Sampling Bias and Class Imbalance in Maximum-likelihood Logistic Regression

Logistic regression is a widely used statistical method to relate a binary response variable to a set of explanatory variables and maximum likelihood is the most commonly used method for parameter estimation. A maximum-likelihood logistic regression (MLLR) model predicts the probability of the event from binary data defining the event. Currently, MLLR models are used in a myriad of fields including geosciences, natural hazard evaluation, medical diagnosis, homeland security, finance, and many others. In such applications, the empirical sample data often exhibit class imbalance, where one class is represented by a large number of events while the other is represented by only a few. In addition, the data also exhibit sampling bias, which occurs when there is a difference between the class distribution in the sample compared to the actual class distribution in the population. Previous studies have evaluated how class imbalance and sampling bias affect the predictive capability of asymptotic classification algorithms such as MLLR, yet no definitive conclusions have been reached.     

MPA design using sliding windows: Case study designating a research area

Coastal managers presently rely on a limited set of decision support tools for designing marine protected areas (MPAs) or subzones. A new approach, defining potential sizes and shapes of MPA boundaries early in the design process, is presented in a case study. A sliding window of the same dimensions as potential boundary configurations was regularly shifted throughout the study area and used to quantify variables representing preferred biophysical and socioeconomic characteristics. The technique offers advantages in spatially restricted areas, areas where habitat connectivity is critical, and situations wherein providing stakeholders with an up-front understanding of potential boundaries is required.     

Preferential low-pH dissolution of pyroxene in plagioclase-pyroxene mixtures: Implications for martian surface materials

Acid weathering of plagioclase-pyroxene mixtures has been investigated with an open system kinetic dissolution model. The modeling reveals that elevated plagioclase/pyroxene ratios observed in some low-albedo martian regions and atmospheric dust could be partially caused by preferential dissolution of pyroxenes at pHs below ∼3-4. Surface materials with smaller grain sizes, affected by lower pH fluids, and/or exposed to longer durations of acid weathering would be enriched in plagioclase. If preferential dissolution is responsible for the observed mineral ratios, the dissolution process likely occurred on a large scale, such as weathering by acid atmospheric precipitates. If dissolution was continuous, modeled timeframes required to produce a high plagioclase/pyroxene ratio are short on geologic timescales; however, it is likely that acid weathering on Mars was episodic, possibly occurring over a longer period of time.     

Three-dimensional liquefaction potential analysis using geostatistical interpolation

We applied three-dimensional geostatistical interpolation to evaluate the extent of liquefiable materials at two sites that liquefied during the 1994 Northridge Earthquake. The sites were the Balboa Blvd site and the Wynne Ave. site located in the alluvial San Fernando Valley. The estimated peak ground accelerations at the sites are 0.84 g (Balboa Blvd) and 0.51 g (Wynne Ave.). These sites were chosen because surface effects due to liquefaction were not predicted using available techniques based on thickness and depth of liquefiable layers (Ishihara [Ishihara K. Stability of natural deposits during earthquakes. Proceedings of the 11th international conference on soil mechanics and foundation engineering, vol. 1. Rotterdam, The Netherlands: A.A. Balkema; 1985. p. 321–76.]) and the Liquefaction Potential Index (Iwasaki et al. [Iwasaki T, Tatsuoka F, Tokida K, Yasuda S. A practical method for assessing soil liquefaction potential based on case studies at various sites in Japan. In: Proceedings of the second international conference on microzonation, San Francisco; 1978. p. 885–96.]). During the earthquake, both sites experienced surface effects including ground cracking and extension as a result of liquefaction. Foundations and buried utilities were damaged at both sites. The sites were investigated after the event by researchers with the United States Geologic Survey using standard penetration tests (SPT) and cone penetration tests. In this paper, liquefaction potential was estimated for each soil sample using results from SPTs according to the updated Seed and Idriss simplified procedure. The probability of liquefaction was estimated by applying an indicator transform to the results of the liquefaction potential calculation. We compared our results to detailed geologic mapping of the sites performed by other researchers. Using geostatistical interpolation to estimate the probability of liquefaction is a useful supplement to geologic evaluation of liquefaction potential. The geostatistical analysis provides an estimate of the continuous volume of liquefiable soil along with an assessment of confidence in an interpolation. The probability of liquefaction volumes compare well with those predicted using geologic interpretations.     

