build_Q

Compute the quadratic term arising in the full conditional distribution
of a Bayesian trend filtering model with <code>D = 1</code> or <code>D = 2</code>.
This function exploits the known <code>D</code>-banded structure of <code>Q</code>
to compute the matrix directly, using objects in the Matrix package.

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

build_Q function

<dl><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 1</code> vector of evolution error variances</dd>
<dt>D</dt>
<dd>the degree of differencing (one or two)</dd></dl>

Arguments

Compute the quadratic term in Bayesian trend filtering — build_Q

<dl>

<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 1</code> vector of evolution error variances</dd>


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

</dl>

build_Q: Compute the quadratic term in Bayesian trend filtering

Description

Usage

Value

Arguments