Spatial interpolation of high-frequency monitoring data

Climate modelers generally require meteorological information on regular grids, but monitoring stations are, in practice, sited irregularly. Thus, there is a need to produce public data records that interpolate available data to a high density grid, which can then be used to generate meteorological maps at a broad range of spatial and temporal scales. In addition to point predictions, quantifications of uncertainty are also needed. One way to accomplish this is to provide multiple simulations of the relevant meteorological quantities conditional on the observed data taking into account the various uncertainties in predicting a space-time process at locations with no monitoring data. Using a high-quality dataset of minute-by-minute measurements of atmospheric pressure in north-central Oklahoma, this work describes a statistical approach to carrying out these conditional simulations. Based on observations at 11 stations, conditional simulations were produced at two other sites with monitoring stations. The resulting point predictions are very accurate and the multiple simulations produce well-calibrated prediction uncertainties for temporal changes in atmospheric pressure but are substantially overconservative for the uncertainties in the predictions of (undifferenced) pressure.Comment: Published in at http://dx.doi.org/10.1214/08-AOAS208 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

State Fish Stocking Programs at Risk: Takings Under the Endangered Species Act

Part I of this article provides a brief background to fish stocking practices in the United States, including a discussion of beneficial fish stocking practices, as well as some of the allegations surrounding the detrimental effects. Part II of this article provides some necessary background on section 9 of the ESA, the “actual injury” prong, the “significant impairment” prong, and their application to fish stocking. Part III of this article sets forth recommendations for future clarification and increased consistency on these issues. Specifically, this article supports the use of two rules that can help reconcile the uncertain landscape surrounding a taking based on habitat modification. First, “actual injury” should be found where there is injury to either an individual or a population of protected species. Second, the degree of proof required to establish an “injury” where essential behaviors are impaired should be bifurcated into two tests, depending on which behavioral pattern is being adversely affected. Together, these rules can bring resolution not only to scenarios like fish stocking, but also to other future fact patterns scrutinized under the habitat modification analysis. Part IV of this article demonstrates how application of these rules to states can further the goals of the ESA, both through voluntary reevaluation of fish stocking programs, and through application for an Incidental Take Permit and corresponding Habitat Conservation Plan. These rules can provide two different paths to the same goal: to minimize adverse impacts to endangered and threatened species

Spatial variation of total column ozone on a global scale

The spatial dependence of total column ozone varies strongly with latitude, so that homogeneous models (invariant to all rotations) are clearly unsuitable. However, an assumption of axial symmetry, which means that the process model is invariant to rotations about the Earth's axis, is much more plausible and considerably simplifies the modeling. Using TOMS (Total Ozone Mapping Spectrometer) measurements of total column ozone over a six-day period, this work investigates the modeling of axially symmetric processes on the sphere using expansions in spherical harmonics. It turns out that one can capture many of the large scale features of the spatial covariance structure using a relatively small number of terms in such an expansion, but the resulting fitted model provides a horrible fit to the data when evaluated via its likelihood because of its inability to describe accurately the process's local behavior. Thus, there remains the challenge of developing computationally tractable models that capture both the large and small scale structure of these data.Comment: Published at http://dx.doi.org/10.1214/07-AOAS106 in the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

A Tale of Two Debt Crises: A Stochastic Optimal Control Analysis

Banks should evaluate whether a borrower is likely to default. I apply several techniques in the extensive mathematical literature of stochastic optimal control/dynamic programming to derive an optimal debt in an environment where there are risks on both the asset and liabilities sides. The vulnerability of the borrowing firm to shocks from either the return to capital, the interest rate or capital gain, increases in proportion to the difference between the Actual and Optimal debt ratio, called the excess debt. As the debt ratio exceeds the optimum, default becomes ever more likely. This paper is “A Tale of Two Crises” because the analysis is applied to the agricultural debt crisis of the 1980s and to the sub-prime mortgage crisis of 2007. A measure of excess debt is derived, and we show that it is an early warning signal of a crisis.optimization, banking, stochastic optimal control, agriculture debt crisis, subprime mortgage crisis