Particle Metropolis Hastings using gradient and Hessian information

This code reproduces the comparison between the three algorithms considered in the publications [J18], [C70] and [C60]. Three examples of parameter inference are included;

  • Linear Gaussian state space model (using bootstrap particle filtering with the filter smoother for estimating the Hessian).
  • Linear Gaussian state space model (using fully-adapted particle filtering with the fixed-lag smoother for estimating the Hessian).
  • Hull-White stochastic volatility model (using bootstrap particle filtering with the filter smoother for estimating the Hessian).

Python code

This code is written by Johan Dahlin and it is available here, see also Johan’s software page.

Relevant papers

All the details are available in this paper,

Johan Dahlin, Fredrik Lindsten and Thomas B. Schön. Particle Metropolis Hastings using gradient and Hessian informationStatistics and Computing, 2014. (accepted for publication). [arXiv]

Earlier papers include,

[C70] Johan Dahlin, Fredrik Lindsten and Thomas B. Schön. Second-order Particle MCMC for Bayesian parameter inference, in Proceedings of the 18th World Congress of the International Federation of Automatic Control (IFAC), Cape Town, South Africa, August 2014. [pdf]

[C60] Johan Dahlin, Fredrik Lindsten and Thomas B. Schön. Particle Metropolis Hastings using Langevin dynamics, in Proceedings of the 38th International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Vancouver, Canada, May 2013. [pdf]

 © Thomas Schön 2022