Exact Maximum Likelihood Estimate of a Finite Population Size

1987 ◽  
Vol 1 (2) ◽  
pp. 225-236 ◽  
Author(s):  
Jose Galvão Leite ◽  
Jorge Oishi ◽  
Carlos Alberto de Bragança Pereira
Keyword(s):  
Maximum Likelihood ◽  
Population Size ◽  
Finite Population ◽  
Sequential Sampling ◽  
Likelihood Functions ◽  
Exact Analytical Expression ◽  
Sampling Process ◽  
Capture Recapture ◽  
Using Data ◽  
Exact Maximum Likelihood

Using data obtained by the general capture/recapture sequential sampling process, an exact analytical expression for the maximum likelihood (ML) estimate of the population size, N, is introduced. As a consequence, it is shown that bounded likelihood functions have at most two maxima. For the simple one-by-one case the ML estimate is unique.

scholarly journals On Local Linear Approximations to Diffusion Processes

2011 ◽  
Vol 2011 ◽  
pp. 1-26
Author(s):  
X. L. Duan ◽  
Z. M. Qian ◽  
W. A. Zheng
Keyword(s):  
Maximum Likelihood ◽  
Diffusion Processes ◽  
Gaussian Approximation ◽  
Diffusion Models ◽  
Likelihood Method ◽  
Unknown Parameters ◽  
Likelihood Functions ◽  
The Past ◽  
Local Linear ◽  
Exact Maximum Likelihood

Diffusion models have been used extensively in many applications. These models, such as those used in the financial engineering, usually contain unknown parameters which we wish to determine. One way is to use the maximum likelihood method with discrete samplings to devise statistics for unknown parameters. In general, the maximum likelihood functions for diffusion models are not available, hence it is difficult to derive the exact maximum likelihood estimator (MLE). There are many different approaches proposed by various authors over the past years, see, for example, the excellent books and Kutoyants (2004), Liptser and Shiryayev (1977), Kushner and Dupuis (2002), and Prakasa Rao (1999), and also the recent works by Aït-Sahalia (1999), (2004), (2002), and so forth. Shoji and Ozaki (1998; see also Shoji and Ozaki (1995) and Shoji and Ozaki (1997)) proposed a simple local linear approximation. In this paper, among other things, we show that Shoji's local linear Gaussian approximation indeed yields a good MLE.

scholarly journals Latent Class Analysis for Estimating an Unknown Population Size – with Application to Censuses

2021 ◽  
Vol 37 (3) ◽  
pp. 673-697
Author(s):  
Bernard Baffour ◽  
James J. Brown ◽  
Peter W.F. Smith
Keyword(s):  
Latent Class Analysis ◽  
Population Size ◽  
Latent Class ◽  
Population Estimation ◽  
Class Analysis ◽  
Multiple Sources ◽  
Capture Recapture ◽  
Using Data ◽  
Log Linear ◽  
Us Census

Abstract Estimation of the unknown population size using capture-recapture techniques relies on the key assumption that the capture probabilities are homogeneous across individuals in the population. This is usually accomplished via post-stratification by some key covariates believed to influence individual catchability. Another issue that arises in population estimation from data collected from multiple sources is list dependence, where an individual’s catchability on one list is related to that of another list. The earlier models for population estimation heavily relied upon list independence. However, there are methods available that can adjust the population estimates to account for dependence among lists. In this article, we propose the use of latent class analysis through log-linear modelling to estimate the population size in the presence of both heterogeneity and list dependence. The proposed approach is illustrated using data from the 1988 US census dress rehearsal.

scholarly journals Population Size Estimation using Multiple Respondent-Driven Sampling Surveys

2019 ◽  
Author(s):  
Brian J Kim ◽  
Mark S Handcock
Keyword(s):  
Population Size ◽  
Population Size Estimation ◽  
Respondent Driven Sampling ◽  
Size Estimation ◽  
Successive Sampling ◽  
Sampling Process ◽  
National Hiv Behavioral Surveillance ◽  
Statistical Validity ◽  
Capture Recapture ◽  
Hard To Reach Populations

Abstract Respondent-driven sampling (RDS) is commonly used to study hard-to-reach populations since traditional methods are unable to efficiently survey members due to the typically highly stigmatized nature of the population. The number of people in these populations is of primary global health and demographic interest and is usually hard to estimate. However, due to the nature of RDS, current methods of population size estimation are insufficient. We introduce a new method of estimating population size that uses concepts from capture-recapture methods while modeling RDS as a successive sampling process. We assess its statistical validity using information from the CDC’s National HIV Behavioral Surveillance system in 2009 and 2012.

Investigation of Accuracy of a Calibrated Estimator of a Ratio by Modelling

2005 ◽  
Vol 10 (4) ◽  
pp. 333-342
Author(s):  
V. Chadyšas ◽  
D. Krapavickaitė
Keyword(s):  
Mean Square Error ◽  
Taylor Series ◽  
Random Sampling ◽  
Finite Population ◽  
Taylor Series Expansion ◽  
Simple Random Sampling ◽  
Population Parameter ◽  
Mean Square ◽  
Parameter Ratio ◽  
Using Data

Estimator of finite population parameter – ratio of totals of two variables – is investigated by modelling in the case of simple random sampling. Traditional estimator of the ratio is compared with the calibrated estimator of the ratio introduced by Plikusas [1]. The Taylor series expansion of the estimators are used for the expressions of approximate biases and approximate variances [2]. Some estimator of bias is introduced in this paper. Using data of artificial population the accuracy of two estimators of the ratio is compared by modelling. Dependence of the estimates of mean square error of the estimators of the ratio on the correlation coefficient of variables which are used in the numerator and denominator, is also shown in the modelling.

