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Sufficient statistics are derived for the population size and parameters of commonly used closed population mark-recapture models. Rao-Blackwellization details for improving estimators that are not functions of the statistics are presented. As Rao-Blackwellization entails enumerating all sample reorderings consistent with the sufficient statistic, Markov chain Monte Carlo resampling procedures are provided to approximate the computationally intensive estimators. Simulation studies demonstrate that significant improvements can be made with the strategy. Supplementary materials for this article are available online.
Rao-Blackwellization is a notion often occurring in the MCMC literature, with possibly different meanings and connections with the original Rao--Blackwell theorem (Rao, 1945 and Blackwell,1947), including a reduction of the variance of the resulting
We investigate a Poisson sampling design in the presence of unknown selection probabilities when applied to a population of unknown size for multiple sampling occasions. The fixed-population model is adopted and extended upon for inference. The compl
In microbiome studies, one of the ways of studying bacterial abundances is to estimate bacterial composition based on the sequencing read counts. Various transformations are then applied to such compositional data for downstream statistical analysis,
When drawing causal inference from observational data, there is always concern about unmeasured confounding. One way to tackle this is to conduct a sensitivity analysis. One widely-used sensitivity analysis framework hypothesizes the existence of a s
We propose a method to test for the presence of differential ascertainment in case-control studies, when data are collected by multiple sources. We show that, when differential ascertainment is present, the use of only the observed cases leads to sev