Sparse Bayesian trend filtering has two penalties: (1) a penalty on the first (D = 1) or second (D = 2) differences of the conditional expectation and (2) a penalty on the conditional expectation, i.e., shrinkage to zero.
btf_sparse(
y,
evol_error = "DHS",
zero_error = "DHS",
D = 2,
obsSV = "const",
nsave = 1000,
nburn = 1000,
nskip = 4,
mcmc_params = list("mu", "yhat", "evol_sigma_t2", "obs_sigma_t2", "zero_sigma_t2",
"dhs_phi", "dhs_mean", "dhs_phi_zero", "dhs_mean_zero", "h", "h_smooth"),
computeDIC = TRUE,
verbose = TRUE,
D_asv = 1,
evol_error_asv = "HS",
nugget_asv = TRUE
)A named list of the nsave MCMC samples for the parameters named in mcmc_params
the T x 1 vector of time series observations
the evolution error distribution; must be one of 'DHS' (dynamic horseshoe prior), 'HS' (horseshoe prior), 'BL' (Bayesian lasso), or 'NIG' (normal-inverse-gamma prior)
the shrinkage-to-zero distribution; must be one of 'DHS' (dynamic horseshoe prior), 'HS' (horseshoe prior), 'BL' (Bayesian lasso), or 'NIG' (normal-inverse-gamma prior)
degree of differencing (D = 1, or D = 2)
Options for modeling the error variance. It must be one of the following:
const: Constant error variance for all time points.
SV: Stochastic Volatility model.
ASV: Adaptive Stochastic Volatility model.
number of MCMC iterations to record
number of MCMC iterations to discard (burnin-in)
number of MCMC iterations to skip between saving iterations, i.e., save every (nskip + 1)th draw
named list of parameters for which we store the MCMC output; must be one or more of:
"mu" (conditional mean)
"yhat" (posterior predictive distribution)
"evol_sigma_t2" (evolution error variance)
"zero_sigma_t2" (shrink-to-zero error variance)
"obs_sigma_t2" (observation error variance)
"dhs_phi" (DHS AR(1) coefficient for evolution error)
"dhs_mean" (DHS AR(1) unconditional mean for evolution error)
"dhs_phi_zero" (DHS AR(1) coefficient for shrink-to-zero error)
"dhs_mean_zero" (DHS AR(1) unconditional mean for shrink-to-zero error)
"h" (log variances or log of "obs_sigma_t2". Only used when obsSV = "ASV")
"h_smooth" (smooth estimate of log variances. Only used when obsSV = "ASV" and nugget_asv = TRUE)
logical; if TRUE, compute the deviance information criterion DIC
and the effective number of parameters p_d
logical; should R report extra information on progress?
integer; degree of differencing (0, 1, or 2) for the ASV model. Only used when obsSV = "ASV".
character; evolution error distribution for the ASV model. Must be one of the five options used in evol_error. Only used when obsSV = "ASV".
logical; if TRUE, fits the nugget variant of the ASV model. Only used when obsSV = "ASV".
Each penalty is determined by a prior, which include:
the dynamic horseshoe prior ('DHS');
the static horseshoe prior ('HS');
the Bayesian lasso ('BL');
the normal stochastic volatility model ('SV');
the normal-inverse-gamma prior ('NIG').
In each case, the prior is a scale mixture of Gaussians. Sampling is accomplished with a (parameter-expanded) Gibbs sampler, mostly relying on a dynamic linear model representation.