Estimating the population size of people who inject drugs in Ho Chi Minh City, Vietnam: A two-survey capture-recapture exercise (Preprint)

2019 ◽  
Author(s):  
Abu Abdul-Quader
Keyword(s):  
Population Size ◽  
Illicit Drugs ◽  
People Who Inject Drugs ◽  
Care Service ◽  
Ho Chi Minh City ◽  
Size Estimation ◽  
Population Size Estimates ◽  
Capture Recapture ◽  
The City ◽  
Size Estimates

BACKGROUND Population size estimation of people who inject drugs (PWID) in Ho Chi Minh City (HCMC), Vietnam relied on the UNAIDS Estimation and Projection Package and reports from the city police department. The two estimates vary widely. OBJECTIVE To estimate the population size of people who inject drugs in Ho Chi Minh City, Vietnam METHODS Using Respondent-driven sampling (RDS), we implemented two-source capture-recapture method to estimate the population size of PWID in HCMC in 2017 in 7 out of 24 districts. The study included men or women aged at least 18 years who reported injecting illicit drugs in the last 90 days and who had lived in the city the past six months. We calculated two sets of size estimates, the first assumed that all participants in each survey round resided in the district where the survey was conducted, the second, used the district of residence as reported by the participant. District estimates were summed to obtain an aggregate estimate for the seven districts. To calculate the city total, we weighted the population size estimates for each district by the inverse of the stratum specific sampling probabilities. RESULTS The first estimate resulted in a population size of 19,155 (95% CI: 17,006–25,039). The second one generated a smaller population size estimate of 12,867 (95% CI: 11,312–17,393). CONCLUSIONS The two-survey capture-recapture exercise provided two disparate estimates of PWID in HCMC. For planning HIV prevention and care service needs among PWID in HCMC, both estimates may need to be taken into consideration together with size estimates from other sources.

scholarly journals The wildcat Felis silvestris in northern Turkey: assessment of status using camera trapping

Oryx ◽  
2011 ◽  
Vol 45 (1) ◽  
pp. 112-118 ◽  
Author(s):  
Özgün Emre Can ◽  
İrfan Kandemi̇r ◽  
İnci̇ Togan
Keyword(s):  
Population Size ◽  
Camera Traps ◽  
Sampling Effort ◽  
Felis Silvestris ◽  
Forest Patch ◽  
Western Turkey ◽  
Lack Of Information ◽  
The Status ◽  
Capture Recapture ◽  
Estimate Population Size

AbstractThe wildcat Felis silvestris is a protected species in Turkey but the lack of information on its status is an obstacle to conservation initiatives. To assess the status of the species we interviewed local forestry and wildlife personnel and conducted field surveys in selected sites in northern, eastern and western Turkey during 2000–2007. In January–May 2006 we surveyed for the wildcat using 16 passive infrared-trigged camera traps in Yaylacı k Research Forest, a 50-km2 forest patch in Yenice Forest in northern Turkey. A total sampling effort of 1,200 camera trap days over 40 km2 yielded photo-captures of eight individual wildcats over five sampling occasions. Using the software MARK to estimate population size the closed capture–recapture model M0, which assumes a constant capture probability among all occasions and individuals, best fitted the capture history data. The wildcat population size in Yaylacı k Research Forest was estimated to be 11 (confidence interval 9–23). Yenice Forest is probably one of the most important areas for the long-term conservation of the wildcat as it is the largest intact forest habitat in Turkey with little human presence, and without human settlements, and with a high diversity of prey species. However, it has been a major logging area and is not protected. The future of Yenice Forest and its wildcat population could be secured by granting this region a protection status and enforcing environmental legislation.

scholarly journals Estimation of a closed population size of tadpoles in temporary pond

2017 ◽  
Vol 78 (2) ◽  
pp. 328-336
Author(s):  
M. S. C. S. Lima ◽  
J. Pederassi ◽  
C. A. S. Souza
Keyword(s):  
Population Size ◽  
Bayes Theorem ◽  
Venn Diagram ◽  
Temporary Pond ◽  
Larval Phase ◽  
Closed Population ◽  
Lotic Environment ◽  
Capture Recapture ◽  
Kolmogorov Smirnov ◽  
Smirnov Test

Abstract The practice of capture-recapture to estimate the diversity is well known to many animal groups, however this practice in the larval phase of anuran amphibians is incipient. We aimed at evaluating the Lincoln estimator, Venn diagram and Bayes theorem in the inference of population size of a larval phase anurocenose from lotic environment. The adherence of results was evaluated using the Kolmogorov-Smirnov test. The marking of tadpoles for later recapture and methods measurement was made with eosin methylene blue. When comparing the results of Lincoln-Petersen estimator corresponding to the Venn diagram and Bayes theorem, we detected percentage differences per sampling, i.e., the proportion of sampled anuran genera is kept among the three methods, although the values are numerically different. By submitting these results to the Kolmogorov-Smirnov test we have found no significant differences. Therefore, no matter the estimator, the measured value is adherent and estimates the total population. Together with the marking methodology, which did not change the behavior of tadpoles, the present study helps to fill the need of more studies on larval phase of amphibians in Brazil, especially in semi-arid northeast.

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