Bayesian Population Size Estimation Using Dirichlet Process Mixtures

Manrique-Vallier, Daniel

doi:10.1111/biom.12502

Cited by 57 publications

(87 citation statements)

References 37 publications

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“…As Dunson and Xing (2009) showed, the NPLCM has full support in C. Thus it is consistent for estimating cell probabilities in any contingency table. Additional practical advantages include its computational tractability and scalability, its tolerance to severely sparse contingency tables and its minimal need for tuning by the user (see for example Si and Reiter (2013), Manrique-Vallier and and Manrique-Vallier (2016) for example applications in different domains).…”

Section: Non-parametric Latent Class Models For Categorical Data Syntmentioning

confidence: 99%

Bayesian Non-Parametric Generation Of Fully Synthetic Multivariate Categorical Data in the Presence of Structural Zeros

Manrique-Vallier

2018

Journal of the Royal Statistical Society Series A: Statistics in Society

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Summary Statistical agencies are increasingly adopting synthetic data methods for disseminating microdata without compromising the privacy of respondents. Crucial to the implementation of these approaches are flexible models, able to capture the nuances of the multivariate structure in the original data. In the case of multivariate categorical data, preserving this multivariate structure also often involves satisfying constraints in the form of combinations of responses that cannot logically be present in any data set—like married toddlers or pregnant men—also known as structural zeros. Ignoring structural zeros can result in both logically inconsistent synthetic data and biased estimates. Here we propose the use of a Bayesian non‐parametric method for generating discrete multivariate synthetic data subject to structural zeros. This method can preserve complex multivariate relationships between variables, can be applied to high dimensional data sets with massive collections of structural zeros, requires minimal tuning from the user and is computationally efficient. We demonstrate our approach by synthesizing an extract of 17 variables from the 2000 US census. Our method produces synthetic samples with high analytic utility and low disclosure risk.

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Section: Non-parametric Latent Class Models For Categorical Data Syntmentioning

confidence: 99%

Bayesian Non-Parametric Generation Of Fully Synthetic Multivariate Categorical Data in the Presence of Structural Zeros

Manrique-Vallier

2018

Journal of the Royal Statistical Society Series A: Statistics in Society

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“…Bird and King, 2018). The discussion in this article applies to capture-recapture or multiplesystems estimation models with sufficient statistics that depend only on the inclusion patterns of the different individuals (e.g., Fienberg, 1972;Bishop, Fienberg and Holland, 1975;Castledine, 1981;George and Robert, 1992;Madigan and York, 1997;Fienberg, Johnson and Junker, 1999;Manrique-Vallier, 2016).…”

Section: Population Size Estimationmentioning

confidence: 99%

“…Linkageaveraging for population size estimation can be used with any Bayesian partitioning approach to record linkage and duplicate detection, and any model for population size estimation that depends only on the capture histories' frequencies of the individuals in the lists. We now use the linkage results described in Section 5.2 obtained from the approach of Sadinle (2014), along with the population size methodology of Manrique-Vallier (2016).…”

Section: Graphicalmentioning

confidence: 99%

“…Using transitive closure we obtain an ad-hoc constructed distribution of partitions of the records which we can use to implement an ad-hoc version of the linkageaveraged estimate of N . We then proceeded to compute a linkage-averaged posterior using the models of Madigan and York (1997) and Manrique-Vallier (2016), which lead to posterior means of 15,636 and 14,999, and 99% credible intervals of [6389, 25532] and [5806, 35326], respectively. In this case the ad-hoc mixture model for record linkage leads to similar results as those obtained using the method of Sadinle (2014).…”

Section: Graphicalmentioning

confidence: 99%

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Bayesian propagation of record linkage uncertainty into population size estimation of human rights violations

Sadinle¹

2018

Ann. Appl. Stat.

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Multiple-systems or capture-recapture estimation are common techniques for population size estimation, particularly in the quantitative study of human rights violations. These methods rely on multiple samples from the population, along with the information of which individuals appear in which samples. The goal of record linkage techniques is to identify unique individuals across samples based on the information collected on them. Linkage decisions are subject to uncertainty when such information contains errors and missingness, and when different individuals have very similar characteristics. Uncertainty in the linkage should be propagated into the stage of population size estimation. We propose an approach called linkageaveraging to propagate linkage uncertainty, as quantified by some Bayesian record linkage methodologies, into a subsequent stage of population size estimation. Linkage-averaging is a two-stage approach in which the results from the record linkage stage are fed into the population size estimation stage. We show that under some conditions the results of this approach correspond to those of a proper Bayesian joint model for both record linkage and population size estimation. The two-stage nature of linkage-averaging allows us to combine different record linkage models with different capture-recapture models, which facilitates model exploration. We present a case study from the Salvadoran civil war, where we are interested in estimating the total number of civilian killings using lists of witnesses' reports collected by different organizations. These lists contain duplicates, typographical and spelling errors, missingness, and other inaccuracies that lead to uncertainty in the linkage. We show how linkage-averaging can be used for transferring the uncertainty in the linkage of these lists into different models for population size estimation.

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“…That being said, these models are much more complex and much longer to run than mixed models, and determining the number of clusters can be particularly challenging, especially for traits following a binary distribution (see Hamel et al 2017a for a review of the challenges with mixture modelling). If one is not interested in obtaining cluster-specific parameters to contrast life-history tactics, then one alternative is to use infinite mixture models in a Bayesian framework, which does not require settling the number of clusters (Rasmussen 2000, Manrique-Vallier 2016. Obviously, different methods offer different possibilities for quantifying variance within a population, and the choice will depend on the question addressed and the biological knowledge acquired so far for the trait studied.…”

Section: Mixture Modellingmentioning

confidence: 99%

Quantifying individual heterogeneity and its influence on life‐history trajectories: different methods for different questions and contexts

Hamel

Gaillard

Douhard

et al. 2017

Oikos

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Heterogeneity among individuals influences the life‐history trajectories we observe at the population level because viability selection, selective immigration and emigration processes, and ontogeny change the proportion of individuals with specific trait values with increasing age. Here, we review the two main approaches that have been proposed to account for these processes in life‐history trajectories, contrasting how they quantify ontogeny and selection, and proposing ways to overcome some of their limitations. Nearly all existing approaches to model individual heterogeneity assume either a single normal distribution or a priori known groups of individuals. Ontogenetic processes, however, can vary across individuals through variation in life‐history tactics. We show the usefulness of describing ontogenetic processes by modelling trajectories with a mixture model that focuses on heterogeneity in life‐history tactics. Additionally, most methods examine individual heterogeneity in a single trait, ignoring potential correlations among multiple traits caused by latent common sources of individual heterogeneity. We illustrate the value of using a joint modelling approach to assess the presence of a shared latent correlation and its influence on life‐history trajectories. We contrast the strengths and limitations of different methods for different research questions, and we exemplify the differences among methods using empirical data from long‐term studies of ungulates.

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Bayesian Population Size Estimation Using Dirichlet Process Mixtures

Cited by 57 publications

References 37 publications

Bayesian Non-Parametric Generation Of Fully Synthetic Multivariate Categorical Data in the Presence of Structural Zeros

Bayesian Non-Parametric Generation Of Fully Synthetic Multivariate Categorical Data in the Presence of Structural Zeros

Bayesian propagation of record linkage uncertainty into population size estimation of human rights violations

Quantifying individual heterogeneity and its influence on life‐history trajectories: different methods for different questions and contexts

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