btf_reg: MCMC Sampler for Bayesian Trend Filtering: Regression

In drkowal/dsp: Dynamic Shrinkage Processes

MCMC Sampler for Bayesian Trend Filtering: Regression

Description

Run the MCMC for Bayesian trend filtering regression with a penalty on first (D=1) or second (D=2) differences of each dynamic regression coefficient. 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_reg(
  y,
  X = NULL,
  evol_error = "DHS",
  D = 1,
  useObsSV = FALSE,
  nsave = 1000,
  nburn = 1000,
  nskip = 4,
  mcmc_params = list("mu", "yhat", "beta", "evol_sigma_t2", "obs_sigma_t2", "dhs_phi",
    "dhs_mean"),
  use_backfitting = FALSE,
  computeDIC = TRUE,
  verbose = TRUE
)

Arguments

y	the T x 1 vector of time series observations
X	the T x p matrix of time series predictors
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)
D	degree of differencing (D = 1 or D = 2)
useObsSV	logical; if TRUE, include a (normal) stochastic volatility model for the observation error variance
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) "yhat" (posterior predictive distribution) "beta" (dynamic regression coefficients) "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)
use_backfitting	logical; if TRUE, use backfitting to sample the predictors j=1,...,p (faster, but usually less MCMC efficient)
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.

Examples

# Example 1: all signals
simdata = simRegression(T = 200, p = 5, p_0 = 0)
y = simdata$y; X = simdata$X
out = btf_reg(y, X)
for(j in 1:ncol(X))
 plot_fitted(rep(0, length(y)),
             mu = colMeans(out$beta[,,j]),
             postY = out$beta[,,j],
             y_true = simdata$beta_true[,j])

## Not run: 
# Example 2: some noise, longer series
simdata = simRegression(T = 500, p = 10, p_0 = 5)
y = simdata$y; X = simdata$X
out = btf_reg(y, X, nsave = 1000, nskip = 0) # Short MCMC run for a quick example
for(j in 1:ncol(X))
  plot_fitted(rep(0, length(y)),
              mu = colMeans(out$beta[,,j]),
              postY = out$beta[,,j],
              y_true = simdata$beta_true[,j])

## End(Not run)

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