Extreme Values 

 Every year, the host university of the Political Methodology conference invites a local scholar from some other discipline to share his or her research with the political science methods community.  This year's special presentation, by James Elsner of the Florida State University Department of Geography, was sadly prescient.  Professor Elsner's talk,   "Bayesian Inference of Extremes: An Application in Modeling Coastal Hurricane Winds,"   applied extreme value theory in a Bayesian context to estimate the frequency with which hurricanes above a given strength make landfall in the United States.  The devastating impact of Hurricane Katrina amply illustrates the importance of estimating maximum intensities; news reports suggest that as little as a foot or two of water overtopping the levees and eroding them from below may have caused the breaches that flooded New Orleans. 

 Extreme value theory provides a way to estimate the distribution of the maximum or minimum of a set of independent events.  While this could be done directly if the distribution of the underlying events was known, in practice it is preferable to use the extremal types theorem to estimate the distribution of the maximum or minimum directly from data.  The theorem states that, with appropriate transformations, the distribution of extreme values converges in the limit to one of three classes of distribution - Gumbel, Frechet, or Weibull - regardless of the shape of the underlying distribution. 

 There are several challenges in estimating the distribution of extreme values.  The three classes of limit distributions for extreme values have different behavior in the extreme tail: one family has a finite limit, while the other two have no limit but decay at different rates.  To the extent that we are interested in "extreme" extremes, these differences could have substantive implications.  Compounding this problem, observations in the extreme tail are likely to be sparse.  Finally, one might expect that the quality of data is lower when extreme maxima or minima are occurring.  Consider Katrina: most of the instrumentation for recording wind speeds, storm surge, and rainfall rates were knocked out well before the height of the storm. (Nor is this just a problem with weather phenomena; imagine trying to measure precisely daily price changes during a period of hyperinflation).  The Bayesian approach pursued in this work seems promising, as is allows the uncertainty in both the data itself and in the functional form to be modeled explicitly. 

 In talking with other grad students after the presentation, I think the consensus was that, while interesting methodologically and sobering substantively, it was hard to see how we would apply these methods in our own work.  A quick Google search suggests that this approach is (not surprisingly) well established in financial economics, but not much else from the social sciences.  With a little more time to reflect, however, I think that this may be more due to a lack of theoretical creativity on our part.  Coming from the formal side of political science, I could see how thinking about extreme values might provide some insight into how political systems are knocked out of equilibrium, much like the levees in New Orleans.