1Ezra Hauer, Haarlem Nov. 2009

Prediction in Road Safety

1. What is Prediction and When is it Needed?

a. When setting safety targets, predict what would be safety in the future if no new initiatives will be taken.

b. When estimating safety effect, predict what would have been safety in the past had there been no initiatives.

Similarity: Both predictions pertain to ‘potential’ events.Difference: (a) is in the future. Circumstances unknown at time of prediction; (b) is in the past. Circumstances known at time of prediction.

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Illustration:New safety targets set by CCMTA in October 2000 (Vision 2010).

What would safety in the future be if no new initiatives taken?

If straight line then P for 2010 is about 1800

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What would safety in the future be if no new initiatives taken?

If exponential then P for 2010 is about 2000

Problem:There are many ways to predict and even more predictions,Which prediction to choose?

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The CCMTA (October 2000):“The national target calls for a 30% decrease in the average number of road users killed and seriously injured during the 2008-2010 period over comparable 1996-2001 figures. … Achievement of these targets would reduce Canada’s road fatality total to fewer than 2,100 by 2010.”

But, where is the prediction in this?

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2. Same Data, Different Predictions, Which is best?

Suppose that I am at the end of 1985 and want to predict for the next 10 years

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1. Straight Line

2. Second degree polynomial

Alternative Methods of Prediction

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3. Hoerl Function

4. Holt Smoothing,5. Oppe-Koornstra model

Which is best?

More Methods of Prediction

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3.How to Measure Prediction Quality

Years 1986 1987 1988 … 1994 1995

s Steps Ahead 1 2 3 … 9 10

P OLS linear, n=5 199.9 188.4 176.9 … 107.9 96.4

X Fatalities 245 236 200 … 151 157

D Differences 45.1 47.6 26.6 … 43.1 60.6

d Relative Differences (D/X) 0.18 0.20 0.14 … 0.29 0.39

OLS, Linear Predictions for 10 years following 1985

Years 1985 1986 1987 … 1993 1994

s Steps Ahead 1 2 3 … 9 10

P OLS linear, n=5 210.1 198.6 187.1 … 118.1 106.6X Fatalities 214 245 236 … 153 151D Differences 3.9 46.4 48.9 … 34.9 44.4d Relative Differences (D/X) 0.02 0.19 0.21 … 0.23 0.29

OLS, Linear Predictions for 10 years following 1984

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Last Data Year

Steps Ahead

1 2 … 9 10

1956 -0.11 0.05 … 0.18 0.17

1957 0.03 -0.08 … 0.05 -0.09

… … … … … …

1996 0.14 0.05 … 0.12 0.06

1997 -0.04 0.17 … -0.16 -0.11

Avg(d) -0.01 -0.01 -0.06 -0.06

σavg(d) 0.13 0.20 0.55 0.61

σ0 0.13 0.20 0.56 0.62

n=5

Attributes of prediction quality

44 rows

d, relativedifferences

The Basis idea: Judge the quality of a prediction method by how it would have performed had it been used in the past.

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Q1: If (for Saskatchewan) prediction is by OLS then what n is best?

4. Now some questions can be answered

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A1: If (for Saskatchewan) prediction is by OLS then n=10 is best?

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Q2: For Saskatchewan, is OLS better than QLS?

OLS

QLS

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Results for two Provinces:For Saskatchewan, Hoerl Function with n=10 and 19 best;For Ontario, Linear (n=10), Holt (A) and Hoerl (n=12) were best

5. Summary and Discussion

a. Prediction is not estimation nor curve fitting; it is about ‘what will happen if’ or ‘what would have happened if’

b. To say which of two prediction methods is better one has to have a yardstick for quality.I suggested to compute how the two methods would have performed in the past, had they been used and to compare their

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c. Broad Conclusions will emerge only after the approach will be applied to many data sets and tried with many methods of prediction.