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Old 13th Sep 2009, 02:35
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Ian Bryce
 
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A word on statistical techniques - how to predict from sparse data.
Leadsled said in post 259:

"Perhaps you could explain why [Ambidji] have excluded the long period of time (often with higher movement rates than the last nine years) when there were ZERO MACs".
A good question - it is a common problem that the actual data is too thin to analyse normally. We have 40 years data but when split into decades there are too few MACs to get a smooth curve.
One is tempted to take an average of the lot - but this gives equal weight to ancient data when practices and technologies were different.
Or one can take the latest year, decade, 20 yrs etc - but the weighting jumps from zero to full at some arbitrary date.

A sounder approach is to apply most significance to the latest data (eg decade), less to the previous decade, and even less to the previous again, etc. There is no sharp cutoff. One only needs to decide on a "relaxation period" where the technology has changed a certain amount, and where the relative weighting falls to 1/e = 0.368.

It is called "exponentially reducing weighting" and is all in Wiki.

I used this method (page 9), taking a relaxation period of 30 years (the results are not very sensitive to this). Thus to predict future MACS, we take a weighted average of all past data. The actuals for 2000-09 are weighted with 1.0, for 1990-99 with 0,717, for 1980-89 with 0.513, and for 1969-70 with 0.368. The result for BK is a rate of 0.16 pa. (The Springside MAC model, unifying all 6 aerodromes, later gives 0.14 for BK.

This method optimally combines the empty decade with the high decade, and all the other data. One rule for all sites. No discussion or selection of the "best feeling" data is necessary.

Last edited by Ian Bryce; 13th Sep 2009 at 02:37. Reason: clarity.
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