One persistent way that human beings misrepresent the world is through the gambler's fallacy, and there's a kind of implied gambler's fallacy that works its way into journalism quite often. It's hugely important to anyone who cares about research and journalism about research.
Although I have a BSc in Math and have taken stats courses in grad school, I am no expert in probability. And I have only a layman’s knowledge earthquakes, so I am hoping others with more knowledge will correct any of the following.
First, to Ian Madin's view that we would not be "overdue" for an earthquake until we were three standard deviations from the mean. In a normal distribution (which the occurrence of earthquakes is not) three standard deviations above the norm means that 99.7% of the data points are below that. If a woman is at the third standard deviation for female height, she is taller than 99.7% of all women.
For earthquakes, the metric is number of years since the last one. To be at the third standard deviation, means that in all other cases, 99.7% of the quakes would have happened by now. I would suggest that this would mean a quake is more than “overdue”. It is very, very likely in the next few years.
The other point: the Gambler’s Fallacy depends on the spins of the roulette wheel being independent. Historical results have no bearing on the next spin. I explain this to people by suggesting that if I took a quarter out of my pocket and flipped it, what would be the probability of a head? If history mattered, we would have no idea because we do not know where that quarter has been and how many times it may have been flipped (OK, this is pretty well what you said. I just want to emphasize the importance of the events being independent). In fact, if a roulette wheel had produced 10 blacks in a row, your best bet would be black as there would be some evidence that the wheel may not be fair.
Years since the last earthquake are NOT independent. As time goes on, the pressure in the tectonic plates builds up and a quake becomes more likely. In the first few years after a big one, the pressure is off and the chance of another big one is essentially zero. So, to say that because there has not been a Big One from the Cascadia Fault since 1700, we are closer to the major destructive earthquake is not wrong.
I suspect, too, that as time goes on, the next quake is more likely to be a big one as the pressure has built up creating more potential energy for when the fault finally gives.
Although I have a BSc in Math and have taken stats courses in grad school, I am no expert in probability. And I have only a layman’s knowledge earthquakes, so I am hoping others with more knowledge will correct any of the following.
First, to Ian Madin's view that we would not be "overdue" for an earthquake until we were three standard deviations from the mean. In a normal distribution (which the occurrence of earthquakes is not) three standard deviations above the norm means that 99.7% of the data points are below that. If a woman is at the third standard deviation for female height, she is taller than 99.7% of all women.
For earthquakes, the metric is number of years since the last one. To be at the third standard deviation, means that in all other cases, 99.7% of the quakes would have happened by now. I would suggest that this would mean a quake is more than “overdue”. It is very, very likely in the next few years.
The other point: the Gambler’s Fallacy depends on the spins of the roulette wheel being independent. Historical results have no bearing on the next spin. I explain this to people by suggesting that if I took a quarter out of my pocket and flipped it, what would be the probability of a head? If history mattered, we would have no idea because we do not know where that quarter has been and how many times it may have been flipped (OK, this is pretty well what you said. I just want to emphasize the importance of the events being independent). In fact, if a roulette wheel had produced 10 blacks in a row, your best bet would be black as there would be some evidence that the wheel may not be fair.
Years since the last earthquake are NOT independent. As time goes on, the pressure in the tectonic plates builds up and a quake becomes more likely. In the first few years after a big one, the pressure is off and the chance of another big one is essentially zero. So, to say that because there has not been a Big One from the Cascadia Fault since 1700, we are closer to the major destructive earthquake is not wrong.
I suspect, too, that as time goes on, the next quake is more likely to be a big one as the pressure has built up creating more potential energy for when the fault finally gives.