title: Comparison of the performance of particle filter algorithms applied to tracking of a disease epidemic.
abstract: 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.
authors.affiliation: Department of Statistics and Applied Probability, University of California, Santa Barbara, CA 93106, USA. Electronic address: sheinson@pstat.ucsb.edu.
authors.forename: Daniel M
authors.initials: DM
authors.lastname: Sheinson
authors.affiliation: Department of Statistics, Iowa State University, Ames, IA 50011, USA. Electronic address: niemi@iastate.edu.
authors.forename: Jarad
authors.initials: J
authors.lastname: Niemi
authors.affiliation: Department of Statistics and Applied Probability, University of California, Santa Barbara, CA 93106, USA. Electronic address: meiring@pstat.ucsb.edu.
authors.forename: Wendy
authors.initials: W
authors.lastname: Meiring
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D058872:Epidemics / Q000706:statistics & numerical data*; D006801:Humans; D008390:Markov Chains; D055641:Mathematical Concepts; D009010:Monte Carlo Method; D017711:Nonlinear Dynamics; D013269:Stochastic Processes
keywords: Bayesian estimation; Epidemiological modeling; Particle filtering; Sequential Monte Carlo; State-space modeling