具有不正确检测数据的Capture-Recapture模型

本文讨论了软件测试中具有不正确检测数据的Capture-Recapture(C-R)模型,给出了估计软件缺陷个数的计算公式,扩大了原C-R模型的应用范围。用Monte Carlo方法对该模型进行了评估验证,并与原C-R模型做了模拟比较。

Bayesian Estimation of Population Size via Capture-Recapture Model with Time Variation and Behavioral Response

We consider the problem of population estimation using capture-recapture data, where capture probabilities can vary between sampling occasions and behavioural responses. The original model is not identifiable without further restrictions. The novelty of this article is to expand the current research practice by developing a hierarchical Bayesian approach with the assumption that the odds of recapture bears a constant relationship to the odds of initial capture. A real-data example of deer mice population is given to illustrate the proposed method. Three simulation studies are developed to inspect the performance of the proposed Bayesian estimates. Compared with the maximum likelihood estimates discussed in Chao et al. (2000), the hierarchical Bayesian estimate provides reasonably better population estimation with less mean square error;moreover, it is sturdy to underline relationship between the initial and re-capture probabilities. The sensitivity study shows that the proposed Bayesian approach is robust to the choice of hyper-parameters. The third simulation study reveals that both relative bias and relative RMSE approach zero as population size increases. A R-package is developed and used in both data example and simulation.

Ascertainment Corrected Prevalence Rate (ACPR) of Leukopenia in Workers Exposed to Benzene in Small-Scale Industries Calculated With Capture-Recapture Methods

ACPRs of leukopenia in peripheral blood of workers exposed to benzene in small-scale industries are calculated using capture-recapture methods. The results from two figures with 6-month apart demonstrate that the ACPR in workers exposed to benzene is 36.81(29. 14-44.48)%, significantly higher than that of control 12.71(7.20-18.22)% (P<0.05),with a relative risk of 2.9. The prevalences of 4 cross-sectional investigations in exposure group calculated with routine method are 18.73%, 26.37%, 27.93%, and 36.76% respectively;in controls, 8.38%, 6.85%, 7.94%, and 15.00% respectively and all fall in the range of 95% CI of ACPR. It is suggested that the methods of calculating ACPR by capture-recapture methods is simple, feasible and efficient, with the results more precise than with traditional methods.

Capture-Recapture模型与车险事故总体预测

车险事故总体预测问题一直是车辆保险公司研究的重点内容之一,目前最为常用的方法是与泊松分布相关的模型.基于车辆保险中索赔数据的结构特征,构建了Capture-Recapture模型,并使用一组车辆保险数据,利用Capture-Recapture及常用的零膨胀泊松等模型分别建模分析,得出了一些新的结论,即Capture-Recapture模型拟合效果整体较优,从而为车辆保险公司更好预测事故总体提供一定的理论依据.

Estimation of Population-Size Changes and HIV Prevalence among Female Sex Workers from 2006 to 2009 in Kaiyuan,Yunnan,China

Objective This study is to estimate the population size and prevalence of HIV and herpes simplex virus type 2 （HSV-2） infections among female sex workers （FSWs） in Kaiyuan, Yunnan Province, China. Methods Eight cross-sectional studies were conducted among FSWs in Kaiyuan from 2006 to 2009. Based on the data from two study time points each year, the total numbers of FSWs and HIV positive FSWs were estimated by using the capture-recapture technique （CR）. Results Estimated sizes of FSWs in Kaiyuan were 1 629, 1 672, 1 186, and 1 014 in the respective years from 2006 to 2009. Although the crude prevalence rates of HIV and HSV-2 varied over time, the adjusted prevalence among this population was relatively stable at 10%-12% and the adjusted HSV-2 prevalence ranged from 67% to72%. Conclusion The reason for the slight decrease of the size of the FSW population is unknown. The adjusted prevalence rates of HIV and HSV-2 among them were stable over the course of this study.

