Optimal Experimental Design for Partially Observable Pure Birth Processes
<|reference_start|>Optimal Experimental Design for Partially Observable Pure Birth Processes: We develop an efficient algorithm to find optimal observation times by maximizing the Fisher information for the birth rate of a partially observable pure birth process involving $n$ observations. Partially observable implies that at each of the $n$ observation time points for counting the number of individuals present in the pure birth process, each individual is observed independently with a fixed probability $p$, modeling detection difficulties or constraints on resources. We apply concepts and techniques from generating functions, using a combination of symbolic and numeric computation, to establish a recursion for evaluating and optimizing the Fisher information. Our numerical results reveal the efficacy of this new method. An implementation of the algorithm is available publicly.<|reference_end|>
@article{eshragh2024optimal,
    title={Optimal Experimental Design for Partially Observable Pure Birth
  Processes},
    author={Ali Eshragh, Matthew P. Skerritt, Bruno Salvy, Thomas McCallum},
    journal={arXiv preprint arXiv:2402.09772},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.09772},
    primaryClass={math.ST cs.NA math.NA stat.TH}
}