Optimal designs minimize the number of experimental runs (samples) needed to accurately estimate model parameters, resulting in algorithms that, for instance, efficiently minimize parameter estimate variance. Governed by knowledge of past observations, adaptive approaches adjust sampling constraints online as model parameter estimates are refined, continually maximizing expected information gained or variance reduced. We apply adaptive Bayesian inference to estimate transition rates of Markov chains, a common class of models for stochastic processes in nature. Unlike most previous studies, our sequential Bayesian optimal design is updated with each observation, and can be simply extended beyond two-state models to birth-death processes and multistate models. By iteratively finding the best time to obtain each sample, our adaptive algorithm maximally reduces variance, resulting in lower overall error in ground truth parameter estimates across a wide range of Markov chain parameterizations and conformations.

翻译：最优设计通过最小化准确估计模型参数所需的实验次数（样本量），从而生成例如高效最小化参数估计方差的算法。基于历史观测信息，自适应方法在模型参数估计逐步精确的过程中动态调整采样约束，持续最大化预期信息增益或方差缩减。我们应用适应性贝叶斯推断来估计马尔可夫链的转移速率——这是自然界随机过程中常见的一类模型。与以往多数研究不同，我们的序贯贝叶斯最优设计会在每次观测后更新，并可简便地从两态模型扩展至生灭过程及多态模型。通过迭代确定获取每个样本的最佳时机，我们的自适应算法最大程度地降低了方差，从而在广泛马尔可夫链参数化与构型下，显著减小了真实参数估计的整体误差。