Patricia L. Smith

Splines as a Useful and Convenient Statistical Tool

Abstract The framework for a unified statistical theory of spline regression assuming fixed knots using the truncated polynomial or “+” function representation is presented. In particular, a partial ordering of some spline models is introduced to clarify their relationship and to indicate the hypotheses that can be tested by using either standard multiple regression procedures or a little-used conditional test developed by Hotelling (1940). The construction of spline models with polynomial pieces of different degrees is illustrated. A numerical example from a chemical experiment is given by using the GLM procedure of the statistical software package SAS (Barr et al. 1976).

Adriamycin-induced changes in the surface membrane of sarcoma 180 ascites cells

Adriamycin increases (a) the rate of agglutination of Sarcoma 180 cells by concanavalin A after brief exposure of 2-3 h and (b) membrane fluidity as measured by ESR within 30 min of exposure at concentrations of the anthracycline of 10(-7)-10(-5) M. The effect of adriamycin on agglutination is not due to an increase in the number of surface receptors for concanavalin A, since the extent of binding of the lectin is not altered by adriamycin and no change occurs in the rate of occupancy of the concanavalin A binding sites by the lectin in cells treated with the antibiotic. The order parameter, a measurement of membrane fluidity, decreases in cells exposed to adriamycin and is dose-related. The results indicate that adriamycin can induce changes in the surface membrane of Sarcoma 180 cells within a brief period of exposure to a low but cytotoxic level of this agent.

A primer for sampling solids, liquids, and gases: based on the seven sampling errors of Pierre Gy

Preface Foreword by Francis F. Pitard List of terms and symbols 1. Some views of sampling 2. The material: sampling and material variation 3. The tools and techniques: sampling, sample collection, and sample handling 4. The process: sampling and process variation 5. A strategy: putting theory into practice Appendix A. Introduction to Gys seven sampling errors Appendix B. The variance of the fundamental error Appendix C. Obtaining a sequential random sample Appendix D. Calculation of the Variogram Appendix E. Experiments Appendix F. Sampling safely References Index.

Hypothesis testing in b-spline regression

Linea0r combinations of B-spline coefficients which provide statistically meaningful hypothesis tests are identified. These tests include the importance of breakpoints, continuity constraints, and higher order terms.The important linear combinations turn out to be contrasts whose coefficients are determined by differencing the left- and right-hand limits of the B-splines or their derivatives at certain knots. A FORTRAN program for testing single degree of freedom hypotheses is discussed.

On the Computation of Optimal Designs for Certain time Series Models with Applications to Optimal Quantile Selection for Location or Scale Parameter Estimation

Using the results of Chow (Ph.D. dissertation, Texas A & M Univ., 1978) on the optimal placement of knots in the approximation of functions by piecewise polynomials, we present an algorithm for the computation of optimal designs for certain time series models considered by Eubank, Smith and Smith (Ann. Statist., 9 (1981), pp. 486–493), (Tech. Rep. 150, Southern Methodist Univ., 1981). The ideas underlying this algorithm form a unified approach to the computation of optimal spacings for the sample quantiles used in the asymptotically best linear unbiased estimator of a location or scale parameter.

