Fast block variance estimation procedures for inhomogeneous spatial point processes

We introduce two new variance estimation procedures that usenon-overlapping and overlapping blocks, respectively. The non-overlappingblocks estimator can be viewed as the limit of the thinned blockbootstrap estimator recently proposed in Guan Loh (2007), byletting the number of thinned processes and bootstrap samplestherein both increase to infinity. The non-overlapping blocksestimator can be obtained quickly since it does not requireany thinning or bootstrap steps, and it is more stable. Theoverlapping blocks estimator further improves the performanceof the non-overlapping blocks with a modest increase in computationtime. A simulation study demonstrates the superiority of theproposed estimators over the thinned block bootstrap estimator.     

A computationally efficient optimization kernel for material parameter estimation procedures

Estimating material parameters is an important part in the study of soft tissue mechanics. Computational time can easily run to days, especially when all available experimental data are taken into account. The material parameter estimation procedure is examplified on a set of homogeneous simple shear experiments to estimate the orthotropic constitutive parameters of myocardium. The modification consists of changing the traditional least-squares approach to a weighted least-squares. This objective function resembles a L(2)-norm type integral which is approximated using Gaussian quadrature. This reduces the computational time of the material parameter estimation by two orders of magnitude.     

Improved procedures for estimation of disease prevalence using ranked set sampling

Ranked set sampling (RSS) is a sampling procedure that can be considerably more efficient than simple random sampling (SRS). When the variable of interest is binary, ranking of the sample observations can be implemented using the estimated probabilities of success obtained from a logistic regression model developed for the binary variable. The main objective of this study is to use substantial data sets to investigate the application of RSS to estimation of a proportion for a population that is different from the one that provides the logistic regression. Our results indicate that precision in estimation of a population proportion is improved through the use of logistic regression to carry out the RSS ranking and, hence, the sample size required to achieve a desired precision is reduced. Further, the choice and the distribution of covariates in the logistic regression model are not overly crucial for the performance of a balanced RSS procedure.     

Accounting for decay of linkage disequilibrium in haplotype inference and missing-data imputation

Although many algorithms exist for estimating haplotypes from genotype data, none of them take full account of both the decay of linkage disequilibrium (LD) with distance and the order and spacing of genotyped markers. Here, we describe an algorithm that does take these factors into account, using a flexible model for the decay of LD with distance that can handle both "blocklike" and "nonblocklike" patterns of LD. We compare the accuracy of this approach with a range of other available algorithms in three ways: for reconstruction of randomly paired, molecularly determined male X chromosome haplotypes; for reconstruction of haplotypes obtained from trios in an autosomal region; and for estimation of missing genotypes in 50 autosomal genes that have been completely resequenced in 24 African Americans and 23 individuals of European descent. For the autosomal data sets, our new approach clearly outperforms the best available methods, whereas its accuracy in inferring the X chromosome haplotypes is only slightly superior. For estimation of missing genotypes, our method performed slightly better when the two subsamples were combined than when they were analyzed separately, which illustrates its robustness to population stratification. Our method is implemented in the software package PHASE (v2.1.1), available from the Stephens Lab Web site.     

Multivariate multiple test procedures based on nonparametric copula estimation

Multivariate multiple test procedures have received growing attention recently. This is due to the fact that data generated by modern applications typically are high‐dimensional, but possess pronounced dependencies due to the technical mechanisms involved in the experiments. Hence, it is possible and often necessary to exploit these dependencies in order to achieve reasonable power. In the present paper, we express dependency structures in the most general manner, namely, by means of copula functions. One class of nonparametric copula estimators is constituted by Bernstein copulae. We extend previous statistical results regarding bivariate Bernstein copulae to the multivariate case and study their impact on multiple tests. In particular, we utilize them to derive asymptotic confidence regions for the family‐wise error rate (FWER) of multiple test procedures that are empirically calibrated by making use of Bernstein copulae approximations of the dependency structure among the test statistics. This extends a similar approach by Stange et al. (2015) in the parametric case. A simulation study quantifies the gain in FWER level exhaustion and, consequently, power that can be achieved by exploiting the dependencies, in comparison with common threshold calibrations like the Bonferroni or ?idák corrections. Finally, we demonstrate an application of the proposed methodology to real‐life data from insurance.     

Simple estimation and test procedures in capture-mark-recapture mixed models

The need to consider in capture-recapture models random effects besides fixed effects such as those of environmental covariates has been widely recognized over the last years. However, formal approaches require involved likelihood integrations, and conceptual and technical difficulties have slowed down the spread of capture-recapture mixed models among biologists. In this article, we evaluate simple procedures to test for the effect of an environmental covariate on parameters such as time-varying survival probabilities in presence of a random effect corresponding to unexplained environmental variation. We show that the usual likelihood ratio test between fixed models is strongly biased, and tends to detect too often a covariate effect. Permutation and analysis of deviance tests are shown to behave properly and are recommended. Permutation tests are implemented in the latest version of program E-SURGE. Our approach also applies to generalized linear mixed models.     

