Improved Estimation of Coefficients in Regression Models with Incomplete Prior Information

The method of mixed regression is considered for the estimation of coefficients in a linear regression model when incomplete prior information is available, and two families of improved estimators stemming from Stein-rule are proposed. Their properties are studied when disturbances are normal but small.     

Optimal Experimental Design and Accuracy of Parameter Estimation for Nonlinear Regression Models Used in Long-term Selection

An experimental design problem is considered for the analysis of long-term selection experiments with nonlinear regression models. For a 3-parametric exponential regression function whose parameters have also a reasonable biological interpretation approximate formulas for the determination of the necessary number of observations at each generation are constructed in such a way that the half expected length of an (1 — α)-confidence interval for a chosen parameter is not greater than a given value. In this sense the accuracy of the parameter estimators can be described.     

A Method of Estimation of Change Points in Multiphasic Growth Models

The least-squares estimation (LSE) of change points and the phase parameters is considered for two growth models with piecewise continuously connected exponential and stationary phases. The calculation of a LSE is reduced to the solution of a finite number of simpler least-squares problems for which methods of calculation are well known.     

A model for thermograms

Thermograms are curves resulting from thermal analysis and are of great interest in the study of various food and biological products physical properties. A method to separate underlying peaks is proposed, and statistical properties of estimates for some characteristic parameters are derived. The total number of peaks can be estimated with a sequential analysis of the residual plots. For each new peak, a statistical criterion is proposed to check whether it is significantly different from the noise of the recording. As an example, the method is applied to a summer milk fat fusion thermogram.     

Parameter Estimation for the Bateman Function via Moments of the Empirical Curve

The parameters of the function f(t)=c(e^?at-e^?bt) are related in a simple way to the moments ^∞ tⁿf(t)^dt(n=0, 1, 2). Using empirical values of f, the moments can be estimated by numerical integration. Therefrom estimates of the parameters are obtained by elementary algebra.     

Point and Interval Estimation of the Population Size Using a Zero‐Truncated Negative Binomial Regression Model

This paper presents the zero‐truncated negative binomial regression model to estimate the population size in the presence of a single registration file. The model is an alternative to the zero‐truncated Poisson regression model and it may be useful if the data are overdispersed due to unobserved heterogeneity. Horvitz–Thompson point and interval estimates for the population size are derived, and the performance of these estimators is evaluated in a simulation study. To illustrate the model, the size of the population of opiate users in the city of Rotterdam is estimated. In comparison to the Poisson model, the zero‐truncated negative binomial regression model fits these data better and yields a substantially higher population size estimate. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Poisson Regression with Change‐Point Prior in the Modelling of Disease Risk around a Point Source

Bayesian estimation of the risk of a disease around a known point source of exposure is considered. The minimal requirements for data are that cases and populations at risk are known for a fixed set of concentric annuli around the point source, and each annulus has a uniquely defined distance from the source. The conventional Poisson likelihood is assumed for the counts of disease cases in each annular zone with zone‐specific relative risk and parameters and, conditional on the risks, the counts are considered to be independent. The prior for the relative risk parameters is assumed to be piecewise constant at the distance having a known number of components. This prior is the well‐known change‐point model. Monte Carlo sampling from the posterior results in zone‐specific posterior summaries, which can be applied for the calculation of a smooth curve describing the variation in disease risk as a function of the distance from the putative source. In addition, the posterior can be used in the calculation of posterior probabilities for interesting hypothesis. The suggested model is suitable for use in geographical information systems (GIS) aimed for monitoring disease risks. As an application, a case study on the incidence of lung cancer around a former asbestos mine in eastern Finland is presented. Further extensions of the model are discussed.     

A Hierarchical Model for Estimating Change in American Woodcock Populations

Abstract The Singing-Ground Survey (SGS) is a primary source of information on population change for American woodcock (Scolopax minor). We analyzed the SGS using a hierarchical log-linear model and compared the estimates of change and annual indices of abundance to a route regression analysis of SGS data. We also grouped SGS routes into Bird Conservation Regions (BCRs) and estimated population change and annual indices using BCRs within states and provinces as strata. Based on the hierarchical model–based estimates, we concluded that woodcock populations were declining in North America between 1968 and 2006 (trend = −0.9%/yr, 95% credible interval: −1.2, −0.5). Singing-Ground Survey results are generally similar between analytical approaches, but the hierarchical model has several important advantages over the route regression. Hierarchical models better accommodate changes in survey efficiency over time and space by treating strata, years, and observers as random effects in the context of a log-linear model, providing trend estimates that are derived directly from the annual indices. We also conducted a hierarchical model analysis of woodcock data from the Christmas Bird Count and the North American Breeding Bird Survey. All surveys showed general consistency in patterns of population change, but the SGS had the shortest credible intervals. We suggest that population management and conservation planning for woodcock involving interpretation of the SGS use estimates provided by the hierarchical model.     

A Bayesian Decision Procedure for Selecting Prognostic Variables Associated with Survival for Data in which Censoring is Prevalent

A Bayesian procedure is developed for the selection of concomitant variables in survival models. The variables are selected in a step-up procedure according to the criterion of maximum expected likelihood, where the expectation is over the prior parameter space. Prior knowledge of the influence of these covariates on patient prognosis is incorporated into the analysis. The step-up procedure is stopped when the Bayes factor in favor of omitting the variable selected in a particular step exceeds a specified value. The resulting model with the selected variables is fitted using Bayes estimates of the coefficients. This technique is applied to Hodgkin's disease data from a large Cooperative Clinical Trial Group and the results are compared to the results from the classical likelihood selection procedure.     

Fidelity Estimation for a Hierarchical Classifier

To estimate the correct classification rate of a classifier, many different methods exist (test sample, bootstrap, cross validation). The test sample is a method with very small expense. Sometimes, only a small number of objects is available (seldom diseases, high costs for experiments). When we split the sample in training set and test set, we get good or bad fidelity estimations but, unfortunately, vice versa a big or small confidence interval for the estimation. Overcoming this dilemma is only possible for simple classifiers. Such a simple classifier is investigated and a direct fidelity estimation is proposed.     

On the Estimation of the Nearest Neighbour Distribution,G(t), for Point Processes

A new method is proposed for estimating G(t), the distribution function of the distance from an object to its nearest neighbour in a spatial point process. The new method makes more complete use of the information available and has a smaller mean squared error than that of the existing alternatives. The method appears equally effective with random, clustered and regular patterns.