Sheinson Daniel M, Niemi Jarad, Meiring Wendy
Department of Statistics and Applied Probability, University of California, Santa Barbara, CA 93106, USA.
Department of Statistics, Iowa State University, Ames, IA 50011, USA.
Math Biosci. 2014 Sep;255:21-32. doi: 10.1016/j.mbs.2014.06.018. Epub 2014 Jul 9.
We present general methodology for sequential inference in nonlinear stochastic state-space models to simultaneously estimate dynamic states and fixed parameters. We show that basic particle filters may fail due to degeneracy in fixed parameter estimation and suggest the use of a kernel density approximation to the filtered distribution of the fixed parameters to allow the fixed parameters to regenerate. In addition, we show that "seemingly" uninformative uniform priors on fixed parameters can affect posterior inferences and suggest the use of priors bounded only by the support of the parameter. We show the negative impact of using multinomial resampling and suggest the use of either stratified or residual resampling within the particle filter. As a motivating example, we use a model for tracking and prediction of a disease outbreak via a syndromic surveillance system. Finally, we use this improved particle filtering methodology to relax prior assumptions on model parameters yet still provide reasonable estimates for model parameters and disease states.
我们提出了用于非线性随机状态空间模型中序贯推断的通用方法，以同时估计动态状态和固定参数。我们表明，基本粒子滤波器可能会因固定参数估计中的退化而失效，并建议对固定参数的滤波分布使用核密度近似，以使固定参数能够再生。此外，我们表明固定参数上“看似”无信息的均匀先验会影响后验推断，并建议使用仅由参数支持界定的先验。我们展示了使用多项式重采样的负面影响，并建议在粒子滤波器中使用分层或残差重采样。作为一个激励示例，我们使用一个通过症状监测系统跟踪和预测疾病爆发的模型。最后，我们使用这种改进的粒子滤波方法来放宽对模型参数的先验假设，但仍为模型参数和疾病状态提供合理估计。
