Estimating Mean Surface Backscatter from GPM Surface Backscatter Observations

The radar on the Global Precipitation Measurement (GPM) mission observes precipitation at 13.6 GHz (Ku-band) and 35.6 GHz (Ka-band) and also receives echoes from the earth’s surface. Statistics of surface measurements for non-raining conditions are saved in a database for later use in estimating the precipitation path-integrated attenuation. Previous work by Meneghini and Jones (2011) showed that while averaging over larger latitude/longitude bins increase the number of samples, it can also increase sample variance due to spatial inhomogeneity in the data. As a result, Meneghini and Kim (2017) proposed a new, adaptive method of database construction, in which the number of measurements averaged depends on the spatial homogeneity. The purpose of this work is to re-visit previous, single-frequency results using dual-frequency data and optimal interpolation (kriging). Results include that (1) temporal inhomogeneity can create similar results as spatial, (2) Ka-band behavior is similar to Ku-band, (3) the Ku-/Ka-band difference has less spatial inhomogeneity than either band by itself, and (4) kriging and the adaptive method can reduce the sample variance. The author concludes that finer spatial and temporal resolution is necessary in constructing the database for single frequencies but less so for the Ku-/Ka-band difference. The adaptive approach reduces sample standard deviation with a relatively modest computational increase.

Patient Expectations of Assigned Treatments Impact Strength of Randomised Control Trials

Patient engagement with treatments potentially poses problems for interpreting the results and meaning of Randomised Control Trials (RCTs). If patients are assigned to treatments that do, or do not, match their expectations, and this impacts their motivation to engage with that treatment, it will affect the distribution of outcomes. In turn, this will impact the obtained power and error rates of RCTs. Simple Monto Carlo simulations demonstrate that these patient variables affect sample variance, and sample kurtosis. These effects reduce the power of RCTs, and may lead to false negatives, even when the randomisation process works, and equally distributes those with positive and negative views about a treatment to a trial arm.

Large-Sample Variance of Fleiss Generalized Kappa

Cohen’s kappa coefficient was originally proposed for two raters only, and it later extended to an arbitrarily large number of raters to become what is known as Fleiss’ generalized kappa. Fleiss’ generalized kappa and its large-sample variance are still widely used by researchers and were implemented in several software packages, including, among others, SPSS and the R package “rel.” The purpose of this article is to show that the large-sample variance of Fleiss’ generalized kappa is systematically being misused, is invalid as a precision measure for kappa, and cannot be used for constructing confidence intervals. A general-purpose variance expression is proposed, which can be used in any statistical inference procedure. A Monte-Carlo experiment is presented, showing the validity of the new variance estimation procedure.

Calibration of Distributionally Robust Empirical Optimization Models

In “Calibration of Robust Empirical Optimization Models,” Gotoh, Kim, and Lim study the statistical properties of ɸ-divergence distributionally robust optimization with concave rewards. They show that worst-case sensitivity of the expected reward to deviations from the nominal is equal to the in-sample variance and that significant out-of-sample variance (sensitivity) reduction is possible with little impact on the mean if the robustness parameter is properly chosen. The authors also explain theoretically why the out-of-sample expected reward of robust solutions can sometimes “beat” that of sample average optimization, a phenomenon that has been observed empirically, and that the difference is typically small. This paper highlights that robust solutions are not “too conservative” if both mean and variance (sensitivity) are considered when selecting the size of the uncertainty set (e.g., via the bootstrap).

THE SOIL MOISTURE RETENTION PATTERN OF SOME SELECTED OF ORGANIC MEDIA UNDER A GREENHOUSE STRUCTURE

This research aimed to investigate the soil moisture retention of some selected organic media for growing cucumber plant. The experiment was conducted in a greenhouse structure and moisture content of each of the organic media was determined by a calibrated moisture meter, which was taken before and after the irrigation. The water application was uniform, using a drip irrigation kit for potted system with a capacity of 75cl storage each for the treatments. The pH values of each of the organic media used shows moderate alkalinity. The mean and sample variance of the moisture retention pattern for each of the media gave; saw dust (3.61, 0.073), maize husk (3.41, 0.044), rice husk (3.92, 0.034), eucalyptus leaves (3.27, 0.021), sawdust + soil (2.76, 0.0416), maize husk + soil (2.94, 0.153), rice husk + soil (3.88, 0.069), eucalyptus leaves + soil (2.76, 0.041), eucalyptus leaves + soil unsterilized (3.77, 0.074), and sandy loamy (23.345, 0.009). Moisture retention pattern of the selected media show high moisture retention in sandy loam while other media show a low moisture retention in approximately ratio 6:1, the sample variance shows small variance indicating how the data point spread out. It can be assumed that low retention could be as a result of the presence of fibre or coarse particles given room for large pore spaces that allows easy moisture drain from the organic media. It can also be deduced from the results that maize husk is least suitable for growing purposes because of unsteady moisture retention pattern.