Introduction

GenericSSMs.jl is a Julia package that provides building blocks for conducting statistical inference of state-space models (SSMs) using particle filters. The package is designed to be small and modular, attempting to provide sensible and reasonably fast, non-allocating primitives for writing particle filtering algorithms.

GenericSSMs.jl assumes that the user is somewhat familiar with state-space models and their Feynman-Kac representations. This documentation provides a very short introduction to these topics. The references therein can be used to find more information.

The main features of GenericSSMs.jl are:

• an interface for defining an SSM using a Feynman-Kac representation that may depend on arbitrary data and parameters (a "generic SSM")
• particle filtering & conditional particle filtering [Andrieu, Doucet, Holenstein (2010)] for generic SSMs
• tracebacking strategies for the conditional particle filter:
  • ancestor tracing [Andrieu, Doucet, Holenstein (2010)]
  • backward sampling [Whiteley (2010)]
• unconditional simulation from generic SSMs at state and/or observation level
• prediction from generic SSMs at state and/or observation level
• a generic resampling API for user-defined resampling algorithms
  • default resampling algorithms are provided via Resamplings.jl

References

• Andrieu, C., Doucet, A., and Holenstein, R. (2010) Particle Markov chain Monte Carlo methods. Journal of the Royal Statistical Society: Series B. 72(3):269-342.
• Whiteley, N. (2010) Discussion on "Particle Markov chain Monte Carlo methods". Journal of the Royal Statistical Society: Series B. 72(3):306-307.