High-conviction estimators

We shall find estimates hm in numerical cases consisting of experimental data (Section XI.A) and simulated data (Section XI.B). In all cases, high-conviction form (20) will be assumed because the solutions hm are relatively easy to form and because of the ease with which prior knowledge Qm may be varied. In Section XI.A low photon occupancy nm/zm will be assumed, whereas in Section XI.B both low and high occupancies will be allowed. Note that low occupancy is consistent with maximum entropy according to Section IX.B, that is, particlelike behavior for the photons, whereas high occupancy is consistent with wavelike behavior for the photons. How, then, does the wave or particle nature of photons affect the estimates ... 

It is important to realize, however, that this similarity is a coincidence of the case. Jansson s boundedness constraint always tends toward smoothness near the bounds, regardless of a priori knowledge of object class, whereas our ML estimator [Eqs. (17) and (19)] can be constrained toward bumpy solutions, the bumps consistent with the prior knowledge at hand. In the high-conviction case that we are treating here, the bumps would be manifest in the inputs Qm. We next study the effect of varying the Qm in some computer simulations. 

The formal model has one other benefit that is quite critical for application of the DECP, and that is the ability to adjust the model to arrive at different tradeoffs between the two types of errors misses and false alarms. As modeled above, the regression models minimized all errors. However, for law enforcement purposes, it is much more important to miss some drug-impaired drivers (and thus accept a high level of misses), than to arrest unimpaired drivers (and accept a high level of false alarms). This is because criminal conviction must be rest on evidence that is beyond reasonable doubt , and obviously an estimate that is associated with a high level of false alarms fails this test. 

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