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

Estimation de la taille de la population dans les expériences de capture-recapture

La thèse présentée ici traite du problème de l'estimation de la taille de la population dans les modèles de capture-recapture. Elle s'intéresse, en particulier, à la question de l'estimation de la taille de la population dans le cadre d'une expérience de capture-recapture à structure d'échantillonnage imbriquée, qui combine les méthodes de population fermée à l'intérieur des périodes primaires (PP) et de population ouverte d'une PP à une autre : le design robuste. Cette thèse propose une méthodologie d'estimation de la taille de la population et de l'incertitude associée aux estimateurs obtenus dans le contexte du design robuste. Dans un premier temps, on aborde le problème de l'estimation des paramètres du design robuste dans le cas d'un nombre suffisamment élevé d'occasions de capture. On généralise le papier fondamental de Jolly (1965) au design robuste en proposant une procédure séquentielle d'estimation des paramètres pour la classe des modèles de design robuste présentés dans Rivest and Daigle (2004) et un estimateur de la variance des paramètres par bootstrap paramétrique. Ces résultats théoriques ont été appliqués à des données d'activation d'applications sur les téléphones intelligents. Les données sont recueillies sur une période d'un an et demi et concernent des utilisateurs de téléphones intelligents qui ont visité un grand concessionnaire automobile basé aux États-Unis. Dans un deuxième temps, on s'intéresse à l'estimation de la taille de la population à partir de deux sources d'information du design robuste: les données à l'intérieur d'une PP (ou intra-période) et les données d'une PP à une autre (ou inter-période). On démontre que les estimateurs de la taille de la population obtenus avec les informations intra-période et inter-période sont asymptotiquement indépendants pour une large classe de modèles de population fermée à l'intérieur des PP. Ainsi, l'estimateur du maximum de vraisemblance pour la taille de la population dans le cas du design robuste est asymptotiquement équivalent à un estimateur pondéré pour le modèle de population ouverte et le modèle de population fermée. On montre que l'estimateur pondéré diffère de celui donné dans Kendall et al. (1995); on démontre que leur estimateur n'est pas efficace, puis on donne une formule explicite pour son efficacité comparativement à l'estimateur pondéré. La perte d'efficacité est ensuite évaluée dans une étude de simulation, puis à travers un exemple tiré de Santostasi et al. (2016) et qui traite de l'estimation de la taille de la population d'une espèce de dauphins vivant dans le Golfe de Corinthe (Grèce). Enfin, on se propose d'étendre les résultats du problème précédent aux modèles de design robuste présentés dans Kendall et al. (1995) et implémentés dans MARK (White and Burnham, 1999). Dans le contexte du design robuste, on dérive l'estimateur du maximum de vraisemblance pour la taille de la population; on propose également trois méthodes d'estimation de la variance de l'erreur associée à l'estimateur. On démontre ensuite que l'estimateur du maximum de vraisemblance pour la taille de la population est plus efficace que l'estimateur des moments proposé par Kendall et al. (1995); la perte d'efficacité de l'estimateur de Kendall ainsi que la performance des trois méthodes d'estimation de la variance de l'erreur associée à l'estimateur du maximum de vraisemblance sont évaluées via une étude de simulation.This thesis deals with the capture-recapture estimation of population sizes under a hierarchical study design where a capture-recapture experiment, involving secondary capture occasions, is carried out within each sampling period (SP) of an open population model: the robust design. This thesis proposes a methodology for the estimation of population sizes under the robust design and the uncertainty associated with the estimators. The first problem deals with the estimation of the parameters of a robust design with an arbitrary large number of capture occasions. To do so, we generalize the seminal paper of Jolly (1965) to the robust design and propose a sequential estimation procedure for the class of robust design models presented in Rivest and Daigle (2004). A simple parametric bootstrap variance estimator for the model parameters is also proposed. These results are used to analyze a data set about the mobile devices that visited the auto-dealerships of a major auto brand in a US metropolitan area over a period of one year and a half. The second problem deals with the estimation of population sizes using two sources of information for the robust design: the within and the between primary period data. We prove that the population size estimators derived from the two sources are asymptotically independent for a large class of closed population models. In this context, the robust design maximum likelihood estimator of population size is shown to be asymptotically equivalent to a weighted sum of the estimators for the open population Jolly-Seber model (Jolly 1965; Seber 1965) and for the closed population model. This article shows that the weighted estimator is more efficient than the moment estimator of Kendall et al.(1995). A closed form expression for the efficiency associated with this estimator is given and the loss of precision is evaluated in a MonteCarlo study and in a numerical example about the estimation of the size of dolphin populations living in the Gulf of Corinth (Greece) and discussed by Santostasi et al. (2016). The third problem deals with the estimation of population sizes under the robust design models presented in Kendall et al. (1995) and implemented in MARK (White and Burnham, 1999). We derive the maximum likelihood estimator for the population size and propose three methods of estimation for its uncertainty. We prove that the derived maximum likelihood estimator is more efficient than the moment estimator provided in Kendall et al. (1995). The loss of precision associated with the Kendall estimator and the performance of the three methods of estimation for the variance of the maximum likelihood estimator are evaluated in a MonteCarlo study

