This research paper presents a study investigating if sensor data from an automatic milking rotary could be used to model cow somatic cell count (composite milk SCC: CMSCC). CMSCC is valuable for udder health monitoring and individual cow udder health surveillance could be improved by predicting CMSCC between routine samplings. Data regularly recorded in the automatic milking rotary, in one German dairy herd, were collected for analysis. The cows (Holstein-Friesian, n = 372) were milked twice daily and sampled once weekly in afternoon milkings for 8 weeks for CMSCC. From the potential independent variables, including quarter conductivity, milk flow, blood in milk, kick-offs, not milked quarters and incomplete milkings, new variables that combined quarter data were created. Past period records, i.e. lags, of up to seven days before the actual CMSCC sampling event were added in the dataset to investigate if they were of use in modeling the cell count. Univariable generalized additive models (GAM) were used to screen the data to select potential independent variables. Furthermore, several multivariable GAM were fitted in order to compare the importance of the potential independent variables and to explore how the model performance would be affected by using data from various number of days before the CMSCC sampling event. The result of the model selection showed that the best explanation of CMSCC was provided by the model incorporating all significant variables from the variable screening for the seven preceding days, including the day of the CMSCC sampling event. However, using data from only three days before the CMSCC sampling event is suggested to be sufficient to model CMSCC. Variables combining conductivity quarter data, together with quarter conductivity, are suggested to be important in describing CMSCC. We conclude that CMSCC can be modeled with a high degree of explanation using the information routinely recorded by the milking robot.

Unlike chain ladder, the loss ratio method requires volume measures. Typically, these volumes are assumed to be known. In practice, however, accurate volume measures are rarely available. We interpret the available volumes as estimators for the true volume measures and analyze the consequences for the loss ratio method. In particular, we calculate the mean squared error of prediction, including uncertainty of volume measures, and derive approximately optimal weights for the observed incremental loss ratios. We then introduce a generalization of the loss ratio method that is tailored to the situation of uncertain volume measures and calculate the prediction uncertainty of this generalized loss ratio method.

Yield loss of hard red spring wheat due to competition from common milkweed was measured in grower fields in Minnesota. Wheat yield loss was measured using the area of influence and additive competitive methods. Simple linear regression of wheat yield and percentage wheat yield loss against distance from a common milkweed shoot gave r 2 values of 0.013 and 0.015, respectively, indicating limited value of the area of influence model for common milkweed in spring wheat. In an additive competition model, wheat yield was reduced 47% at the highest density of 12 common milkweed shoots m−2. Coefficients of determination for percentage yield loss regressed against common milkweed shoot density were 0.548, 0.547, and 0.529 for simple linear, nonlinear rectangular hyperbolic, and linear square root function models, respectively. Regression of percentage yield loss against common milkweed biomass resulted in r 2 values of 0.566, 0.645, and 0.658 for simple linear, nonlinear rectangular hyperbolic, and linear square root function models, respectively. Restrictions of common milkweed density due to factors other than competition limited yield loss response to the simple linear phase of both the nonlinear rectangular hyperbolic and the linear square root function models previously described.

Earth has been habitable through most of its history, but the anthropogenically mediated greenhouse effect, if sufficiently strong, can threaten Earth's long-standing equability. This paper's main aim is to determine the strength of the anthropogenic greenhouse effect (the climate sensitivity) from observational data and basic physics alone, without recourse to the parameterisations of earth-system models and their inevitable uncertainties. A key finding is that the sensitivity can be constrained by harmonising historical records of land and ocean temperatures with observations of potential climate-change drivers in a non-steady state, energy-balance equation via a least-squares optimisation. The global temperature increase, for a CO2 doubling, is found to lie (95 % confidence limits) between 3.0oC and 6.3oC, with a best estimate of +4oC. Under a business-as-usual scenario, which assumes that there will be no significant change in people's attitudes and priorities, Earth's surface temperature is forecast to rise by 7.9oC over the land, and by 3.6oC over the oceans, by the year 2100. Global temperature rise has slowed in the last decade, leading some to question climate predictions of substantial 21st-Century warming. A formal runs test, however, shows that the recent slowdown is part of the normal behaviour of the climate system.

The backfitting algorithm is an iterative procedure for fitting additive models in which, at each step, one component is estimated keeping the other components fixed, the algorithm proceeding component by component and iterating until convergence. Convergence of the algorithm has been studied by Buja, Hastie, and Tibshirani (1989). We give a simple, but more general, geometric proof of the convergence of the backfitting algorithm when the additive components are estimated by penalized least squares. Our treatment covers spline smoothers and structural time series models, and we give a full discussion of the degenerate case. Our proof is based on Halperin's (1962) generalization of von Neumann's alternating projection theorem.