ALTERNATIVE PROCEDURES FOR ESTIMATION OF NONLINEAR REGRESSION PARAMETERS

Biological research data are often represented using nonlinear model specifications that lend themselves to the testing of relevant hypotheses concerning the model parameters. This is typically achieved with classical nonlinear least squares techniques such as Gauss-Newton or Levenberg-Marquardt which allow for both the estimation and inference phases of the analysis. Under some circumstances, however, sensitivity to data or model specifications may lead these methods to fail convergence tests or exhibit nonlinearity in the parameter estimates, which will in turn limit the usefulness of inferential results. In such cases, other estimation methods may present a means of avoiding these problems while providing analogous results. The genetic algorithm combined with bootstrapping and Bayesian estimation are two such alternatives. Genetic algorithms represent a nonparametric approach which, when augmented with bootstrap methods, result in both parameter estimation and approximation of the distribution(s). Bayesian estimation, on the other hand, leads directly to parameter distribution and achieves the required moments. These methods and classical nonlinear least squares are demonstrated utilizing a four- parameter cumulative Wei bull function fitted to onion seed germination data

COMPARING BINOMIAL BOOTSTRAP AND BAYESIAN ESTIMATION METHODS IN ASSESSING THE AGREEMENT BETWEEN CLASSIFIED IMAGES AND GROUND TRUTH DATA.

The degree of agreement between classification and ground truth in remotely sensed data is often quantified with an error matrix and summarized using agreement measures such as Cohen\u27s kappa. In the case of ground truth however, the kappa statistic can be shown to be a transformation of the marginal proportions commonly referred to as omissional and commissional error rates. A more meaningful statistical interpretation of remote sensing results and less ambiguous conclusions can be obtained via direct utilization of these measures. Several estimation techniques have been suggested for these marginal proportions. In this study, we will develop the exact binomial, bootstrap and Bayesian estimation methods for omissional and commissional errors. Emphasis will be placed on comparing the various estimation methods and their corresponding empirical distributions. Results are demonstrated with reference to a study designed to evaluate the detectability of yellow hawkweed and oxeye daisy using multispectral digital imagery in Northern Idaho

BAYESIAN ANALYSIS OF DOSE-RESPONSE CALIBRATION CURVES

The statistical analysis of dose-response experiments typically models observed responses as a function of an applied dosage series. The estimated dose-response curve is used in predicting future responses, however, it is also commonly rewritten in an inverted form where dose is expressed as a function of the response. This modified calibration curve is useful in cases where observed responses are available, but their associated dosages are unknown. Traditional statistical techniques for the estimation of unknown doses from the dose-response curve are problematic, involving approximate solutions and methods. Alternatively, this type of inverse calibration problem naturally falls into the framework of Bayesian analysis. That is, one wishes to estimate the probability of an unknown dose value at an observed value of the response given the underlying relationship between the dose and response. This paper examines some potential Bayesian solutions to the calibration problem under various assumptive conditions. The required methodology in each case will be outlined for a dichotomous response variable and a logistic dose-response function. Empirical results will be demonstrated using data from an organic pesticide dose-response trial

USING LANDSCAPE CHARACTERISTICS AS PRIOR INFORMATION FOR BAYESIAN CLASSIFICATION OF REMOTELY SENSED IMAGERY

Yellow starthistle is a dominant weed of north-central Idaho canyon grasslands. The distribution of yellow starthistle can be affected by general landscape characteristics, such as land use, as well as specific terrain related features such as elevation, slope, and aspect. Slope and aspect can be considered as indicators of plant community composition and distribution. Hence, these variables may be incorporated into prediction models to estimate the likelihood of yellow starthistle occurrence. An empirically derived nonlinear model based on landscape characteristics was developed to predict the likelihood of yellow starthistle occurrence in north central Idaho (Shafii, et al. 1999). While the model was employed to predict the invasion potential of yellow starthistle into new areas, it could also be used as auxiliary data for classifying this weed species in remotely sensed imagery. To accomplish this, the predicted values of the model are regarded as prior information on the presence of yellow starthistle. A Bayesian image classification algorithm using this prior information is then applied to a corresponding set of remotely sensed data. The end result is a map indicating the posterior probabilities of yellow starthistle occurrence given the landscape characteristics. This technique is demonstrated considering the presence and absence of prior information and is shown to result in lower omissional and commissional error rates when the landscape characteristics are utilized

