Woodpecker ID Probabilities
This puzzle has direct relevance to the evaluation of sight records of Ivory-billed Woodpeckers in habitats in which Pileated Woodpeckers are known to be common. Given that there are so few (if any) Ivory-billed Woodpeckers in the Big Woods of Arkansas (or anywhere else, for that matter) relative to the number of Pileated Woodpeckers, and taking into consideration the "base rate" (an important principal that is often neglected, is explained here), it is more likely that a bird identified as an Ivory-billed Woodpecker is actually a misidentified Pileated Woodpecker.
Let’s assume, for the sake of argument and illustration, that a mature bottomland hardwood forest somewhere in the southern U.S. harbors two types of large woodpeckers, dark-winged and white-winged; 99 percent of the birds have dark wings and 1 percent have white wings. Let’s also assume that an experienced observer is able to correctly identify the woodpeckers to species based on wing color 99.5 percent of the time. Plugging these numbers into the formula, we find that the post-hoc probability of the observer being able to correctly identify a fly-by white-winged woodpecker is 67 percent (not 99.5 percent). The probability of a correct identification declines rapidly with declines in either observer ability or the proportion of white-winged woodpeckers. For example, if the observer’s ability to correctly identify flying woodpeckers to species is reduced slightly to a still-respectable 95 percent, then the post-observation probability of the observer’s identification of a white-winged woodpecker being correct plummets to just 16 percent! And if the proportion of white-winged woodpeckers in the population is reduced to 0.5 percent while holding observer ability steady at 99.5 percent, then the post-observation probability of a white-winged woodpecker ID being correct drops to 50 percent.
So, part of the problem of assessing the validity of sightings of Ivory-billed Woodpedckers lies in numbers which remain largely unknown: (1) the proportion of Ivory-billed Woodpeckers relative to Pileated Woodpeckers in various tracts of bottomland hardwood forests in the southern U.S., and (2) the probability with which field observers are able to make correct identifications of large woodpeckers. Given the current status of the Ivory-billed Woodpecker, the former number will always be at or near zero. The latter number will vary from one observer to another and from one habitat to another, and I have no way of knowing if it is close to 100 percent or nearer to 95 percent. Are the identification skills of volunteer observers tested before they are sent into the field?
At any rate, the base numbers alone seem to favor Pileated Woodpeckers to such a degree that "extraordinary evidence" would be required to accept any sighting of an Ivory-billed Woodpecker as scientifically valid.