Socioeconomic impacts of innovative dairy supply chain practices. The case of the Laiterie du Berger in the Senegalese Sahel

This study analyzes the Laiterie Du Berger (LDB)'s milk supply chain and its contribution to strengthening the food security and socioeconomic resources of Senegalese Sahelian pastoral households. Porter's value chain model is used to characterize the innovations introduced by the LDB dairy in its milk inbound logistics and supplier relationships. A socioeconomic food security index and qualitative data are used to assess the dairy's supply chain's contribution to strengthen smallholder households' livelihoods. Data for this research were obtained through individual surveys, focus groups and in-depth interviews of LDB managers and milk suppliers. Results show that milk income contributes significantly to household food security. Suppliers who stabilize their dairy income between rainy and dry seasons, diversify income sources and have larger herds are more likely to remain food secure. The LDB innovations contribute by helping herders access biophysical and economic resources, leading to better livestock feed and household food security. (Résumé d'auteur

Effect of Preanalytical Processing of ThinPrep Specimens on Detection of High-Risk Human Papillomavirus by the Aptima HPV Assay

Two important preanalytical protocols performed on liquid-based cytological specimens, namely, automated cytology processing and glacial acetic acid (GAA) treatment, may occur prior to the arrival of specimens in a molecular diagnostics laboratory. Ninety-two ThinPrep vials previously positive for high-risk human papillomavirus (HPV) via the Cervista HPV HR test were preselected and alternated with 92 previously negative ThinPrep vials. The specimen set was processed in a consecutive fashion by an automated cytology processor without fastidious decontamination precautions. Carryover potential was subsequently assessed by performance of the Aptima HPV assay on aliquots from reprocessed ThinPrep vials. All previously negative ThinPrep vials yielded a negative result following routine automated cytology processing, despite close proximity to known-positive ThinPrep vials. In separate experiments, aliquots from 236 ThinPrep vials were forwarded for tandem analysis with and without GAA treatment. Data from GAA- and mock-treated specimens generated by Aptima HPV were compared to correlate data generated by Cervista. A 99.2% concordance of Aptima HPV results from GAA-treated and mock-treated specimens was noted. This result differed from the concordance result derived from Cervista (91.5%; P \u3c 0.0002). Of the initially positive Cervista results, 21.9% reverted to negative following GAA treatment; the correlate value was 2.7% for Aptima HPV (P = 0.01). While deleterious effects of GAA treatment on genomic DNA were noted with Cervista (P = 0.0015), GAA treatment had no significant effects on Aptima HPV specimen signal/cutoff ratios or amplification of internal control RNA (P ≥ 0.07). The validity of an Aptima HPV result is independent of GAA treatment and routine automated cytology processing