Information criteria for inhomogeneous spatial point processes

The theoretical foundation for a number of model selection criteria is established in the context of inhomogeneous point processes and under various asymptotic settings: infill, increasing domain, and combinations of these. For inhomogeneous Poisson processes we consider Akaike information criterion and the Bayesian information criterion, and in particular we identify the point process analogue of sample size needed for the Bayesian information criterion. Considering general inhomogeneous point processes we derive new composite likelihood and composite Bayesian information criteria for selecting a regression model for the intensity function. The proposed model selection criteria are evaluated using simulations of Poisson processes and cluster point processes.Comment: 6 figure

Glyphosate, Other Herbicides, And Transformation Products In Midwestern Streams, 2002

The use of glyphosate has increased rapidly, and there is limited understanding of its environmental fate. The objective of this study was to document the occurrence of glyphosate and the transformation product aminomethylphosphonic acid (AMPA) in Midwestern streams and to compare their occurrence with that of more commonly measured herbicides such as acetochlor, atrazine, and metolachlor. Water samples were collected at sites on 51 streams in nine Midwestern states in 2002 during three runoff events: after the application of pre-emergence herbicides, after the application of post-emergence herbicides, and during harvest season. All samples were analyzed for glyphosate and 20 other herbicides using gas chromatography/mass spectrometry or high performance liquid chromatography/mass spectrometry. The frequency of glyphosate and AMPA detection, range of concentrations in runoff samples, and ratios of AMPA to glyphosate concentrations did not vary throughout the growing season as substantially as for other herbicides like atrazine, probably because of different seasonal use patterns. Glyphosate was detected at or above 0.1 μg/l in 35 percent of pre-emergence, 40 percent of post-emergence, and 31 percent of harvest season samples, with a maximum concentration of 8.7 μg/l. AMPA was detected at or above 0.1 μg/l in 53 percent of pre-emergence, 83 percent of post-emergence, and 73 percent of harvest season samples, with a maximum concentration of 3.6 μg/l. Glyphosate was not detected at a concentration at or above the U.S. Environmental Protection Agency’s maximum contamination level (MCL) of 700 μg/l in any sample. Atrazine was detected at or above 0.1 μg/l in 94 percent of pre-emergence, 96 percent of postemergence, and 57 percent of harvest season samples, with a maximum concentration of 55 μg/l. Atrazine was detected at or above its MCL (3 μg/l) in 57 percent of pre-emergence and 33 percent of postemergence samples