Consistency and central limit results for the maximum likelihood estimator in the Admixture Model

IF 1.4 4区生物学 Q4 ECOLOGY

Theoretical Population Biology Pub Date : 2025-12-01 Epub Date: 2025-10-08 DOI:10.1016/j.tpb.2025.10.001

Carola Sophia Heinzel

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引用次数: 0

Abstract

In the Admixture Model, the probability of an individual having a certain number of alleles at a specific marker depends on the allele frequencies in

K

ancestral populations and the fraction of the individual’s genome originating from these ancestral populations.

This study investigates consistency and central limit results of maximum likelihood estimators (MLEs) for the ancestry and the allele frequencies in the Admixture Model, complimenting previous work by Pfaff et al. (2004); Pfaffelhuber and Rohde (2022). Specifically, we prove consistency of the MLE, if we estimate the allele frequencies and the ancestries. Furthermore, we prove central limit theorems, if we estimate the ancestry of a finite number of individuals and the allele frequencies of finitely many markers, also addressing the case where the true ancestry lies on the boundary of the parameter space.

Finally, we use the new theory to quantify the uncertainty of the MLEs for the data of the 1000 Genomes Project.

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混合模型中最大似然估计量的一致性和中心极限结果

在混合模型中，个体在特定标记上具有一定数量等位基因的概率取决于K个祖先群体中的等位基因频率和个体基因组中来自这些祖先群体的部分。本研究调查了混合模型中祖先和等位基因频率的最大似然估计（MLEs）的一致性和中心极限结果，补充了Pfaff等人（2004）的先前工作；Pfaffelhuber and Rohde（2022）。具体来说，如果我们估计等位基因频率和祖先，我们证明了MLE的一致性。此外，我们证明了中心极限定理，如果我们估计有限个个体的祖先和有限个标记的等位基因频率，也解决了真正的祖先位于参数空间边界的情况。最后，我们利用新理论量化了千人基因组计划数据的mle的不确定性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Theoretical Population Biology 生物-进化生物学

CiteScore

2.50

自引率

14.30%

发文量

审稿时长

6-12 weeks

期刊介绍： An interdisciplinary journal, Theoretical Population Biology presents articles on theoretical aspects of the biology of populations, particularly in the areas of demography, ecology, epidemiology, evolution, and genetics. Emphasis is on the development of mathematical theory and models that enhance the understanding of biological phenomena. Articles highlight the motivation and significance of the work for advancing progress in biology, relying on a substantial mathematical effort to obtain biological insight. The journal also presents empirical results and computational and statistical methods directly impinging on theoretical problems in population biology.