Approximate Bayesian computation: Estimation by approximate Bayesian computation (ABC)

Description

The approximate Bayesian computation (ABC) algorithm for estimating the parameters of a partially-observed Markov process.

Usage

# S4 method for pomp
abc(object, Nabc = 1, start,
    proposal, probes, scale, epsilon,
    verbose = getOption("verbose"), …)
# S4 method for probed.pomp
abc(object, probes,
    verbose = getOption("verbose"), …)
# S4 method for abc
abc(object, Nabc, start, proposal,
    probes, scale, epsilon,
    verbose = getOption("verbose"), …)
# S4 method for abc
continue(object, Nabc = 1, …)
# S4 method for abc
conv.rec(object, pars, …)
# S4 method for abcList
conv.rec(object, …)
# S4 method for abc
plot(x, y, pars, scatter = FALSE, …)
# S4 method for abcList
plot(x, y, …)

Arguments

object

An object of class pomp.

Nabc

The number of ABC iterations to perform.

start

named numeric vector; the starting guess of the parameters.

proposal

optional function that draws from the proposal distribution. Currently, the proposal distribution must be symmetric for proper inference: it is the user's responsibility to ensure that it is. Several functions that construct appropriate proposal function are provided: see MCMC proposal functions for more information.

probes

List of probes (AKA summary statistics). See probe for details.

scale

named numeric vector of scales.

epsilon

ABC tolerance.

verbose

logical; if TRUE, print progress reports.

pars

Names of parameters.

scatter

optional logical; If TRUE, draw scatterplots. If FALSE, draw traceplots.

abc object.

Ignored.

…

Additional arguments. These are currently ignored.

Running ABC

abc returns an object of class abc. One or more abc objects can be joined to form an abcList object.

Re-running ABC iterations

To re-run a sequence of ABC iterations, one can use the abc method on a abc object. By default, the same parameters used for the original ABC run are re-used (except for tol, max.fail, and verbose, the defaults of which are shown above). If one does specify additional arguments, these will override the defaults.

Continuing ABC iterations

One can continue a series of ABC iterations from where one left off using the continue method. A call to abc to perform Nabc=m iterations followed by a call to continue to perform Nabc=n iterations will produce precisely the same effect as a single call to abc to perform Nabc=m+n iterations. By default, all the algorithmic parameters are the same as used in the original call to abc. Additional arguments will override the defaults.

Methods

Methods that can be used to manipulate, display, or extract information from an abc object:

conv.rec(object, pars): returns the columns of the convergence-record matrix corresponding to the names in pars. By default, all rows are returned.
c: Concatenates abc objects into an abcList.
plot: Diagnostic plots.
covmat(object, start, thin, expand): computes the empirical covariance matrix of the ABC samples beginning with iteration start and thinning by factor thin. It expands this by a factor expand^2/n, where n is the number of parameters estimated. The intention is that the resulting matrix is a suitable input to the proposal function mvn.rw.

References

J.-M. Marin, P. Pudlo, C. P. Robert, and R. J. Ryder, Approximate Bayesian computational methods. Statistics and Compuing 22:1167--1180, 2012.

T. Toni and M. P. H. Stumpf, Simulation-based model selection for dynamical systems in systems and population biology, Bioinformatics 26:104--110, 2010.

T. Toni, D. Welch, N. Strelkowa, A. Ipsen, and M. P. H. Stumpf, Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems Journal of the Royal Society, Interface 6:187--202, 2009.