Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1107.5423

Population size estimation based upon ratios of recapture probabilities

Irene Rocchetti·John Bunge·Dankmar Böhning
View original source ↗Read source document ↗Export metadata ↓

Abstract

Estimating the size of an elusive target population is of prominent interest in many areas in the life and social sciences. Our aim is to provide an efficient and workable method to estimate the unknown population size, given the frequency distribution of counts of repeated identifications of units of the population of interest. This counting variable is necessarily zero-truncated, since units that have never been identified are not in the sample. We consider several applications: clinical medicine, where interest is in estimating patients with adenomatous polyps which have been overlooked by the diagnostic procedure; drug user studies, where interest is in estimating the number of hidden drug users which are not identified; veterinary surveillance of scrapie in the UK, where interest is in estimating the hidden amount of scrapie; and entomology and microbial ecology, where interest is in estimating the number of unobserved species of organisms. In all these examples, simple models such as the homogenous Poisson are not appropriate since they do not account for present and latent heterogeneity. The Poisson-Gamma (negative binomial) model provides a flexible alternative and often leads to well-fitting models. It has a long history and was recently used in the development of the Chao-Bunge estimator. Here we use a different property of the Poisson-Gamma model: if we consider ratios of neighboring Poisson-Gamma probabilities, then these are linearly related to the counts of repeated identifications.

Explore related subjects

stat.AP

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Irene Rocchetti, John Bunge, Dankmar Böhning. 2011-07-27. Population size estimation based upon ratios of recapture probabilities. https://doi.org/10.1214/10-aoas436

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Geospatial Foundation Models Capture Health-Relevant Dimensions of Place Beyond Conventional Social Risk Indices

Area-based social risk indices summarize residents' socioeconomic conditions but incompletely capture physical features of place that may affect health. We evaluated whether numerical representations of physical place produced by four geospatial foundation model families from 2022 satellite data explained residual variance in tract-level associations between the Area Deprivation Index, Social Deprivation Index, and Social Vulnerability Index with health outcomes. We used LightGBM to predict variables from the American Community Survey and 40 chronic disease and health-behavior outcomes from CDC PLACES across 82,646 census tracts in the contiguous United States, evaluating performance across 10 held-out states. Among survey variables, models were moderately predictive of some variables including housing type (R-squared up to 0.54) but weak for disability, unemployment, and income disparity. For health outcomes, models explained up to 54% of variance left unexplained by social risk indices, with the largest gains for annual checkups, arthritis, and high blood pressure. Mean total variance explained by geospatial foundation models across the 40 health-related outcomes increased from 0.31 in the smallest tract-size decile to 0.39 in the largest. Geospatial foundation models capture health-relevant features of place not represented by conventional social risk indices and may usefully augment them in epidemiological analyses.

stat.AP↗
arXiv2026

Transporting summary measures of relative effects from randomised trials to the treated patient population: an application to breast cancer endocrine therapy

Randomised trials often report relative treatment effects, such as risk ratios and hazard ratios, for trial populations. Clinical decision-making, however, often benefits from estimates of absolute treatment effects in the population eligible for treatment. Trial participants may not represent this target population well, and restrictions on access to individual participant trial data can further complicate absolute effect estimation. Routine care data are often representative of the target population but may be subject to uncontrolled confounding. We consider estimation of the average treatment effect on the treated (ATT), an absolute measure, by combining a representative sample of treated routine care patients with summary measures (i.e., estimated risk or hazard ratios) from either a randomised trial or a meta-analysis of trials. Under marginal or conditional transportability assumptions, the ATT is shown to be identifiable. The implications of collapsibility of the effect measure on transportability are discussed, and plug-in estimators of the ATT are presented. Simulation studies are used to assess finite sample performance of the estimators in a range of settings. The proposed methods are applied to estimate the ATT of endocrine therapy on 15-year breast cancer mortality using results from a meta-analysis of randomised trials and England's National Disease Registration Service.

stat.AP↗
arXiv2026

Overcoming Model Misspecification in Bayesian Inference of Molecular Signalling Networks

Bayesian inference of molecular signalling networks usually relies on tractability of the marginal likelihood, enabling the set of possible networks to be efficiently explored. As such, linear models with independent errors and conjugate priors are routinely used. However, the dynamics of molecular signalling are nonlinear, and relevant confounders are often unobserved; failure to account for these complexities will almost certainly lead to over-confident inferences in the standard Bayesian framework. To confront this reality, we develop a post-Bayesian approach to inference of molecular signalling networks, guided by the principle that uncertainty should not vanish when the statistical model is misspecified, even in the infinite-data limit. Technically, we extend the predictively-oriented (PrO) posterior of McLatchie et al. (2025) to the setting of latent variable models, empirically investigating the properties of PrO posteriors in the challenging network inference context.

stat.AP↗