sampleBTF_reg

Compute one draw of the <code>T x p</code> state variable <code>beta</code> in a DLM using back-band substitution methods.
This model is equivalent to the Bayesian trend filtering (BTF) model applied to <code>p</code>
dynamic regression coefficients corresponding to the design matrix <code>X</code>,
assuming appropriate (shrinkage/sparsity) priors for the evolution errors.

Provides efficient Markov chain Monte Carlo (MCMC) algorithms for
dynamic shrinkage processes, which extend global-local shrinkage priors to
the time series setting by allowing shrinkage to depend on its own past.
These priors yield locally adaptive estimates, useful for time series and
regression functions with irregular features. The package includes full MCMC
implementations for trend filtering using dynamic shrinkage on signal differences,
producing locally constant or linear fits with adaptive credible bands.
Also included are models with static shrinkage and normal-inverse-Gamma priors for comparison.
Additional tools cover dynamic regression with time-varying coefficients and
B-spline models with shrinkage on basis differences, allowing for flexible
curve-fitting with unequally spaced data. Some support for heteroscedastic errors,
outlier detection, and change point estimation.
Methods in this package are described in Kowal et al. (2019) <doi:10.1111/rssb.12325>,
Wu et al. (2024) <doi:10.1080/07350015.2024.2362269>, Schafer and Matteson (2024)
<doi:10.1080/00401706.2024.2407316>, and Cho and Matteson (2024) <doi:10.48550/arXiv.2408.11315>.

Toryn Schafer

Dynamic Shrinkage Process and Change Point Detection

Daniel R. Kowal

Haoxuan Wu

Jason B. Cho

David S. Matteson

sampleBTF_reg function

<dl><dt>y</dt>
<dd>the <code>T x 1</code> vector of time series observations</dd>
<dt>X</dt>
<dd>the <code>T x p</code> matrix of time series predictors</dd>
<dt>obs_sigma_t2</dt>
<dd>the <code>T x 1</code> vector of observation error variances</dd>
<dt>evol_sigma_t2</dt>
<dd>the <code>T x p</code> matrix of evolution error variances</dd>
<dt>XtX</dt>
<dd>the <code>Tp x Tp</code> matrix of X'X (one-time cost; see ?build_XtX)</dd>
<dt>D</dt>
<dd>the degree of differencing (one or two)</dd>
<dt>chol0</dt>
<dd>(optional) the <code>m x m</code> matrix of initial Cholesky factorization;
if NULL, use the <code>Matrix</code> package for sampling, otherwise use the <code>spam</code> package</dd></dl>

Arguments

Sampler for first or second order random walk (RW) Gaussian dynamic linear model (DLM) — sampleBTF_reg

<dl>

<dt>y</dt>
<dd>the <code>T x 1</code> vector of time series observations</dd>


<dt>X</dt>
<dd>the <code>T x p</code> matrix of time series predictors</dd>


<dt>obs_sigma_t2</dt>
<dd>the <code>T x 1</code> vector of observation error variances</dd>


<dt>evol_sigma_t2</dt>
<dd>the <code>T x p</code> matrix of evolution error variances</dd>


<dt>XtX</dt>
<dd>the <code>Tp x Tp</code> matrix of X'X (one-time cost; see ?build_XtX)</dd>


<dt>D</dt>
<dd>the degree of differencing (one or two)</dd>


<dt>chol0</dt>
<dd>(optional) the <code>m x m</code> matrix of initial Cholesky factorization;
if NULL, use the <code>Matrix</code> package for sampling, otherwise use the <code>spam</code> package</dd>

</dl>

sampleBTF_reg: Sampler for first or second order random walk (RW) Gaussian dynamic linear model (DLM)

Description

Usage

Value

Arguments