In many population genetic problems, parameter estimation is obstructed by an intractable likelihood function. Therefore, approximate estimation methods have been developed, and with growing computational power, sampling-based methods became popular. However, these methods such as Approximate Bayesian Computation (ABC) can be inefficient in high-dimensional problems. This led to the development of more sophisticated iterative estimation methods like particle filters. Here, we propose an alternative approach that is based on stochastic approximation. By moving along a simulated gradient or ascent direction, the algorithm produces a sequence of estimates that eventually converges to the maximum likelihood estimate, given a set of observed summary statistics. This strategy does not sample much from low-likelihood regions of the parameter space, and is fast, even when many summary statistics are involved. We put considerable efforts into providing tuning guidelines that improve the robustness and lead to good performance on problems with high-dimensional summary statistics and a low signal-to-noise ratio. We then investigate the performance of our resulting approach and study its properties in simulations. Finally, we re-estimate parameters describing the demographic history of Bornean and Sumatran orang-utans.

中文翻译：

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种群遗传推断的近似最大似然估计

在许多群体遗传问题中，参数估计受到难以处理的似然函数的阻碍。因此，已经开发了近似估计方法，并且随着计算能力的增长，基于采样的方法变得流行。然而，这些方法，如近似贝叶斯计算 (ABC)，在高维问题中可能效率低下。这导致了更复杂的迭代估计方法的发展，如粒子滤波器。在这里，我们提出了一种基于随机近似的替代方法。通过沿模拟梯度或上升方向移动，该算法产生一系列估计，最终收敛到最大似然估计，给定一组观察到的汇总统计数据。该策略不会从参数空间的低似然区域采样太多，并且速度很快，即使涉及许多汇总统计信息。我们付出了相当大的努力来提供调整指南，以提高鲁棒性并在高维汇总统计和低信噪比的问题上取得良好的性能。然后，我们研究我们得到的方法的性能，并在模拟中研究它的特性。最后，我们重新估计了描述婆罗洲和苏门答腊猩猩人口历史的参数。