## ‘We’re due for one; it’s time’

The title is a paraphrase. This post is written with some irritation at a NOAA meteorologist, (presumably Dr) Glen Field who, on camera, flaunts his poor knowledge of probability and statistics, and misleads the public in doing so. See this excerpt including one of his slides, down in the lower left, on page 25.

Field argues that, if the mean of a statistical process generating events is, say, 5 per year, and, if, say, it’s been 10 years and each year has seen less than 5 per year, well, then, at year 11 and onwards, we are “due for” an event, because, after all, they have not happened for 10 years. So, he argues,

$P(\text{event}|\text{not seen event for 10 years}) > P(\text{event}|\text{not seen event for 1 year})$

If the events are “truly random”, this means they are Poisson distributed and, to the contrary,

$P(\text{event}|\text{not seen event for 10 years}) = P(\text{event}|\text{not seen event for 1 year})$

That’s because, if the events are “truly random”, they don’t have any memory and judge each year as if no other years existed or had outcomes in any way.

It is possible to example runs of such events. For example, in that lower left slide, Field notes there were 4 major hurricanes of interest (in Massachusetts) in 16 years. Typical forecasts for major hurricanes in Massachusetts run something like having a probability of between 0.01 and 0.03 in any one year. If so, and given Dr Field’s observation of 4 major hurricanes in Massachusetts in 16 years, the change of such a run, assuming 0.03 per year, is about one in two thousand. And the chances of not having a major hurricane in 59 years assuming a chance of 0.03 year, is about one in two hundred. Thus, even assuming a Poisson model, the remarkable thing is the 4 in 16 years, not the none in 59 years.

If Mr/Dr Field does not buy the idea these are Poisson distributed, I’d like to know and thing on what distribution he thinks they might be, to earn these extraordinatory conclusions. It is possible that these are not independent trials because such series are autocorrelated. But, then, doing simple calculations or pointing out remarkable runs as he does is surely misleading.