Compute one draw of the T x p state variable beta in a DLM using back-band substitution methods.
This model is equivalent to the Bayesian trend filtering (BTF) model applied to p
dynamic regression coefficients corresponding to the design matrix X,
assuming appropriate (shrinkage/sparsity) priors for the evolution errors. The sampler
here uses a backfitting method that draws each predictor j=1,...,p conditional on the
other predictors (and coefficients), which leads to a faster O(Tp) algorithm.
However, the MCMC may be less efficient.
sampleBTF_reg_backfit(y, X, beta, obs_sigma_t2, evol_sigma_t2, D = 1)T x p matrix of simulated dynamic regression coefficients beta
the T x 1 vector of time series observations
the T x p matrix of time series predictors
the T x p matrix of previous dynamic regression coefficients
the T x 1 vector of observation error variances
the T x p matrix of evolution error variances
the degree of differencing (one or two)