Estimation of Poisson‐Dirichlet Parameters with Monotone Missing Data

Zhou, Xueqin; Huang, Jinlong; Wu, X.

doi:10.1155/2017/7892507

Cited by 1 publication

(1 citation statement)

References 18 publications

(26 reference statements)

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“…In the literature, there are a few contributions to methods for learning the PD parameters. Carlton (1999) and Zhou et al (2017) consider MLE for

α

and

θ

separately and jointly, providing (Carlton only) caveats on the consistency of the estimators under some conditions. Sibuya and Yamato (2001), following Carlton, show the suboptimality of MLE and present some alternative estimators.…”

Section: The Two‐parameter Poisson–dirichlet Distributionmentioning

confidence: 99%

Learning the two parameters of the Poisson–Dirichlet distribution with a forensic application

Cereda

Corradi

Viscardi

2022

Scandinavian J Statistics

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In forensic science, the rare type match problem arises when the matching characteristic from the suspect and the crime scene is not in the reference database; hence, it is difficult to evaluate the likelihood ratio that compares the defense and prosecution hypotheses. A recent solution consists of modeling the ordered population probabilities according to the two-parameter Poisson-Dirichlet distribution, which is a well-known Bayesian nonparametric prior, and plugging the maximum likelihood estimates of the parameters into the likelihood ratio. We demonstrate that this approximation produces a systematic bias that fully Bayesian inference avoids. Motivated by this forensic application, we consider the need to learn the posterior distribution of the parameters that governs the two-parameter Poisson-Dirichlet using two sampling methods: Markov Chain Monte Carlo and approximate Bayesian computation. These methods are evaluated in terms of accuracy and efficiency. Finally, we compare the likelihood ratio All authors contributed equally to this work.

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“…In the literature, there are a few contributions to methods for learning the PD parameters. Carlton (1999) and Zhou et al (2017) consider MLE for