SMC.Smooth: Generic Sequential Monte Carlo Smoothing with Marginal Weights

Description

Generic sequential Monte Carlo smoothing with marginal weights.

SMC.Smooth(
  SISstep,
  SISstep.Smooth,
  nobs,
  yy,
  mm,
  par,
  xx.init,
  xdim,
  ydim,
  resample.sch,
  funH = identity
)

The function returns the smoothed values.

SISstep: a function that performs one propagation step using a proposal distribution. Its input includes (mm,xx,logww,yyy,par,xdim,ydim), where xx and logww are the last iteration samples and log weight. yyy is the observation at current time step. It should return xx (the samples xt) and logww (their corresponding log weight).
SISstep.Smooth: the function for backward smoothing step.
nobs: the number of observations T.
yy: the observations with T columns and ydim rows.
mm: the Monte Carlo sample size m.
par: a list of parameter values.
xx.init: the initial samples of x_0.
xdim: the dimension of the state variable x_t.
ydim: the dimension of the observation y_t.
resample.sch: a binary vector of length nobs, reflecting the resampling schedule. resample.sch[i]= 1 indicating resample should be carried out at step i.
funH: a user supplied function h() for estimation E(h(x_t) | y_1,...,y_T). Default is identity for estimating the mean. The function should be able to take vector or matrix as input and operates on each element of the input.

Tsay, R. and Chen, R. (2018). Nonlinear Time Series Analysis. John Wiley & Sons, New Jersey.