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Friday, 20 August 2010

The Reverend Thomas Bayes on birding




The very Reverend Thomas Bayes, the son of London Presbyterian minister was thought to have been born in Hertfordshire in about 1702. He studied in my own home town of Edinburgh and amongst other things, attempted to prove that the principal purpose of God was to make us despicable human souls happy. What has the good Reverend got to do with birding I hear you ask? Well, allow me to explain in a rather roundabout manner:

Today I was seawatching from Bass Point. Shortly after securing cracking views of my first ever Great Shearwater from the Lizard, I observed a petrel for about 2 mins as it flew past relatively close.  Detailed description aside, to all intent and purposes, it looked like a Wilson’s Petrel. In fact, based on its appearance, I was about 99% confident it was one. The trouble is, being 99% confident of ID, doesn't mean there’s a 99% probability it actually was one, simply because the obvious confusion species, European Storm Petrel, heavily outnumbers Wilson’s. I don’t know the true figure, but let's say, for the sake of argument, by about 100 to 1. Well, it so happens that the good old Reverend Thomas Bayes came up with a formula for working out this problem, although I don’t think he was thinking about birds when he did. For the mathematically minded, the formula is as follows:

Probability of rare bird = probability of ID x probability of it being one based on numbers / (probability of incorrect ID) x probability of it not being one based on numbers  + probability of correct ID x probability of it being one on numbers).

That entire complicated math leads me to the rather unfortunate conclusion that it there was a 49.7% chance it was one.  Less than 50%! Indeed if I factor in a bit of false expectation due to the fact I’d just seen a Great Shear and the conditions were spot on (say 95% confidence with ID) and we allow European’s to outnumber Wilson’s by 200 to 1, then the figure drops to a woeful 8.7%.

Of course, all of this doesn’t matter one bit if one is certain of identification, but it does get you thinking. I wonder how often the rarities committees take such probabilities into consideration? I suppose they do qualitatively, as mega rare birds increasingly require mega good evidence, but it’s rather worrying that even if one is 99.9% confident with identification of a bird that is outnumbered 1000 to 1 by its potential confusion species, the chances of it actually being one are only 50:50.

3 comments:

  1. I like looking at various formulae for calculating bird occurrences. What strikes me is that often they have good ideas, but the problem is that there is no way of actually calculating the variables scientifically. A few thoughts:

    How do you arrive at the confidence in your ID? A distinctive species may have 20 distinctive features, but if you note 19 out of 20 are you 95% sure? Almost certainly not, because some are more important than others, some need to be in combination, sometimes the absence of one anuls the rest etc. If someone told me they had seen a bird and concluded they were 99.9% or even 99% sure I would want to know what tiny point was holding them back.

    Taking probability of occurence from species with a large data set of previous occurences isn't too bad, but for a"country first" species is the probability 0, and therefore a sighting impossible?

    Similarly if you are 100% positive of an ID (and you have the knowledge to make that call, and there's the caveat) then it is that bird, regardless of the probability. You then get onto the question of its origins...

    The thing that rarities comittees have in their favour is that birds sent to them are meant to be ones where the observer is certain of the ID (and I accept that doesn't mean the bird is the species that is claimed), which means that the Revs formula is not needed.

    Best of luck for the autumn.

    James

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  2. Even now, at the bottom of the BBRC report form it asks: 'Is the record 100% certain?" Personally I feel it's a bit unkind to ask an observer to apply a quantitative value to what is essentially a qualitative process (especially as a records committee is a far from scientific body) because anything less than 100% implies doubt in the observer's mind, and provides ample vindication for the 'not proven' decision!

    Very interesting post, Ilya, with the added bonus of enviable seabirds!

    By the way, with ref. to an earlier post, I'm pretty sure that the big Cory's movement of late July/early Aug 2008 produced much higher counts from the Lizard than from Gwennap (where I saw some of it) though I'm going on memory alone I'm afraid.

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  3. Hi James. The post was written in order to illustrate a point rather than the assign precise figures. The point being that when claiming a rare bird, even the smallest element of uncertainty vastly increases the odds of it not being the bird in question. I didn’t realistically expect anybody to actually apply the formula, just to bear its implications in mind!

    In the particular case of my Wilson’s Petrel, the flight action (much more gliding, less fluttering), the long-winged appearance and apparent lack of a white underwing all were very suggestive of Wilson’s, but of course assigning an exact figure such as 99% is fairly arbitrary.

    As it happens, the BBRC forms does allow you to say the record isn’t 100% certain. Moreover, if there wasn’t any doubt in it at all, there wouldn’t need to be a rarities committee in the first place. The fact that there is one, is reflective of the fact that of course there is doubt, even if the observer in question says that they are (or actually is) 100% certain.
    While I agree with you Gavin, that this can seem unfair I think it does have its uses. For example, I submitted the Lizard Brown Shrike last year as an uncertain record. As such, I don’t necessarily expect it to be accepted, but I still think that having the description and photos on record is of some value to the rarities committee. I suppose in that case though, an interesting point is that the main contended for confusion is proving to be even rarer these days. I’ve also submitted a couple of Sib Chiffs as uncertain , describing exactly what I saw, but recognizing the fact that there is still quite a bit to be learned about the true status of this species within the UK and were exactly you draw the boundary with this taxa.

    The big Cory’s movement was indeed off the Lizard – Tony Blunden being the lucky observer in question. They evidently moved up the Channel, as a few were even recorded up the east coast. I was fortunate enough to find one of the birds that reached Norfolk.

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