Rcapture: Loglinear Models for Capture-Recapture in R

This article introduces Rcapture, an R package for capture-recapture experiments. The data for analysis consists of the frequencies of the observable capture histories over the t capture occasions of the experiment. A capture history is a vector of zeros and ones where one stands for a capture and zero for a miss. Rcapture can fit three types of models. With a closed population model, the goal of the analysis is to estimate the size N of the population which is assumed to be constant throughout the experiment. The estimator depends on the way in which the capture probabilities of the animals vary. Rcapture features several models for these capture probabilities that lead to different estimators for N. In an open population model, immigration and death occur between sampling periods. The estimation of survival rates is of primary interest. Rcapture can fit the basic Cormack-Jolly-Seber and Jolly-Seber model to such data. The third type of models fitted by Rcapture are robust design models. It features two levels of sampling; closed population models apply within primary periods and an open population model applies between periods. Most models in Rcapture have a loglinear form; they are fitted by carrying out a Poisson regression with the R function glm. Estimates of the demographic parameters of interest are derived from the loglinear parameter estimates; their variances are obtained by linearization. The novel feature of this package is the provision of several new options for modeling capture probabilities heterogeneity between animals in both closed population models and the primary periods of a robust design. It also implements many of the techniques developed by R. M. Cormack for open population models.

Rcapture: Loglinear Models for Capture-Recapture in R

This article introduces Rcapture, an R package for capture-recapture experiments. The data for analysis consists of the frequencies of the observable capture histories over the t capture occasions of the experiment. A capture history is a vector of zeros and ones where one stands for a capture and zero for a miss. Rcapture can fit three types of models. With a closed population model, the goal of the analysis is to estimate the size N of the population which is assumed to be constant throughout the experiment. The estimator depends on the way in which the capture probabilities of the animals vary. Rcapture features several models for these capture probabilities that lead to different estimators for N. In an open population model, immigration and death occur between sampling periods. The estimation of survival rates is of primary interest. Rcapture can fit the basic Cormack-Jolly-Seber and Jolly-Seber model to such data. The third type of models fitted by Rcapture are robust design models. It features two levels of sampling; closed population models apply within primary periods and an open population model applies between periods. Most models in Rcapture have a loglinear form; they are fitted by carrying out a Poisson regression with the R function glm. Estimates of the demographic parameters of interest are derived from the loglinear parameter estimates; their variances are obtained by linearization. The novel feature of this package is the provision of several new options for modeling capture probabilities heterogeneity between animals in both closed population models and the primary periods of a robust design. It also implements many of the techniques developed by R. M. Cormack for open population models

A new statistical model for random unit vectors

AbstractThis paper proposes a new statistical model for symmetric axial directional data in dimension p. This proposal is an alternative to the Bingham distribution and to the angular central Gaussian family. The statistical properties for this model are presented. An explicit form for its normalizing constant is given and some moments and limiting distributions are derived. The proposed density is shown to apply to the modeling of 3×3 rotation matrices by representing them as quaternions, which are unit vectors in ℜ4. The moment estimators of the parameters of the new model are calculated; explicit expressions for their sampling variances are given. The analysis of data measuring the posture of the right arm of subjects performing a drilling task illustrates the application of the proposed model

Small Sample Estimators for Two-way Capture Recapture Experiments

The properties of the generalized Waring distribution defined on the non negative integers are reviewed. Formulas for its moments and its mode are given. A construction as a mixture of negative binomial distributions is also presented. Then we turn to the Petersen model for estimating the population size $N$ in a two-way capture recapture experiment. We construct a Bayesian model for $N$ by combining a Waring prior with the hypergeometric distribution for the number of units caught twice in the experiment. Confidence intervals for $N$ are obtained using quantiles of the posterior, a generalized Waring distribution. The standard confidence interval for the population size constructed using the asymptotic variance of Petersen estimator and .5 logit transformed interval are shown to be special cases of the generalized Waring confidence interval. The true coverage of this interval is shown to be bigger than or equal to its nominal converage in small populations, regardless of the capture probabilities. In addition, its length is substantially smaller than that of the .5 logit transformed interval. Thus a generalized Waring confidence interval appears to be the best way to quantify the uncertainty of the Petersen estimator for populations size