Autocalibration of HSPF for Simulation of Streamflow Using a Genetic Algorithm

Hydrologic models are essential to watershed planning and management, particularly in the San Antonio River watershed where competition for scarce water resources is a challenge. As a result, the calibration and validation of hydrologic models are essential steps for their successful application. In this study, we examined the use of a loosely coupled genetic algorithm (GA) as an autocalibration tool for optimization of model parameters for the Hydrologic Simulation Program - Fortran (HSPF), a model frequently used in surface hydrology and water quality modeling. The GA-HSPF model is a more objective and less time-consuming alternative to traditional trial-and-error methods. The objective function was optimized by minimizing the mean absolute error (MAE) between corresponding simulated and observed average daily streamflow in the San Antonio River watershed. The MAE was used to evaluate the fitness of the parameter set in the GA. The calibrated model parameters (LZSN, INFILT, AGWRC, UZSN, DEEPFR, LZETP, and INTFW) were selected based on a sensitivity analysis from a previous study. Goodness-of-fit of the GA calibrated model was evaluated using the Nash-Sutcliffe coefficient of efficiency, MAE, root mean square error, flow duration curves, wavelet analysis, and total volume error. Overall simulation time with 2000 model simulations was 11 days, which can be improved significantly under parallel computing, as GA-HSPF simulations are highly independent. The objective function ceased improvement after approximately 250 simulations, with a minimized MAE of 25.8 m 3 /s. With the exception of DEEPFR, all optimized model parameter values were within the range cited in the literature. Nash-Sutcliffe coefficients in all simulations were above 0.5, suggesting that the simulated flows were in good agreement with the observed flows. Visual comparison between observed and simulated stream flow using time series and flow duration curves showed that the GA calibrated model was unable to simulate peak flow events accurately, particularly in the 0% to 10% exceedence range. It is hypothesized that the storage-based routing scheme in HSPF limits its ability to predict peak flows in this watershed. Comparison between observed and simulated flows in the wavelet domain indicated that the GA calibrated model was not able to preserve the scale and location of some high frequencies, but the scale and location of lower frequencies were preserved. The cyclic nature of the streamflow in this watershed was more prominent in lower frequencies. While overall flow rates were adequately predicted using a GA-HSPF approach, future work in this watershed needs to focus on multi-objective optimization that optimizes both volumes and peak flows. The GA-HSPF model offers an objective and efficient method for calibration and validation, a useful tool in watershed planning efforts.

On the Distribution of the Studentized Bivariate Range

The stltdetltized bivnhte range, R s , it1 a sample from a circrdur normal distribution is espressed as the maximum of a set of F variables. Using a method employed by pearson and Chandra Sekar [7], the exact upper tail distribution for small samples is given. The same procedure provides over-approximations to the percentage points of R s , for larger sample sizes. Methods for obtaining the full distribution are discrussed. The use of the statistic in testitrg for homogeneity is considered.

Modeling Pollutant Buildup and Washoff Parameters for SWMM Based on Land Use in a Semiarid Urban Watershed

SWMM (Storm Water Management Model) has been widely used in urban water resources management. Despite its popularity, no commonly accepted pollutant buildup and washoff parameters are available for urban areas in semi-arid or arid climate, which covers 30% of global land area and is sustaining fast growth. This study provides a method to determine these parameters using inverse modeling and apply it in a semi-arid Texan urban watershed. Because GIS land use data is not available for early 1980s, it was determined from aerial photography from 1984 to 2006, and GIS land use data from 2006. Calibration using Shuffled Complex Evolution – University of Arizona (SCEUA) was used for hydraulic parameters followed by pollutant parameters. Confidence intervals of pollutant parameters were calculated by GLD (Generalized Lambda Distribution). Buildup parameters are clustered in narrow numerical ranges, indicating that spatially uniform factors are responsible for pollutant buildup. Washoff parameters do not cluster and are distributed more evenly, indicating strong influence of local factors such as topography. The results also imply that the commonly used parameter values need major revision.

Geostatistical Error Management: Quantifying Uncertainty for Environmental Sampling and Mapping

My only complaint is that, in their attempt to write an all-encompassing textbook, Tamhane and Dunlop all but omit Bayesian inference. The brevity of the section, the lack of interesting practical examples, and the near absence of exercises from that section are less than satisfying considering the everincreasing role of Bayesian methods within statistics. Despite that fact, the authors have done a marvelous job of presenting an enormous amount of material and should be applauded for doing so. They state that one of their goals was to develop both a textbook and a thorough reference book. Tamhane and Dunlop have certainly accomplished that. As the authors note, however, most curricula do not allow for a two-semester course after a prerequisite of probability. As long as that remains true, Statistics and Data Analysis is not likely to be widely adopted. I do, however, hope that I am wrong.