We consider the problem of inference for the states and parameters of a continuous-time multitype branching process from partially observed time series data. Exact inference for this class of models, typically using sequential Monte Carlo, can be computationally challenging when the populations that are being modelled grow exponentially or the time series is long. Instead, we derive a Gaussian approximation for the transition function of the process that leads to a Kalman filtering algorithm that runs in a time independent of the population sizes. We also develop a hybrid approach for when populations are smaller and the approximation is less applicable. We investigate the performance of our approximation and algorithms to both a simple and a complex epidemic model, finding good adherence to the true posterior distributions in both cases with large computational speed-ups in most cases. We also apply our method to a COVID-19 dataset with time dependent parameters where exact methods are intractable due to the population sizes involved.

翻译：我们考虑基于部分观测时间序列数据对连续时间多类型分支过程的状态与参数进行推断的问题。对此类模型进行精确推断（通常采用序贯蒙特卡罗方法）在模拟种群呈指数增长或时间序列较长时可能面临计算挑战。为此，我们推导了该过程转移函数的高斯近似，从而得到一种运行时间与种群规模无关的卡尔曼滤波算法。针对种群规模较小、近似适用性较低的情况，我们还开发了混合方法。通过简单与复杂流行病模型的双重验证，我们评估了所提近似方法与算法的性能：在多数情况下，两种模型均能良好贴合真实后验分布，且计算速度显著提升。最后，我们将该方法应用于具有时变参数的COVID-19数据集，在该场景中，由于涉及大规模种群，精确推断方法难以实现。