Mixture Models for Estimating the Number of Drug Users in Thailand 2005-2007

It is difficult to measure the sizes of illegal drug user populations directly by using the survey method because of many “hidden drug addicts” and the difficulty of receiving a true response. Systematic and routine information on treatment episodes of drug users is adopted to estimate the population size in this study. Mixture models of zero-truncated Poisson distributions using the nonparametric maximum likelihood estimators (NPMLE) by means of capture-recapture repeated count data were used to project the number of drug users. The method was applied to surveillance data of drug users identified by treatment episodes in over 1140 health treatment centers in Thailand from the Bureau of Health Service System Development, Ministry of Public Health. We presented how this mixture model could be utilized to construct the unobserved frequency of drug users with no treatment episode and further estimated the total population size of drug users in the country from 2005 to 2007. The result of simulation was confirmed that mixture model is suitable when population is large. By means of mixture models, the estimations for the number of drug users were fitted with excellent goodness-of-fit values and we were also compared to the conventional Chao estimates. The NPMLE for the total number of drug users in Thailand 2005, 2006, and 2007 were 184,045 (95% CI: 181,297-86,793), 230,665 (95% CI: 226,611-234,719), 299,670 (95% CI: 294,217-305,123), respectively, also 125,265 (95% CI: 123,092-127,142), 166,287 (95% CI: 163,222-169,352), 228,898 (95% CI: 224,766 - 233,030) for the number of methamphetamine (Yaba) users, and 11,559 (95% CI: 10,234-12,884), 11,333 (95% CI: 9276-13,390), 8953 (95% CI: 7878-10,028) for the number of heroin users, respectively. The numbers of marijuana, kratom-plant, opium, and inhalant users were underestimated because their symptoms were mild and not severe enough to remedy in health treatment centers which led to the smaller size of the total number of drug users. The well-estimated sizes of heroin and methamphetamine addicts are high reliable because they are based on clearly evident count with a severe addiction problem to health treatment centers. The estimation by means of mixture models can be recommended to monitor drug demand trend and drug health service routinely;it is easy to calculate via the available programs MIXTP based on request.

Plausible combinations: An improved method to evaluate the covariate structure of Cormack-Jolly-Seber mark-recapture models

Mark-recapture models are extensively used in quantitative population ecology, providing estimates of population vital rates, such as survival, that are difficult to obtain using other methods. Vital rates are commonly modeled as functions of explanatory covariates, adding considerable flexibility to mark-recapture models, but also increasing the subjectivity and complexity of the modeling process. Consequently, model selection and the evaluation of covariate structure remain critical aspects of mark-recapture modeling. The difficulties involved in model selection are compounded in Cormack-Jolly-Seber models because they are composed of separate sub-models for survival and recapture probabilities, which are conceptualized independently even though their parameters are not statistically independent. The construction of models as combinations of sub-models, together with multiple potential covariates, can lead to a large model set. Although desirable, estimation of the parameters of all models may not be feasible. Strategies to search a model space and base inference on a subset of all models exist and enjoy widespread use. However, even though the methods used to search a model space can be expected to influence parameter estimation, the assessment of covariate importance, and therefore the ecological interpretation of the modeling results, the performance of these strategies has received limited investigation. We present a new strategy for searching the space of a candidate set of Cormack-Jolly-Seber models and explore its performance relative to existing strategies using computer simulation. The new strategy provides an improved assessment of the importance of covariates and covariate combinations used to model survival and recapture probabilities, while requiring only a modest increase in the number of models on which inference is based in comparison to existing techniques.

Community workers contribution for data quality improvement in routine health information system: Live births number estimation by capture recapture method

The lack of reliable vital statistics raises questions about the role of the health information system in acquiring such data, which are essential for planning health services and for the general management of the population’s needs. This study analyzed completeness of the vital data registration system and assessed the potential contribution of a community worker net-work to this system in rural Benin. The capture-recapture method was used in this interventional study to estimate the number of live births from three sources: the Routine Health Information System, the municipality, and community workers in two groups of villages. Log linear modelling was carried out with a Bayesian Information Criterion-weighted estimate of the number of live births. The exhaustiveness of the Routine Health Information System was improved by the contribution of the community workers from 29.3% to 42.5% in the first group, and from 61.7% to 77.5% in the second group. Estimating live births by the capture method in rural settings based on the contribution of community workers could be a more efficient alternative to censuses in acquiring reliable vital statistics.

