Will I See a Falling Tree ?

And should I update my Prior ?

A conspicuous feature of the woodlands about the East Lyn River is the substantial prevalence of fallen trees, typically covered by moss and lichen.

Yes, they are everywhere. Alongside the trails, across and in the river, and, particularly, on slopes.

It's quite obvious which fell a long, long time ago.

Being from Utah I'm not used to this.

On a particular day, after about two days of rain, this one across the trail near the cottage was new.

Having found an old, rusting saw in the garden tool shed, I engaged in some trail maintenance. I actually did so over a few sessions because the sawing was very slow - I was scared of breaking the blade.

Then I saw additional trees that had fallen down since I had last passed the area, which was only a day or so before.

On the trail.

And across the river at a spot I had waded in to fish.

That got me thinking.

What's the probability that I'll see a falling tree ?

Clearly, it's extremely (!) unlikely, but having seen the new trees, should I update my Prior ?

(That notion is something quite familiar to two likely readers of this note -- W.C. and S.A.)

Now the notion of probability is hard. And what to do with new evidence ? That suggests the notion of subjective degrees of belief and the Reverend Bayes and Bayes Theorem.

Um, no.

But I consider myself a Bayesian Radiologist, always considering new information and evidence when formulating a Differential Diagnosis. So I have to always update the prior probability of a particular diagnosis given such information.

I'm reminded about a talk I gave around the time of COVID-19 on this subject. Here are a few slides from it.

And

And

So, should I now increase the "pre-test odds" of me seeing a falling tree ?

I'm inclined to do so-- but only by a very, very, very small amount.

And I'm not bothered about resting on this bench.

This is what happens when you go for a walk and have ample time to see and for random, languid rumination.