A two-step approach to model precipitation extremes in California based on max-stable and marginal point processes

In modeling spatial extremes, the dependence structure is classically inferred by assuming that block maxima derive from max-stable processes. Weather stations provide daily records rather than just block maxima. The point process approach for univariate extreme value analysis, which uses more historical data and is preferred by some practitioners, does not adapt easily to the spatial setting. We propose a two-step approach with a composite likelihood that utilizes site-wise daily records in addition to block maxima. The procedure separates the estimation of marginal parameters and dependence parameters into two steps. The first step estimates the marginal parameters with an independence likelihood from the point process approach using daily records. Given the marginal parameter estimates, the second step estimates the dependence parameters with a pairwise likelihood using block maxima. In a simulation study, the two-step approach was found to be more efficient than the pairwise likelihood approach using only block maxima. The method was applied to study the effect of El Ni\~{n}o-Southern Oscillation on extreme precipitation in California with maximum daily winter precipitation from 35 sites over 55 years. Using site-specific generalized extreme value models, the two-step approach led to more sites detected with the El Ni\~{n}o effect, narrower confidence intervals for return levels and tighter confidence regions for risk measures of jointly defined events.Comment: Published at http://dx.doi.org/10.1214/14-AOAS804 in the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

CP Violation and Extra Dimensions

It is shown that the new sources of CP violation can be generated in the models with more than one extra dimensions. In the supersymmetric models on the space-time $M^4\times T^2/Z_2$, where the radius moduli have auxiliary vacuum expectation values and the supersymmetry breaking is mediated by the Kaluza-Klein states of gauge supermultiplets, we analyze the gaugino masses and trilinear couplings for two scenarios and obtain that there exist relative CP violating phases among the gaugino masses and trilinear couplings.Comment: Latex, 7 page