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Abstract：
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.
摘要：
我们提出了一种中高维推理方法，非线性，非高斯，部分观察到的马尔可夫过程模型，其过渡密度在分析上是不可行的。具有难以处理的过渡密度的马尔可夫过程出现在由仿真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，但遭受维数的诅咒。通过集成卡尔曼滤波方法提供了改进的可扩展性，但这些都不适合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际和理论可扩展性。此方法适用于具有分析上难以处理的过渡密度的隐式定义模型。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。在这种方法中，粒子在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进行重采样。我们将此粒子滤波器与参数估计方法相结合，以实现对高度非线性时空系统的基于似然的推理。我们在随机Lorenz96模型和链接区域网络中传染病种群动态模型上展示了我们的方法。