Comparison of various procedures for estimation of the classification error in discriminance analysis

The practical use of classification methods depends, for the majority of cases, on whether it is possible to obtain evidence how newly appearing objects of unknown classes-membership can be allocated on the basis of a classifier established by a training sample. In the present paper several error estimation methods are presented and compared with each other. It is shown by means of a practical example in which way the number of characteristics used in the discrimination affects the classification error. Discriminance functions calculated from many characteristics yield a higher error rate than those from fewer characteristics. From the comparison of the error rates and computing times involved in the individual methods recommendations for the selection of practicable estimation methods are given.     

QTL analysis: unreliability and bias in estimation procedures

Several statistical methods which employ multiple marker data are currently available for the analysis of quantitative trait loci (QTL) in experimental populations. Although comparable estimates of QTL location and effects have been obtained by these methods, using simulated and real data sets, their accuracy and reliability have not been extensively investigated. The present study specifically examines the merit of using F₂ and doubled haploid populations for locating QTL and estimating their effects. Factors which may affect accuracy and reliability of QTL mapping, such as the number and position of the markers available, the accuracy of the marker locations and the size of the experimental population used, are considered. These aspects are evaluated for QTL of differing heritabilities and locations along the chromosome.A population of 300 F₂ individuals and 150 doubled haploid lines gave estimates of QTL position and effect which were comparable, albeit extremely unreliable. Even for a QTL of high heritability (10%), the confidence interval was 35 cM. There was little increase in reliability to be obtained from using 300, rather than 200, F₂ individuals and 100 doubled haploid lines gave similar results to 150. QTL estimates were not significantly improved either by using the expected, rather than the observed, marker positions or by using a dense map of markers rather than a sparse map. A QTL which was asymmetrically located in the linkage group resulted in inaccurate estimates of QTL position which were seriously biassed at low heritability of the QTL. In a population of 300 F₂ individuals the bias increased from 4 cM to 20 cM, for a QTL with 10% and 2% heritability respectively.     

Manure sampling procedures and nutrient estimation by the hydrometer method for gestation pigs

Three manure agitation procedures were examined in this study (vertical mixing, horizontal mixing, and no mixing) to determine the efficacy of producing a representative manure sample. The total solids content for manure from gestation pigs was found to be well correlated with the total nitrogen (TN) and total phosphorus (TP) concentrations in the manure, with highly significant correlation coefficients of 0.988 and 0.994, respectively. Linear correlations were observed between the TN and TP contents and the manure specific gravity (correlation coefficients: 0.991 and 0.987, respectively). Therefore, it may be inferred that the nutrients in pig manure can be estimated with reasonable accuracy by measuring the liquid manure specific gravity. A rapid testing method for manure nutrient contents (TN and TP) using a soil hydrometer was also evaluated. The results showed that the estimating error increased from +/-10% to +/-30% with the decrease in TN (from 1000 to 100 ppm) and TP (from 700 to 50 ppm) concentrations in the manure. Data also showed that the hydrometer readings had to be taken within 10 s after mixing to avoid reading drift in specific gravity due to the settling of manure solids.     

Statistical methods for model comparison in parameter estimation problems for distributed systems

In this note we outline some recent results on the development of a statistical testing methodology for inverse problems involving partial differential equation models. Applications to several problems from biology are presented. The statistical tests, which are in the spirit of analysis of variance (ANOVA), are based on asymptotic distributional results for estimators and residuals in a least squares approach.Research supported in part under grants NSF MCS 8504316, NASA NAG-1-517, and AFOSRF-49620-86-C-0111. Part of this research was carried out while the first author was a visiting scientist at the Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA, which is operated under NASA contracts NASI-18107 and NASI-18605     

Recursive on-line estimation of the specific growth rate from off-gas analysis for the adaptive control of fed-batch processes

A recursive estimation algorithm for the specific growth rate of aerobic fed-batch processes was developed. The estimate (t) is independent of the state estimates X(t) of the process. This improves the stability of the closed loop system. The performance of the nonlinear control system was tested on fermentations with streptomyces tendae with great success. The methodology of the nonlinear control system is very general. Thus, it can be applied to substrate control problems of any other aerobic fed-batch process.     

Alternative estimation procedures for Pr(X less than Y) in categorized data

Consider two independent random variables X and Y. The functional R = Pr(X less than Y) [or gamma = Pr(X less than Y) - Pr(Y less than X)] is of practical importance in many situations, including clinical trials, genetics, and reliability. In this paper several approaches to estimation of gamma when X and Y are presented in discretized (categorical) form are analyzed and compared. Asymptotic formulas for the variances of the estimators are derived; use of the bootstrap to estimate variances is also discussed. Computer simulations indicate that the choice of the best estimator depends on the value of gamma, the underlying distribution, and the sparseness of the data. It is shown that the bootstrap provides a robust estimate of variance. Several examples are treated.