sampleBTF_sparse: Sampler for first or second order random walk (RW) Gaussian...

In drkowal/dsp: Dynamic Shrinkage Processes

Sampler for first or second order random walk (RW) Gaussian dynamic linear model (DLM) with additional shrinkage to zero

Description

Compute one draw of the T x 1 state variable mu in a DLM using back-band substitution methods. This model is equivalent to the Bayesian trend filtering (BTF) model, assuming appropriate (shrinkage/sparsity) priors for the evolution errors, with an additional shrinkage-to-zero prior.

Usage

sampleBTF_sparse(
  y,
  obs_sigma_t2,
  evol_sigma_t2,
  zero_sigma_t2,
  D = 1,
  chol0 = NULL
)

Arguments

y	the T x 1 vector of time series observations
obs_sigma_t2	the T x 1 vector of observation error variances
evol_sigma_t2	the T x 1 vector of evolution error variances
zero_sigma_t2	the T x 1 vector of shrink-to-zero variances
D	the degree of differencing (one or two)
chol0	(optional) the m x m matrix of initial Cholesky factorization; if NULL, use the Matrix package for sampling, otherwise use the spam package

Value

T x 1 vector of simulated states

Note

Missing entries (NAs) are not permitted in y. Imputation schemes are available.

Examples

# Simulate some data:
T = 1000
y = seq(0, 10, length.out = T) + rnorm(T)
plot(y) # plot the data

obs_sigma_t2 = rep(1, T)  # These could be static or dynamic
evol_sigma_t2 = rep(0.001, T)
zero_sigma_t2 = rep(1, T)

# Simulate one draw of the states:
mu = sampleBTF_sparse(y = y, obs_sigma_t2, evol_sigma_t2, zero_sigma_t2, D = 1)
lines(mu, lwd=8, col='blue') # add the states to the plot

drkowal/dsp documentation built on July 19, 2023, 11:42 a.m.