL DEFENSE INTELLIGENCE COLLEGET-70 Days


• PS is a measure of overall error

• low PS is better

• Graph suggests curvilinear relationship with time

Total Error over Time


• PS composed of Bias, Slope, Scatter, and Variance of the outcome

• Graph suggests decrease in error is primarily due to improvement in slope

• Slope is a measure of discrimination

• High slope is better

Components of Error


• The observed slope was modeled.

• Curvilinear relationship modeled with Days and Days2

• Adj R2 = .834, p=.01• H1 supported.

Discrimination improves as date approaches.

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Modeling Slope Over Time


• Scatter is a measure of ‘spread’ of probability estimates.

• Slight linear trend not significant.

• H2 not supported.

Scatter Over Time

NATIONAL DEFENSE INTELLIGENCE COLLEGEBias Over Time

• Questions recoded such that probability ‘0’ represented a continuation of status-quo, and probability ‘1’ represents a change in status-quo

• Analysts were biased toward predicting a change in the status-quo

– Indicated by positive bias numbers – t(6)=4.73, p < .01

• H3 not supported. • BUT significant results in the direction

opposite that hypothesized.• Linear trend over time not statistically

significant.


Lt Col James E. Kajdasz, Ph.D., [email protected]

The views expressed in this presentation are those of the author and do not reflect the official policy or position of the Department of Defense or the U.S.

Government.

Measuring Forecaster Performance

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