Selected Papers on Extreme Value Analysis
From heat waves to hurricanes, it is often the extremes of environmental processes that are the most critical to understand probabilistically due to their impacts on society. Statistical techniques are crucial for accurately quantifying the likelihood of extreme events and monitoring changes in their frequency and intensity. Extreme events are by definition rare, therefore estimation of local climate characteristics can be improved by borrowing strength across nearby locations. While methods for univariate extreme data are welldeveloped, modeling spatiallyreferenced extreme data is an active area of research. My work on extremes focuses of developing computationallyfeasible Bayesian models for complex environmental processes such as extreme precipitation, temperature, and air pollution.

Reich BJ, Shaby BJ, Cooley D (2013). A hierarchical model for seriallydependent extremes: A study of heat waves in the western US. JABES.
Heat waves take a major toll on human populations, with negative impacts on the economy, agriculture, and human health. As a result, there is great interest in studying the changes over time in the probability and magnitude of heat waves. In this paper we propose a hierarchical Bayesian model for seriallydependent extreme temperatures. We assume the marginal temperature distribution follows the generalized Pareto distribution (GPD) above a locationspecific threshold, and capture dependence between subsequent days using a transformed maxstable process. Our model allows both the parameters in the marginal GPD and the temporal dependence function to change over time. This permits Bayesian inference on the change in likelihood of a heat wave. We apply this methodology to daily high temperatures in nine cities in the western US for 19792010. Our analysis reveals increases in the probability of a heat wave in several US cities. 

Reich, Cooley, Foley, Napelenok, Shaby (2013). Extreme value analysis for evaluating ozone control strategies. AOAS.
Tropospheric ozone has been linked to respiratory and cardiovascular endpoints and adverse effects on vegetation and ecosystems. Regional photochemical models have been developed to study the impacts of emission reductions on ozone levels. The standard approach is to run the deterministic model under new emission levels and attribute the change in ozone concentration to the emission control strategy. However, running the model requires substantial computing time, and this approach does not provide a measure of uncertainty for the change in ozone levels. Recently, a reduced form model (RFM) has been proposed to approximate the complex model as a simple function of a few relevant inputs. We develop a new approach to make full use of the RFM to study the effects of various control strategies on the probability and magnitude of extreme ozone events. We fuse the model output with monitoring data to calibrate the RFM by modeling the conditional distribution of monitoring data given the RFM using a combination of flexible semiparametric quantile regression for the center of the distribution where data are abundant and a parametric extreme value distribution for the tail where data are sparse. Due to the simplicity of the RFM, we are able to embed the RFM in our Bayesian hierarchical framework to obtain a full posterior for the model input parameters, and propagate this uncertainty to the estimation of the effects of the control strategies. We use the new framework to evaluate three potential control strategies, and find that reducing mobilesource emissions has a larger impact than reducing pointsource emissions or a combination of several emission sources. 

Reich, Shaby (2012). A hierarchical maxstable spatial model for extreme precipitation. AOAS.
Extreme environmental phenomena such as major precipitation events manifestly exhibit spatial dependence. Maxstable processes are a class of asymptoticallyjustified models that are capable of representing spatial dependence among extreme values. While these models satisfy modeling requirements, they are limited in their utility because their corresponding joint
likelihoods are unknown for more than a trivial number of spatial locations, preventing, in particular, Bayesian analyses. In this paper, we propose a new random effects model to account for spatial dependence. We show that our specification of the random effect distribution leads to a maxstable process that has the popular Gaussian extreme value process (GEVP) as a limiting case. The proposed model is used to analyze the yearly maximum precipitation from a regional climate model. 