For the above calculation we had a great deal of knowledge about the variance of the noise entering the model. If you don't know the variances, it might be possible to estimate them. We can, for example search over some or all of the noise terms in addition to the adjustments times. The file wfkal2.voc does this for everything starting at a value of 20. Note that MEAS INVENTORY VARIANCE is not included since the payoff definition does not use the measured inventory.
When we optimize, we get the results:
Maximum payoff found at:.
INVENTORY DRIVE VARIANCE = 12.1912 (33)
WORKFORCE DRIVE VARIANCE = 1.18771 (1.3)
MEAS WORKFORCE VARIANCE = 0.667975 (.5)
TIME CORRECT INVENTORY = 3.66288 (4)
*TIME ADJUST WORKFORCE = 13.0956 (12)
It takes over 500 simulations, but the numbers are reasonably good — the correct values are shown to the right. The variance measures as not that accurate, but the measurements of the parameters are quite reasonable. The actual values are also all well within the 95% confidence bounds.
Using filtering combined with optimization it is possible to accurately estimate structural parameters in a model with limited knowledge of the stochastic characteristics of the model. This is the magic of Schweppe Statistics. See Information Resources for more references.
