Bayesian sequential Monte Carlo: The Liu and West Bayesian particle filter

Description

Modified versions of the Liu and West (2001) algorithm.

Usage

"bsmc2"(object, params, Np, est, smooth = 0.1, tol = 1e-17, verbose = getOption("verbose"), max.fail = 0, transform = FALSE, ...)
"bsmc"(object, params, Np, est, smooth = 0.1, ntries = 1, tol = 1e-17, lower = -Inf, upper = Inf, verbose = getOption("verbose"), max.fail = 0, transform = FALSE, ...)

Arguments

object

An object of class pomp or inheriting class pomp.

params, Np

Specifications for the prior distribution of particles. See details below.

est

Names of the rows of params that are to be estimated. No updates will be made to the other parameters. If est is not specified, all parameters for which there is variation in params will be estimated.

smooth

Kernel density smoothing parameters. The compensating shrinkage factor will be sqrt(1-smooth^2). Thus, smooth=0 means that no noise will be added to parameters. Generally, the value of smooth should be chosen close to 0 (i.e., shrink~0.1).

ntries

Number of draws from rprocess per particle used to estimate the expected value of the state process at time t+1 given the state and parameters at time t.

tol

Particles with log likelihood below tol are considered to be “lost”. A filtering failure occurs when, at some time point, all particles are lost. When all particles are lost, the conditional log likelihood at that time point is set to be log(tol).

lower, upper

optional; lower and upper bounds on the priors. This is useful in case there are box constraints satisfied by the priors. The posterior is guaranteed to lie within these bounds.

verbose

logical; if TRUE, print diagnostic messages.

max.fail

The maximum number of filtering failures allowed. If the number of filtering failures exceeds this number, execution will terminate with an error.

transform

logical; if TRUE, the algorithm operates on the transformed scale.

...

currently ignored.

Value

post: A matrix containing draws from the approximate posterior distribution.
prior: A matrix containing draws from the prior distribution (identical to params on call).
eff.sample.size: A vector containing the effective number of particles at each time point.
smooth: The smoothing parameter used (see above).
nfail: The number of filtering failures encountered.
cond.log.evidence: A vector containing the conditional log evidence scores at each time point.
log.evidence: The estimated log evidence.
weights: The resampling weights for each particle.

Details

There are two ways to specify the prior distribution of particles. If params is unspecified or is a named vector, Np draws are made from the prior distribution, as specified by rprior. Alternatively, params can be specified as an npars x Np matrix (with rownames).

bsmc uses version of the original algorithm that includes a plug-and-play auxiliary particle filter. bsmc2 discards this auxiliary particle filter and appears to give superior performance for the same amount of effort.

References