Sampling a two dimensional matrix

A new sampling design for populations whose units can be arranged as an matrix is proposed. The sample must satisfy some constraints: row and column sample sizes are set in advance. The proposed sampling method gives the same selection probability to all the sample matrices that satisfy the constraints. Three algorithms to select a sample uniformly in the feasible set are presented: an exact algorithm based on the multivariate hypergeometric distribution, an MCMC algorithm, and the cube method. Their performances are evaluated using Monte Carlo simulations. The designs for sampling elements in a given row or a given column are investigated and the single inclusion and joint selection probabilities under the proposed design are evaluated. Several variance estimators are proposed for the Horvitz–Thompson estimator of the population mean of the survey variable and their performances are compared in a Monte Carlo study. A numerical example dealing with a creel survey of fishermen found at 9 sites over 36 days is presented

A new copula regression model for hierarchical data

This paper proposes multivariate copula models for hierarchical data. They account for two types of correlation: one is between variables measured on the same unit and the other is a correlation between units in the same cluster. This model is used to carry out copula regression for hierarchical data that gives cluster specific prediction curves. In the simple case where a cluster contains two units and where two variables are measured on each one, the new model is constructed within a D-vine. Then we focus on situations where two variables are measured on the units of a cluster of arbitrary size. The proposed copula density has an explicit form; it is expressed in terms of three copula families. We study the properties of the model; compare it to the linear mixed model and end with special cases. When the three copula families and the marginal distributions are normal, the model is equivalent to a normal linear mixed model with random, cluster specific, intercepts. The method to select the three copula families and to estimate their parameters are proposed. We perform a Monte Carlo study of the parameter estimators. A data set on the marks of students in several school is used to implement the proposed model and to compare its performance to standard normal mixed linear models

Double Counts in Aerial Surveys to Estimate Polar Bear Numbers During the Ice-Free Period

The double-count technique in aerial surveys, a variant of the mark and recapture method, was tested over islands offshore northern Quebec to estimate the number of polar bears that retreated there in the summers of 1986 and 1987. One front observer and two lateral ones surveyed six areas from aboard a twin engine DC-3 aircraft, independently reporting the number of animals they saw to the crew navigator. Bears were classified as being seen both in front and on the side, in front only or on the side only, making it possible to estimate correction factors. Although the observed strip covered 1.75 km on each side of the aircraft, the bear visibility rate exceeded 60% for lateral observers; the low vegetation of the islands and the contrasting colour of bears explain this high visibility. Corrected bear density varied between 0.4 and 14.2 animals per 100 sq km according to year and area. The double-count technique could be used to estimate the size of bear populations retreating on the islands and the coasts of Hudson Bay during the ice-free period, but its costs would have to be evaluated and compared with current techniques before including this method in management programs.Key words: polar bear, census, double count, Hudson Bay, Quebec, summer, Ursus maritimusMots clés: Baie d’Hudson, été, décompte double, inventaire, Québec, ours blanc, Ursus maritimu

Multiple viewpoint modelling framework enabling integrated product-process design

Nowadays, companies have to cope with numerous constraints at organisational and technical levels in order to improve their competitiveness edges such as productivity, efficiency, and flexibility. Integrated product-process design becomes more and more complex to manage because of increasingly customized products related to various stakeholders and concerns geographically distributed. It is still represents a huge challenge, especially in the early phases of product development process. In such a context, the management of information within integrated product-process design highlights needs in a consistent engineering model that enables product lifecycle management (PLM) integration. The paper presents a novel multiple viewpoint framework called multiple viewpoint assembly oriented, considering product design and assembly process domains in the broader context of concurrent engineering and PLM. The proposed framework describes the consistency, the propagation of information change, and mechanisms of views generation among the product lifecycle stages in order to support assembly oriented design philosophy. A new modelling language called System Modeling Language is used to describe the proposed model from a systems engineering point of view. The implementation of the model in a Web-service called PEGASUS as an application for PLM systems is describe

Capturing and analysing how designers use CAD software

Current Computer-Aided Design (CAD) packages support the storage of the final design models and solutions in different formats, and PLM software manages the high-level information about the design process, such as the versioning of the design solutions. However, the processes happening inside the CAD software are not being fully captured. Information such as the sequence of actions (create a sketch, set a distance constraint, remove a pocket, modify the diameter of a through hole, etc.), versioning of the created objects, etc. is missing. This information can be used to understand how a designer uses CAD software to generate geometric representations. In design companies, capturing this information during a product design project would help to evaluate the designer’s way of working with CAD software. In design education, collecting information on how design students generate geometric representations would allow teachers to identify the areas of misunderstanding, improve the education process by representing the optimal way of working, and help teachers to correctly evaluate their students’ performance in using CAD software. This paper proposes a framework to support an analysis of how designers use CAD software to generate geometric representations. This framework consists of structured models and an approach which guides the actor in capturing the design process. We use CATIA as a CAD software solution, but the proposed approach is generic and can be extended to any CAD software. The validity of the proposed approach is illustrated through a case study