This repository contains code for general implementations and specific use cases of the PMPMH algorithm in [1]. The PMPMH algorithm uses a hidden Markov model (HMM) approximation to a state-space model (SSM) to provide an efficient proposal distribution for the latent states, allowing Metropolis-Hastings (M-H) sampling of the latent state vector and model parameters.
PMPMH/functions/gen_blocks.R: generates correctly formatted block indices for block updating of the latent states.
PMPMH/functions/gen_HMM.R: for a specified block of states, calculates the discrete HMM approximation to the SSM for a given set of tuning parameters.
PMPMH/functions/gen_proposal.R: samples a sequence of intervals from the HMM approximation and continuous values for the state at each time point from within those intervals.
PMPMH/functions/run_MH.R: runs one iteration of the M-H algorithm's accept/reject step.
PMPMH/implementations/PMPMH_GaussMix_mod1_approach*.R: use case of PMPMH method for fitting Gaussian mixture SSM Model 1 (Model 1 of the first numerical illustration in [1]) under approach * for defining the grid cells.
PMPMH/implementations/PMPMH_GaussMix_mod2_approach*.R: use case of PMPMH method for fitting Gaussian mixture SSM Model 2 (Model 2 of the first numerical illustration in [1]) under approach * for defining the grid cells.
PMPMH/implementation/PMPMH_Nicholsons_approach*.R: use case of the PMPMH method for SSM fitting to data simulated from Nicholson's blowfly model (2-dimensional numerical illustration of [1]) under approach * for defining the grid cells.
PG/*.R: implementations of the particle Gibbs algorithm (both case studies in [1]). Code based on github.com/nchopin/particles.
PGAS/*.R: implementations of the particle Gibbs with Ancestor sampling algorithm (both case studies in [1]). Code based on github.com/nchopin/particles and [2].
Clone repository to preferred installation of R.The PMPMH functions for general one-dimensional SSMs, and two-dimensional SSMs with conditionally updated states, are already included. For the implementation of examples not given in cloned implementation files, follow the implementation files as a template for supplied arguments.
Required packages: (CRAN) invgamma, truncnorm.
CRAN installation:
#install.packages("invgamma")
library(invgamma)
#install.packages("truncnorm")
library(truncnorm)
This code is maintained by Mary Llewellyn ([email protected])
For troubleshooting or comments, please submit an issue or e-mail.
If you find the PMPMH algorithm useful for your research, you can acknowledge by citing [1].
[1] Llewellyn, M., King, R., Elvira, V. et al. A point mass proposal method for Bayesian state-space model fitting. Stat Comput 33, 111 (2023). https://doi.org/10.1007/s11222-023-10268-6
[2] Lindsten, F., Jordan, M. I., and Schön, T. B. (2014). Particle Gibbs with Ancestor Sampling. Journal of Machine Learning Research, 15(63):2145–2184.