Statistical Poo

What you are looking at below is a photo of the hand rail on our front porch steps.  The X is the top of the rail.  The rail descends to the bottom step toward the top of the picture and the post is about three feet high near the bottom of the picture.  See the white specs?  They are three feet below the X.





 
Now.  About those white specs...

Birds come and sit on the rail (I said "sit"),  mostly on the "X"  and they can sit facing any direction in 360 degrees (blue arrow). .  I suspect this is true because of the nice semicircular ring of poo on the porch and on the rail.

Now, to go a little Bayesian on you, our prior estimate of the probability of a bird facing any particular quarter of the blue circle, knowing nothing else, would be p=. 25 for any quarter of the circle.

But studying the data shows us that there is more poo on the porch than on the rail.  This shows us that most birds prefer looking out toward potential cats rather than in towards the front door. Otherwise I'd  be writing about a ring of dead half eaten birds.

We also note that the arc of poo has a gap on the right side.   Hmm.  Arc of Poo?  Sounds like a literary novel doesn't it?

DEEP VOICE: "Coming to bookstores everywhere, "Arc of Poo", by the Murray Award winning author, John Borneman. "

Sorry. Lost focus.

The data shows us that given birds always poo while sitting on a post, that they prefer facing between ENE to NNW. Birds prefer a quarter of the circle slightly off top dead center. Also a few brave birds do like looking at the southern quadrant towards our door given the evidence of poo on top of the rail (it is a nice door!). Bayesian calculations would include an estimate of the prior, P(bird facing north) and P(poo found on south side of rail), our new data expressed as probability of poo in a quadrant given the bird is facing north and the probability that the bird is facing north given no poo is evidenced (constipated bird). 

From this we can calculate a posterior distribution or  the probability that a bird is facing north given poo is found on the southern quadrant.

This leaves two questions.  One.  Why does this matter?

Well. One point is that data and statistics are everywhere. Now bird poo stats may only be of interest to ornithologists  But the larger point is that one should not be afraid to look for patterns and probabilities in everything. These patterns of numbers and other data types help us understand both our professional and our personal lives. You will be surprised what you can learn.

The other point is that this silly bird poo example is a good illustration of Bayesian probability calculations. What if we substituted the presence of a bird facing north with the presence of a cancer in one part of your body? And what if we substitute the evidence of bird poo found, with a test for this type of cancer? 

We now see that calculating the probability of cancer given a positive result of a test would be very good information to know. In fact Bayesian calculations for various medical conditions have shown that in some cases, a positive result on a test may only have a low probability that you actually have the condition. 

Here is a link to more than you want to know about medical testing and Bayesian approach. 

Oh. I said two questions. The other question?  Why am I sitting here on the porch writing about poo when I should be cleaning it up?   Funny. Asked and answered.