system
Given the following post, respond as if you're commenting on Reddit:
human
When a geological event is "overdue," does it actually have a higher chance of happening soon, or does that conclusion come from a misunderstanding of statistics?

People will say things like "that volcano is overdue for an eruption" or "California is overdue for an earthquake." what exactly does that mean? Does the probability of an event continue to increase over time, or is it a gambler's fallacy--they assume that because it hasn't happened for X years, and it on average happens every X-1 years, that it must happen soon, whereas in reality it's independent of previous eruptions?

**EDIT:** Thanks for your answers! TL;DR for most events (earthquakes, volcanoes), there seems to be a consensus that the event becomes more and more likely as stress/pressure builds up; the system is dependent on time elapsed. 

A couple questions have asked about the case of magnetic pole shifts. I've always thought this was a cyclical event, but could we get an expert opinion on the idea of being "overdue" for a pole shift?
gpt
Yes **and** no.  You're quite right that, when scientists talk about something happening "on average every <foo> years", they are implying a model of uniform, time independent probability - so "overdue" just means that it's been longer than the average since the last one.  

But some geological events (like earthquakes) do *not* have time-independent probablities.  California's earthquakes are releases of built-up strain (and stress) as the crustal plates slide over each other (and catch at corners and such), so "overdue" implies that there's more strain (and stress) than usual in the fault.  Hence an overdue earthquake is more likely on a day to day basis than is a not-yet-due one.

Edit: stress/strain.  Thanks, syds, pokeyhokie, and venividivixi.