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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2309.05998 |
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| _version_ | 1866914837032861696 |
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| author | Igelbrink, Jan Lukas Ischebeck, Jasper |
| author_facet | Igelbrink, Jan Lukas Ischebeck, Jasper |
| contents | Cheek and Johnston (Journal of Mathematical Biology, 2023) consider a continuous-time Bienaymé-Galton-Watson tree conditioned on being alive at time $T$. They study the reproduction events along the ancestral lineage of an individual randomly sampled from all those alive at time $T$. We give a short proof of an extension of their main results to the more general case of Bellman-Harris processes. Our proof also sheds light onto the probabilistic structure of the rate of the reproduction events. A similar method will be applied to explain (i) the different ancestral reproduction bias appearing in work by Geiger (Journal of Applied Probability, 1999) and (ii) the fact that the sampling rule considered by Chauvin, Rouault and Wakolbinger (Stochastic Processes and their Applications, 1991) leads to a time homogeneous process along the ancestral lineage. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_05998 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Ancestral reproductive bias in continuous time branching trees under various sampling schemes Igelbrink, Jan Lukas Ischebeck, Jasper Probability Primary 60J80, secondary 60K05, 92D10 Cheek and Johnston (Journal of Mathematical Biology, 2023) consider a continuous-time Bienaymé-Galton-Watson tree conditioned on being alive at time $T$. They study the reproduction events along the ancestral lineage of an individual randomly sampled from all those alive at time $T$. We give a short proof of an extension of their main results to the more general case of Bellman-Harris processes. Our proof also sheds light onto the probabilistic structure of the rate of the reproduction events. A similar method will be applied to explain (i) the different ancestral reproduction bias appearing in work by Geiger (Journal of Applied Probability, 1999) and (ii) the fact that the sampling rule considered by Chauvin, Rouault and Wakolbinger (Stochastic Processes and their Applications, 1991) leads to a time homogeneous process along the ancestral lineage. |
| title | Ancestral reproductive bias in continuous time branching trees under various sampling schemes |
| topic | Probability Primary 60J80, secondary 60K05, 92D10 |
| url | https://arxiv.org/abs/2309.05998 |