Particle Markov chain Monte Carlo (PMCMC) algorithm

Usage

pmcmc(
  model,
  obs_process,
  data,
  priors,
  n_particles,
  n_iterations,
  theta = NULL,
  covmat = NULL,
  adaptmix = 0.05,
  adaptive = 100,
  post_proposal = NULL,
  init_model = NULL,
  post_particle = NULL,
  chain = NULL,
  verbose = getOption("verbose", FALSE)
)

# S4 method for class 'SimInf_model'
pmcmc(
  model,
  obs_process,
  data,
  priors,
  n_particles,
  n_iterations,
  theta = NULL,
  covmat = NULL,
  adaptmix = 0.05,
  adaptive = 100,
  post_proposal = NULL,
  init_model = NULL,
  post_particle = NULL,
  chain = NULL,
  verbose = getOption("verbose", FALSE)
)

Arguments

model: The model to simulate data from.
obs_process: Specification of the stochastic observation process. The obs_process can be specified as a formula if the model contains only one node and there is only one data point for each time in data. The left hand side of the formula must match a column name in the data data.frame and the right hand side of the formula is a character specifying the distribution of the observation process, for example, Iobs ~ poisson(I). The following distributions are supported: x ~ binomial(size, prob), x ~ poisson(rate) and x ~ uniform(min, max). The observation process can also be a function to evaluate the probability density of the observations given the simulated states. The first argument passed to the obs_process function is the result from a run of the model and it contains one trajectory with simulated data for a time-point, where the trajectory contains n_particles replicates, see trajectory,SimInf_model-method. The second argument to the obs_process function is a data.frame containing the rows for the specific time-point that the function is called for. Note that the function must return the log of the density.
data: A data.frame holding the time series data.
priors: The priors for the parameters to fit. Each prior is specified with a formula notation, for example, beta ~ uniform(0, 1) specifies that beta is uniformly distributed between 0 and 1. Use c() to provide more than one prior, for example, c(beta ~ uniform(0, 1), gamma ~ normal(10, 1)). The following distributions are supported: gamma, lognormal, normal and uniform. All parameters in priors must be only in either gdata or ldata.
n_particles: An integer with the number of particles (> 1) to use at each timestep.
n_iterations: An integer specifying the number of iterations to run the PMCMC.
theta: A named vector of initial values for the parameters of the model. Default is NULL, and then these are sampled from the prior distribution(s).
covmat: A named numeric (npars x npars) matrix with covariances to use as initial proposal matrix. If left unspecified then defaults to diag((theta/10)^2/npars).
adaptmix: Mixing proportion for adaptive proposal. Must be a value between zero and one. Default is adaptmix = 0.05.
adaptive: Controls when to start adaptive update. Must be greater or equal to zero. If adaptive=0, then adaptive update is not performed. Default is adaptive = 100.
post_proposal: An optional function that, if non-NULL, is applied on the model after the proposal has been set for the model, but before running the particle filter. The function must accept one argument of type SimInf_model with the current model of the fitting process. This function can be useful to update, for example, ldata of the model before running a trajectory with proposed parameters. The function must return the model object which is then used in the particle filter.
init_model: An optional function that, if non-NULL, is applied in the particle filter before running each proposal. The function must accept one argument of type SimInf_model with the current model of the fitting process. This function can be useful to specify the initial state of u0 or v0 of the model before running a trajectory with proposed parameters.
post_particle: An optional function that, if non-NULL, is applied after each completed particle. The function must accept three arguments: 1) an object of SimInf_pmcmc with the current state of the fitting process, 2) an object SimInf_pfilter with the last particle and one filtered trajectory attached, and 3) an integer with the iteration in the fitting process. This function can be useful to, for example, monitor, save and inspect intermediate results. Note that the second SimInf_pfilter argument, is non-NULL only for the first particle in the chain, and for accepted particles.
chain: An optional chain to start from. Must be a data.frame or an object that can be coerced to a data.frame. Only the columns in chain with a name that matches the names that will be used if this argument is not provided will be used. When this argument is provided, n_iterations can be 0. Additionally, when the chain argument is provided, then theta and covmat must be NULL.
verbose: prints diagnostic messages when TRUE. The default is to retrieve the global option verbose and use FALSE if it is not set. When verbose=TRUE, information is printed every 100 iterations. For pmcmc, it is possible to get information every nth information by specifying verbose=n, for example, verbose=1 or verbose=10.

References

C. Andrieu, A. Doucet and R. Holenstein. Particle Markov chain Monte Carlo methods. Journal of the Royal Statistical Society, Series B 72, 269–342, 2010. doi:10.1111/j.1467-9868.2009.00736.x

G. O. Roberts and J. S. Rosenthal. Examples of adaptive MCMC. Journal of computational and graphical statistics, 18(2), 349–367, 2009. doi:10.1198/jcgs.2009.06134

Particle Markov chain Monte Carlo (PMCMC) algorithm

Usage

Arguments

References

See also