We propose a method for inference on moderately high-dimensional, nonlinear, non-Gaussian, partially observed Markov process models for which the transition density is not analytically tractable. Markov processes with intractable transition densities arise in models defined implicitly by simulation algorithms. Widely used particle filter methods are applicable to nonlinear, non-Gaussian models but suffer from the curse of dimensionality. Improved scalability is provided by ensemble Kalman filter methods, but these are inappropriate for highly nonlinear and non-Gaussian models. We propose a particle filter method having improved practical and theoretical scalability with respect to the model dimension. This method is applicable to implicitly defined models having analytically intractable transition densities. Our method is developed based on the assumption that the latent process is defined in continuous time and that a simulator of this latent process is available. In this method, particles are propagated at intermediate time intervals between observations and are resampled based on a forecast likelihood of future observations. We combine this particle filter with parameter estimation methodology to enable likelihood-based inference for highly nonlinear spatiotemporal systems. We demonstrate our methodology on a stochastic Lorenz 96 model and a model for the population dynamics of infectious diseases in a network of linked regions.

中文翻译：

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使用引导中间重采样滤波器对高维隐式动态模型进行推理

我们提出了一种对中等高维、非线性、非高斯、部分观察的马尔可夫过程模型进行推理的方法，对于该模型，转变密度在分析上是不易处理的。具有棘手转移密度的马尔可夫过程出现在由模拟算法隐式定义的模型中。广泛使用的粒子滤波方法适用于非线性、非高斯模型，但受到维数灾难的影响。集成卡尔曼滤波器方法提供了改进的可扩展性，但这些方法不适用于高度非线性和非高斯模型。我们提出了一种粒子滤波方法，该方法在模型维度方面具有改进的实践和理论可扩展性。该方法适用于具有分析上难以处理的转变密度的隐式定义的模型。我们的方法是基于以下假设开发的：潜在过程是在连续时间内定义的，并且该潜在过程的模拟器是可用的。在此方法中，粒子以观测之间的中间时间间隔传播，并根据未来观测的预测可能性重新采样。我们将此粒子滤波器与参数估计方法相结合，以实现高度非线性时空系统的基于似然的推理。我们在随机 Lorenz 96 模型和链接区域网络中传染病人口动态模型上展示了我们的方法。