{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/estimating-individual-admixture-from-finite","title":"A central limit theorem concerning uncertainty in estimates of individual admixture","arxiv_id":"2110.08348","date":"2021-10-15","proceeding":null,"authors":["Peter Pfaffelhuber","Angelika Rohde"],"abstract":"The concept of individual admixture (IA) assumes that the genome of individuals is composed of alleles inherited from $K$ ancestral populations. Each copy of each allele has the same chance $q_k$ to originate from population $k$, and together with the allele frequencies $p$ in all populations at all $M$ markers, comprises the admixture model. Here, we assume a supervised scheme, i.e.\\ allele frequencies $p$ are given through a reference database of size $N$, and $q$ is estimated via maximum likelihood for a single sample. We study laws of large numbers and central limit theorems describing effects of finiteness of both, $M$ and $N$, on the estimate of $q$. We recall results for the effect of finite $M$, and provide a central limit theorem for the effect of finite $N$, introduce a new way to express the uncertainty in estimates in standard barplots, give simulation results, and discuss applications in forensic genetics.","url_abs":"https://arxiv.org/abs/2110.08348v2","url_pdf":"https://arxiv.org/pdf/2110.08348v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"estimating-individual-admixture-from-finite","repo_url":"https://github.com/pfaffelh/mninfty","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}