Defining phases of bedload transport using piecewise regression

Differences in the transport rate and size of bedload exist for varying levels of flow in coarse‐grained channels. For gravel‐bed rivers, at least two phases of bedload transport, with notably differing qualities, have been described in the literature. Phase I consists primarily of sand and small gravel moving at relatively low rates over a stable channel surface. Transport rates during Phase II are considerably greater than Phase I and more coarse grains are moved, including material from both the channel surface and subsurface. Transition from Phase I to Phase II indicates initiation and transport of grains comprising the coarse surface layer common in steep mountain channels. While the existence of different phases of transport is generally acknowledged, the threshold between them is often poorly defined. We present the results of the application of a piecewise regression analysis to data on bedload transport collected at 12 gravel‐bed channels in Colorado and Wyoming, USA. The piecewise regression recognizes the existence of different linear relationships over different ranges of discharge. The inflection, where the fitted functions intersect, is interpreted as the point of transition from Phase I to Phase II transport; this is termed breakpoint. A comparison of grain sizes moved during the two phases shows that coarse gravel is rarely trapped in the samplers during Phase I transport, indicating negligible movement of grains in this size range. Gravel larger than about D₁₆ of the channel surface is more consistently trapped during Phase II transport. The persistence of coarse gravel in bedload samples provides good evidence that conditions suitable for coarse grain transport have been reached, even though the size of the sediment approaches the size limits of the sampler (76 mm in all cases). A relative breakpoint (R_br) was defined by the ratio between the discharge at the breakpoint and the 1·5‐year flow (a surrogate for bankfull discharge) expressed as a percentage. The median value of R_br was about 80 percent, suggesting that Phase II begins at about 80 percent of the bankfull discharge, though the observed values of R_br ranged from about 60 to 100 percent. Variation in this value appears to be independent of drainage area, median grain size, sorting of bed materials, and channel gradient, at least for the range of parameters measured in 12 gravel‐bed channels. Published in 2002 by John Wiley & Sons, Ltd.     

Petrology and Isotope Geochemistry of the Pan-African Negash Pluton, Northern Ethiopia: Mafic-Felsic Magma Interactions During the Construction of Shallow-level Calc-alkaline Plutons

The Negash pluton consists of monzogranites, granodiorites,hybrid quartz monzodiorites, quartz monzodiorites and pyroxenemonzodiorites, emplaced at 608 ± 7 Ma (zircon U–Pb)in low-grade volcaniclastic sediments. Field relationships betweenmafic and felsic rocks result from mingling and hybridizationat the lower interface of a mafic sheet injected into partiallycrystallized, phenocryst-laden, granodiorite magma (back-veining),and hybridization during simultaneous ascent of mafic and felsicmagmas in the feeder zone located to the NW of the pluton. Therock suite displays low ⁸⁷Sr/⁸⁶Sr₍₆₀₈₎ (0·70260–0·70350)and positive     

Os isotope systematics in ocean island basalts

New ReOs isotopic results for Os-poor basalts from St. Helena, the Comores, Samoa, Pitcairn and Kerguelen dramatically expand the known range of initial ¹⁸⁶Os/¹⁸⁷Os ratios in OIBs to values as high as 1.7. In contrast to the Os isotopic uniformity of Os-rich basalts from the HIMU islands of Tubuai and Mangaia found by Hauri and Hart [1], our values for St. Helena span most of the known range of Os isotopic variability in oceanic basalts (initial ¹⁸⁷Os/¹⁸⁶Os ranges from 1.2 to 1.7). Generation of such radiogenic Os in the mantle requires melting of source materials that contain large proportions of recycled oceanic crust. The very low Os concentrations of most of the basalts analyzed here, however, leave them susceptible to modification via interaction with materials containing radiogenic Os in the near-surface environment. Thus the high ¹⁸⁶Os/¹⁸⁷Os ratios may result from assimilation of radiogenic Os-rich marine sediments, such as Mn oxides, within the volcanic piles traversed by these magmas en route to the surface. Furthermore, the Os isotopic signatures of Os-rich, olivine-laden OIBs may reflect the accumulation of lithospheric olivine, rather than simply their mantle source characteristics. The extent to which these processes alter the view of the mantle obtained via study of ReOs systematics in oceanic basalts is uncertain. These effects must be quantified before ReOs systematics in OIBs can be used with confidence to investigate the nature of mantle heterogeneity and its causes.