Ortolan is probably right that the Bayes approach is most appropriate when determining if an IBWO sighting is genuine. But to do that you need the following:
(A) The prevalence of IBWO as compared to other large woopecker-like birds.
Bittern's point about visibility could be factored into this figure.
(B) The proportion of sightings by the observer of large woodpecker-like birds incorrectly identified in the past as NOT IBWO.
(C) The proportion of sightings by the observer of large woodpecker-like birds incorrectly identified in the past as IBWO.
True, Bayes considers the sensitivity of a test rather than the competence 1of an observer. This complicates things, because a test is deemed to be the same for all the data gathered, whereas observers' competence may vary.
In any case, we don't know (A) because that's what we're trying to find out!
We don't know (B) because we don't have stats on unremarkable sightings of PIWO or other birds.
And we definitely don't know (C)!
So I'd say the stats approach may be a non-runner!
The testing protocol is the same but since different people respond in a different way to the test (our biochemistry may be surprisingly different when looking into the finer details) the test is not the same and thus, there is no conceptual difference between the sensitivity of a test and the competence of birders.
B) and c) Agreed, but aren´t these the most interesting points? Brave people might step forward and throw in their own estimates of their identification skills in this hypothetical situation. I would think every birder has some gut instinct about his/her skills. Upthread there were numerous claims about being confident in identification, since the two birds are very different.
Truly, stochastic calculations cannot prove the existence of the bird. Nevertheless, I feel it is quite helpful to have a scientifically based rule of how to take advantage of knowing the prevalence of a species for an otherwise not 100% certain identification. "Extraordinary claims require extraordinary proof. " Bayesian calculations do nothing but quantify the degree of extraordinarity required for proof.