Speaker
Description
The Wright-Fisher (W-F) diffusion model is a foundational framework for understanding allele frequency dynamics.
In \cite{roa2024} an exact analytical expression for the transition density strictly within the open interval (0, 1) is derived for the W-F model without mutation.
In this work, we introduce mutation, changing the nature of the barriers 0 and 1 from absorbing states to a reflecting barrier.
The proposed analytical expressions provide a rigorous foundation for parametric inference in population genetics than standard flexible distributions.
This study is consistent with the research conducted by Paul Jenkins and Dario Spano in their seminar papers \cite{jenkins} and \cite{Jenkins2015ExactSO}
Bibliography
@misc{roa2024,
title={Small-time approximation of the transition density for diffusions with singularities. Application to the Wright-Fisher model},
author={Tania Roa and María Inés Fariello and Gerardo Martínez and José León},
year={2024},
eprint={2212.11442},
archivePrefix={arXiv},
primaryClass={stat.ME},
url={https://arxiv.org/abs/2212.11442},
}
@article{jenkins,
author = {Sant, Jaromir and A. Jenkins, Paul and Koskela, Jere and Spanò, Dario},
title = {Convergence of likelihood ratios and estimators for selection in nonneutral Wright–Fisher diffusions},
journal = {Scandinavian Journal of Statistics},
volume = {49},
number = {4},
pages = {1728-1760},
keywords = {asymptotic theory, inference for diffusions, selection, Wright–Fisher diffusion},
doi = {https://doi.org/10.1111/sjos.12572},
url = {https://onlinelibrary.wiley.com/doi/abs/10.1111/sjos.12572},
eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1111/sjos.12572},
abstract = {Abstract A number of discrete time, finite population size models in genetics describing the dynamics of allele frequencies are known to converge (subject to suitable scaling) to a diffusion process termed the Wright–Fisher diffusion. This diffusion evolves on a bounded interval, such that many standard results in diffusion theory, assuming evolution on the real line, no longer apply. In this article we derive conditions to establish ϑ-uniform ergodicity for diffusions on bounded intervals, and use them to prove that the Wright–Fisher diffusion is uniformly in the selection and mutation parameters ergodic, and that the measures induced by the solution to the stochastic differential equation are uniformly locally asymptotically normal. We subsequently use these results to show that the maximum likelihood and Bayesian estimators for the selection parameter are uniformly over compact sets consistent, asymptotically normal, display moment convergence, and are asymptotically efficient for a suitable class of loss functions.},
year = {2022}
}
@article{Jenkins2015ExactSO,
title={Exact simulation of the Wright-Fisher diffusion},
author={Paul A. Jenkins and Dario Span{`o}},
journal={arXiv: Methodology},
year={2015},
url={https://api.semanticscholar.org/CorpusID:293028}
}
