Fast Iterated Filtering

Background: Partially observed Markov process (POMP) models are ubiquitous tools for modeling time series data in many sciences including econometrics, engineering and ecology. However, inference on POMP models is not routine, except for some restricted classes of models. This poster relaxes the constraints by dealing with general POMP models which are nonlinear, non-Gaussian and weakly identifiable. Methods: This poster introduces a novel filter, called fast iterated filtering (FIF), by unifying two state of the art inference algorithms, namely iterated filtering (IF) and data cloning (DC). IF is a simulation-based approach where the state, represented as particles, is iteratively filtered by observations. DC exploits advances of Markov Chain Monte Carlo methodology to achieve maximum likelihood estimators (MLE). Two properties make our proposed approach effective: statistical and computational efficiency. Motivated by the advantages of working with a smooth likelihood surface to tackle multi-modality issues of DC, we sequentially add noise to each state. At first glance, it may seem counter intuitive but noise will be canceled out in the long run through filtering while statistical efficiency can be reached asymptotically. Secondly, computational complexity and its side effect of sample depletion is well known in the particle filter literature. A natural solution is sampling parameter space efficiently. In FIF, we iteratively filter the state processes using the same set of observations. The likelihood is equivalently raised to the power of the number of iterations, the mode of the likelihood is peak near MLE so the particle will be sampled more efficiently in the high dimensional state space model. Results: The algorithm is implemented in an open source R packages called pomp. Due to the built-in properties, any algorithm implemented in pomp is readily available while other algorithms can be easily incorporated for comparison with FIF. We choose IF for comparison as it is a well-proven method for the class of models. The results evaluated over a toy and a large real world data set, indicate the faster convergence rate of our approach compared to IF. In particular, for a Gompertz model, FIF from a random starting point obtained likelihoods 12 log units higher, on average, than IF. In practice, this means that convergence rate toward MLE is much faster. The novel algorithm is even more appealing in the case of hard problems where unidentifiable parameters are present, for example in a Plasmodium vivax malaria transmission model. In this case, 94.5% of the results calculated by FIF are better than IF. In addition, FIF is about 16% faster in average computational time in both cases. Conclusion: Combining two state of the art approaches in FIF has led to many advances including the statistical and computational efficiency. The main contribution of our work is that under weak assumptions, we show the algorithm converges asymptotically in theory and demonstrate that the convergence rate is very impressive in practice.