Estimating abundance and density of Amur tigers along the Sino- Russian border

As an apex predator the Amur tiger(Panthera tigris altaica)could play a pivotal role in maintaining the integ­rity of forest ecosystems in Northeast Asia.Due to habitat loss and harvest over the past century,tigers rapidly declined in China and are now restricted to the Russian Far East and bordering habitat in nearby China.To fa­cilitate restoration of the tiger in its historical range,reliable estimates of population size are essential to assess effectiveness of conservation interventions.Here we used camera trap data collected in Hunchun National Na­ture Reserve from April to June 2013 and 2014 to estimate tiger density and abundance using both maximum likelihood and Bayesian spatially explicit capture-recapture(SECR)methods.A minimum of 8 individuals were detected in both sample periods and the documentation of marking behavior and reproduction suggests the presence of a resident population.Using Bayesian SECR modeling within the 11400 km2 state space,den­sity estimates were 0.33 and 0.40 individuals/100 km^(2) in 2013 and 2014,respectively,corresponding to an es­timated abundance of 38 and 45 animals for this transboundary Sino-Russian population.In a maximum likeli­hood framework,we estimated densities of 0.30 and 0.24 individuals/100 km^(2) corresponding to abundances of 34 and 27,in 2013 and 2014,respectively.These density estimates are comparable to other published estimates for resident Amur tiger populations in the Russian Far East.This study reveals promising signs of tiger recovery in Northeast China,and demonstrates the importance of connectivity between the Russian and Chinese popula­tions for recovering tigers in Northeast China.

Elusive cats in our backyards:persistence of the North Chinese leopard(Panthera pardus japonensis)in a human-dominated landscape in central China

The North Chinese leopard(Panthera pardus japonensis),the least-known big cat,disappeared in most historical range for decades,following the development of modern civilization.Unfortunately,we have scarce knowledge about the status of this big cat so far,apart from anecdotal reports.In this study,we investigated density,distribution,and habitat use of the leopard,the apex predator,in a complex forest landscape in the Loess Plateau.We used a camera-trapping network to obtain population estimates for leopards over 2 years through spatially explicit capture-recapture models.Our results,based on maximum likelihood and Bayesian/MCMC methods,reveal that the largest wild population of the leopard was found widely distributed in remnant forests in central Loess plateau.The population is increasing in our study area,and the density of leopards(1.70(SE=0.48)−2.40(SE=0.67)/100 km^(2))is higher than other areas of China.According to the analysis of 2 seasonal occupancy models,prey species drive partially the leopard habitat use,predicting that the big cat thrives from the recovery of prey community.However,human disturbances,especially oil wells,seem to have negative impacts on the habitat use of leopards.Specifically,it is necessary to have joint efforts by the government and researchers to improve human disturbances management and prey species population density,as well as strengthen the investment in research on the North Chinese leopard,which could all further strengthen protection ability and ensure the long-term survival of this species.

Survival and maturation rates of the African rodent, Mastomys natalensis: density-dependence and rainfall

Survival and maturation rates of female Mastomys natalensis were analysed based on a ten-year monthlycapture-recapture data set. We investigated whether direct and delayed density dependent and independent (rainfall)variables accounted for the considerable variation in demographic traits. It was estimated that seasonal and annualcovariates accounted for respectively 29 and 26% of the total variation in maturation rates and respectively 17 and11% of the variation in survival rates. Explaining the between-year differences in maturation rates with annual pastrainfall or density did not improve the model fit. On the other hand we showed that maturation rates were correlatednegatively with density the previous month and positively to cumulative rainfall over the past three months.Survival estimates of both adults and subadults varied seasonally, with higher estimates during the increase phase(dry season). The subadults were characterised by a very high survival rate (> 0.95) during this phase. In thedecrease phase only minor differences were found between survival rates of subadults and adults. We found that39% of the between-year variation in survival can be explained by accumulated rainfall over the past year.

