btf_bspline0: MCMC Sampler for B-spline Bayesian Trend Filtering: D = 0

In dsp: Dynamic Shrinkage Process and Change Point Detection

MCMC Sampler for B-spline Bayesian Trend Filtering: D = 0

Description

Run the MCMC for B-spline fitting with a penalty the B-spline basis coefficients. The penalty is determined by the prior on the evolution errors, 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 evolution error is a scale mixture of Gaussians. Sampling is accomplished with a (parameter-expanded) Gibbs sampler, mostly relying on a dynamic linear model representation.

Usage

btf_bspline0(
  y,
  times = NULL,
  num_knots = NULL,
  evol_error = "DHS",
  nsave = 1000,
  nburn = 1000,
  nskip = 4,
  mcmc_params = list("mu", "yhat", "beta", "evol_sigma_t2", "obs_sigma_t2", "dhs_phi",
    "dhs_mean"),
  computeDIC = TRUE,
  verbose = TRUE
)

Arguments

y	the T x 1 vector of time series observations
times	the T x 1 vector of observation points; if NULL, assume equally spaced
num_knots	the number of knots; if NULL, use the default of max(20, min(ceiling(T/4), 150))
evol_error	the evolution error distribution; must be one of 'DHS' (dynamic horseshoe prior), 'HS' (horseshoe prior), 'BL' (Bayesian lasso), or 'NIG' (normal-inverse-gamma prior)
nsave	number of MCMC iterations to record
nburn	number of MCMC iterations to discard (burin-in)
nskip	number of MCMC iterations to skip between saving iterations, i.e., save every (nskip + 1)th draw
mcmc_params	named list of parameters for which we store the MCMC output; must be one or more of: "mu" (conditional mean) "beta" (B-spline basis coefficients) "yhat" (posterior predictive distribution) "evol_sigma_t2" (evolution error variance) "obs_sigma_t2" (observation error variance) "dhs_phi" (DHS AR(1) coefficient) "dhs_mean" (DHS AR(1) unconditional mean)
computeDIC	logical; if TRUE, compute the deviance information criterion DIC and the effective number of parameters p_d
verbose	logical; should R report extra information on progress?

Value

A named list of the nsave MCMC samples for the parameters named in mcmc_params

Note

The data y may contain NAs, which will be treated with a simple imputation scheme via an additional Gibbs sampling step. In general, rescaling y to have unit standard deviation is recommended to avoid numerical issues.

The primary advantages of btf_bspline over btf are

1. Unequally-spaced points are handled automatically and

2. Computations are linear in the number of basis coefficients, which may be substantially fewer than the number of time points.

dsp documentation built on Aug. 21, 2025, 5:29 p.m.