Abstract

In this chapter we describe how iterated filtering methods (Ionides et al., 2006, 2015) can be used to analyze available infectious disease outbreak data in the form of time series. The centerpiece of these methods is the assumption that the outbreak data can be modeled as a noisy and only partially observed realization of a disease transmission process that is assumed to be a Markov process (King et al., 2016). The general inference approach is to (1) formulate a suitable Markovian transmission process, (2) connect the data to the transmission process using some suitable observation process, and (3) use iterated filtering to perform inference for the model parameters. The inference method presented here is likelihood-based. It is designed for models where it is relatively easy to draw samples from the Markov process compared to evaluating its transition probabilities. The iterated filtering algorithm is, among others, implemented in the R package pomp (King et al., 2016), which spans a wide collection of simulation, inference, and model selection methods for partially observed Markov processes (POMP). Other simulation-based inference methods for this model class are simulated moments (Kendall et al., 1999), synthetic likelihood (Wood, 2010), non-linear forecasting (Sugihara and May, 1990) or Bayesian approaches such as approximate Bayesian computations (Toni et al., 2009; Liu and West, 2001), and particle Markov chain Monte Carlo (PMCMC) (Andrieu et al., 2010). However, at present iterated filtering methods are the only currently available, frequentist, full-information, simulation-based inference methods for POMP models (Ionides et al., 2015).