### Archives For heavy tails

With the NSW Rural Fire Service fighting more than 50 fires across the state and the unprecedented hellish conditions set to deteriorate even further with the arrival of strong winds the question of the day is, exactly how bad could this get? The answer is unfortunately, a whole lot worse. That’s because we have difficulty as human beings in thinking about and dealing with extreme events… To quote from a post I wrote in the aftermath of the 2009 Victorian Black Saturday fires.

So how unthinkable could it get? The likelihood of a fire versus it’s severity can be credibly modelled as a power law a particular type of heavy tailed distribution (Clauset et al. 2007). This means that extreme events in the tail of the distribution are far more likely than predicted by a gaussian (the classic bell curve) distribution. So while a mega fire ten times the size of the Black Saturday fires is far less likely it is not completely improbable as our intuitive availability heuristic would indicate. In fact it’s much worse than we might think, in heavy tail distributions you need to apply what’s called the mean excess heuristic which really translates to the next worst event is almost always going to be much worse…

So how did we get to this?  Well simply put the extreme weather we’ve been experiencing is a tangible, current day effect of climate change. Climate change is not something we can leave to our children to really worry about, it’s happening now. That half a degree rise in global temperature? Well it turns out it supercharges the heavy tail of bushfire severity. Putting it even more simply it look’s like we’ve been twisting the dragon’s tail and now it’s woken up…

When good voting algorithms go bad

Thinking about the QF72 incident, it struck me that average value based voting methods are based on the calculation of a population statistic. Now population statistics work well when the population is normally distributed, or otherwise clustered around some value. But if the distribution has heavy tails, we can expect that extreme values will occur fairly regularly and therefor the ‘average’ value means much less. In fact for some distributions we may not be able to put a cap on the upper value that an ‘average’ could be, e.g. it could have an infinite value and the idea of an average is therefore meaningless.