STATISTICAL ANALYSIS OF GENOTYPE-BY-ENVIRONMENT INTERACTION USING THE AMMI MODEL AND STABILITY ESTIMATES

Understanding the implication of genotype-by-environment (GE) interaction structure is an important consideration in plant breeding programs. A significant GE interaction for a quantitative trait such as yield can seriously limit efforts in selecting superior genotypes for both new crop introduction and improved cultivar development. Traditional statistical analyses of yield trials provide little or no insight into the particular pattern or structure of the GE interaction. The Additive Main Effects and Multiplicative Interaction (AMMI) statistical model incorporates both additive and multiplicative components of the two-way data structure which can account more effectively for the underlying interaction patterns. Integrating results obtained from biplot graphic displays with those of the genotypic stability analysis enables clustering of genotypes based on similarity of response and the degree of stability in performance across diverse environments. The AMMI model is presented, and its usage in diagnosing the GE interaction structure is discussed. Tai\u27s stability statistics are employed to determine the stability of genotypes tested. Empirical applications are demonstrated using data from a national winter rapeseed variety trial

BAYESIAN NONPARAMETRIC BIOASSAY ESTIMATION

Estimation of unknown pesticide levels in experimental samples is an important aspect of many agricultural and environmental studies. Such measurements are often made utilizing a “standard” dose response curve. This methodology compares the biological response of a target organism at known dosages to the response of the same organism exposed to an unknown sample. These “bioassays” are typically more efficient in time and resources than direct chemical assessment of the unknown sample. The form and choice of the standard curve, however, is subjective and can influence the estimation of the unknown dose. Problems may also arise when incomplete or preliminary information is available for determining the standard curve. One means of reducing the effects of these problems is to use a more generalized nonparametric estimation technique. This work will outline an alternative bioassay method based on a Bayesian nonparametric standard curve estimation framework. Empirical results will be demonstrated using data from a trichorpyr herbicide dose-response trial on lettuce germination

ALTERNATIVE ESTIMATION TECHNIQUES FOR CORRELATED DISCRETE DATA

Binary or multinomial data often occur in agricultural and biological research. Advancements in measurement and video technologies now allow such data to be sequentially recorded through time or space. These data sets, however, can exhibit a serial correlation structure, which in turn, can bias and influence point estimates as well as inferences made regarding the data. Statistical methods using generalized mixed models and probability distributions such as the beta-binomial and correlated binomial have been proposed as potential solutions for estimating the parameters of interest in these cases. In this paper, we will explore the properties of these techniques through simulation studies and demonstrate each scenario using real data related to olfactometer choice tests of a seed eating weevil

Using a Generalized Linear Mixed Model Framework to Account for Spatial Variability in a Comparison of Orchard Sprayer Efficacy

Uniform application of pesticides in vineyard and orchard systems can be difficult to achieve due to variability in the density and structure of the crop canopy. Depending on the equipment used and environmental conditions, applications can result in poor spray coverage, spray drift, and wasted spray which, in turn, are manifested as a combination of poor pesticide efficacy, economic losses and potential environmental problems for the grower. A study was therefore designed and carried out to test new sprayer equipment aimed at addressing these issues. Statistically, the study presented a unique replicated three dimensional spatial design which captured response variability (coverage) both within and across trees in an orchard setting. Application of a generalized linear mixed model framework allowed comparison of sprayer designs in terms of their application efficiencies while accounting for the intra- and inter-tree correlation of the coverage response. Examples demonstrating various models and their associated correlation structures are given and the resulting interpretations discussed

ALTERNATIVE ESTIMATION TECHNIQUES FOR ASSESSING PROBABILITY OF FROST DAMAGE IN SUBALPINE FIR TREES

Subalpine fir (Abies lasiocarpa var. lasiocarpa) is commonly used for nursery stock and Christmas tree applications. Spring frost damage to new buds, however, can jeopardize the longterm investment of growers and reduce the quality of the resulting fir trees. Hence, it is important to evaluate the risk of frost damage when considering prospective growing sites. A prediction model for bud development based on heat units can be used in conjunction with historical climate data to assess the likelihood of frost damage. That is, given the probability of a frost event at a given location and time, and the corresponding probability of bud break at that time, the probability of frost damage can be estimated. Factors affecting estimation, such as multiple environments inherent in the data, as well as temporal variation, must also be considered. These issues will be explored using parametric, non-parametric, and computer intensive estimation techniques. Examples will be demonstrated using data collected from replicated bud break experiments conducted in northern Idaho

AN INDIVIDUAL-PLANT GROWTH SIMULATION MODEL FOR QUANTIFYING PLANT COMPETITION

Plant competition models traditionally have used population or stand level parameters as a basis for modeling. While such models may be valid with regard to average responses, they fail to account for important factors such as within stand variability and spatial relationships. This translates to an assumption of uniformity in growth characteristics among individual plant,S as well as an equidistant spacing arrangement which are unlikely in real populations. One alternative is to model the growth characteristics of individual plants separately which, when combined as a system, will inherently have popUlation attributes related to competition. Competition models of this type allow for various combinations of growth patterns and spatial arrangements. An individual-plant based simulation model is introduced and the relationships of model parameters with existing concepts in plant competition are discussed. Models are calibrated to wild oat (Avenafatua) and spring barley (Hordeum vulgare) using data from replicated field experiments in Northern Idaho