546 research outputs found
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
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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
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