Optimizing the size of the area surveyed for monitoring a Eurasian lynx(Lynx lynx)population in the Swiss Alps by means of photographic capture–recapture

We studied the influence of surveyed area size on density estimates by means of camera-trapping in a low-density felid population(1-2 individuals/100 km^(2)).We applied non-spatial capture-recapture(CR)and spatial CR(SCR)models for Eurasian lynx during winter 2005/2006 in the northwestern Swiss Alps by sampling an area divided into 5 nested plots ranging from 65 to 760 km^(2).CR model density estimates(95%CI)for models M_(0)and M_(h)decreased from 2.61(1.55-3.68)and 3.6(1.62-5.57)independent lynx/100 km^(2),respectively,in the smallest to 1.20(1.04-1.35)and 1.26(0.89-1.63)independent lynx/100 km^(2),respectively,in the largest area surveyed.SCR model density estimates also decreased with increasing sampling area but not significantly.High individual range overlaps in relatively small areas(the edge effect)is the most plausible reason for this positive bias in the CR models.Our results confirm that SCR models are much more robust to changes in trap array size than CR models,thus avoiding overestimation of density in smaller areas.However,when a study is concerned with monitoring population changes,large spatial efforts(area surveyed≥760 km^(2))are required to obtain reliable and precise density estimates with these population densities and recapture rates.

Agent-based models reveal limits of mark-release-recapture estimates for the rare butterfly, Bhutanitis thaidina (Lepidoptera: Papilionidae)

Insect diversity and abundance are in drastic decline worldwide,but quantifying insect populations to better conserve them is a difficult task.Mark-release-recapture(MRR)is widely used as an ecological indicator for insect populations,but the accuracy of MRR estimates can vary with factors such as spatial scale,sampling effort and models of inference.We conducted a 3-year MRR study of B.thaidina in Yanzigou valley,Mt.Gongga but failed to obtain sufficient data for a robust population estimate.This prompted us to integrate B.thaidina life history information to parameterize agent-based models and evaluate the conditions under which successful MRR studies could be conducted.We evaluated:(1)the performance of MRR models under different landscape types,and(2)the influence of experimental design on the accuracy and variance of MRR-based estimates.Our simulations revealed systematic underestimates of true population parameters by MRR models when sampling effort was insufficient.In a total of 2772 simulations,subjective decisions in sampling protocol(e.g.,frequency,number of sampling locations,use of spatially explicit models,type of estimands)accounted for nearly half of the variation in estimates.We conclude that MRR-based estimates could be improved with the addition of more field-specific parameters.

Contrasting size-dependent life history strategies of an insular lizard

In many species with continuous growth,body size is an important driver of life-history tactics and its relative importance is thought to reflect the spatio-temporal variability of selective pressures.We developed a deterministic size-dependent integral projection model for 3 insular neighboring lizard populations with contrasting adult body sizes to investigate how size-related selective pressures can influence lizard life-history tactics.For each population,we broke down differences in population growth rates into contributions from size-dependent body growth,survival,and feeundity.A life table response experiment(LTRE)was used to compare the population dynamics of the 3 populations and quantify the contributions of intrinsic demographic coefficients of each population to the population growth rate(z).Perturbation analyses revealed that the largest adults contributed the most to the population growth rate,but this was not true in the population with the smallest adults and size-independent fertility.Although we were not able to identify a single factor responsible for this difference,the combination of the demographic model on a continuous trait coupled with an LTRE analysis revealed how individuals from sister populations of the same species follow different life strategies and showed different compensatory mechanisms among survival,individual body growth,and fertility.Our results indicate that body size can play a contrasting role even in closely-related and closely-spaced populations.

Population Size Estimation with Covariate Values Missing Non-ignorable

The main purpose of this paper is using capture-recapture data to estimate the population size when some covariate values are missing, possibly non-ignorable. Conditional likelihood method is adopted, with a sub-model describing various missing mechanisms. The derived estimate is proved to be asymptotically normal, and simulation studies via a version of EM algorithm show that it is approximately unbiased. The proposed method is applied to a real example, and the result is compared with previous ones.