Bayesian Inference from Composite Likelihoods, with an Application to Spatial Extremes

Composite likelihoods are increasingly used in applications where the full likelihood is analytically unknown or computationally prohibitive. Although the maximum composite likelihood estimator has frequentist properties akin to those of the usual maximum likelihood estimator, Bayesian inference based on composite likelihoods has yet to be explored. In this paper we investigate the use of the Metropolis--Hastings algorithm to compute a pseudo-posterior distribution based on the composite likelihood. Two methodologies for adjusting the algorithm are presented and their performance on approximating the true posterior distribution is investigated using simulated data sets and real data on spatial extremes of rainfall

Black Power in a Lily-White School: The Black Campus Movement at Concordia College in Moorhead, Minnesota

Between the mid-1950s and through the 1970s, higher educational institutions throughout the United States underwent reforms in the name of what they termed “integration.” For the colleges and universities in the upper Midwest, these reforms included minority student recruitment and the creation of programs oriented towards diversity. Over time, a number of minority students began to act and react to the actions and attitudes of the various administrations, the campuses, and the community, resulting in a demonstration directly connected to the national phenomenon of “The Black Campus Movement,” (BCM) itself a submovement of the larger United States’ Black Power Movement of the mid-twentieth century. The historiography of the BCM has failed to examine more minor instances of the movement, instead focusing on larger institutions, violent demonstrations, or ones with a large proportion of black students compared to white students. This study expands that historiography by introducing a case-study on a BCM demonstration at Concordia College in Moorhead, Minnesota. Concordia was and still is a small, four-year liberal arts college with strong ties to Norwegian heritage and the Lutheran religion. In 1976, Concordia underwent a BCM demonstration when more than half of its very small black student population boycotted their classes and presented a list of demands to the administration. This study how and why this demonstration occurred, places Concordia within the larger historiography of the BCM, and provides a narrative account of how two cultures clashed at a small, predominantly white, Lutheran college in the upper Midwest

Transformed-linear prediction for extremes

We consider the problem of performing prediction when observed values are at their highest levels. We construct an inner product space of nonnegative random variables from transformed-linear combinations of independent regularly varying random variables. The matrix of inner products corresponds to the tail pairwise dependence matrix, which summarizes tail dependence. The projection theorem yields the optimal transformed-linear predictor, which has the same form as the best linear unbiased predictor in non-extreme prediction. We also construct prediction intervals based on the geometry of regular variation. We show that these intervals have good coverage in a simulation study as well as in two applications; prediction of high pollution levels, and prediction of large financial losses

Partial Tail Correlation for Extremes

In order to understand structural relationships among sets of variables at extreme levels, we develop an extremes analogue to partial correlation. We begin by developing an inner product space constructed from transformed-linear combinations of independent regularly varying random variables. We define partial tail correlation via the projection theorem for the inner product space. We show that the partial tail correlation can be understood as the inner product of the prediction errors from transformed-linear prediction. We connect partial tail correlation to the inverse of the inner product matrix and show that a zero in this inverse implies a partial tail correlation of zero. We then show that under a modeling assumption that the random variables belong to a sensible subset of the inner product space, the matrix of inner products corresponds to the previously-studied tail pairwise dependence matrix. We develop a hypothesis test for partial tail correlation of zero. We demonstrate the performance in two applications: high nitrogen dioxide levels in Washington DC and extreme river discharges in the upper Danube basin