exdqlm: Extended Dynamic Quantile Linear Models

Description

Bayesian quantile-regression tools for dynamic state-space models and static regression under the extended asymmetric Laplace error distribution (exAL).

Details

The package centers on native dynamic quantile state-space modeling for univariate time series, while version 0.4.0 also provides a static exAL regression workflow. Across these settings, exdqlm combines model construction helpers, multiple Bayesian inference engines, shrinkage priors for static coefficients, and post hoc synthesis of several fitted quantiles.

Main workflows

• Dynamic/state-space quantile modeling via exdqlmLDVB() and exdqlmMCMC(), with legacy exdqlmISVB() retained for backward compatibility and transfer-function extensions through exdqlmTransferLDVB(), exdqlmTransferMCMC(), and legacy exdqlmTransferISVB().

• Static Bayesian exAL regression via exalStaticLDVB() and exalStaticMCMC().

• Modular state-space construction via polytrendMod(), seasMod(), and regMod().

• Multi-quantile post-processing via quantileSynthesis() for post hoc posterior-predictive synthesis from separately fitted quantiles into a unified predictive distribution.

Distinctive features in 0.4.0

• Dynamic Bayesian quantile state-space inference with LDVB as the main VB engine, MCMC for posterior simulation, and legacy ISVB retained for compatibility and historical comparisons.

• A unified package covering both dynamic exDQLM models and static exAL regression.

• Static shrinkage priors including ridge, regularized horseshoe ("rhs"), and rhs_ns.

• Reduced AL/DQLM paths through dqlm.ind = TRUE in both dynamic and static APIs.

• Standardized VB diagnostics traces via fit$diagnostics$vb_trace for ELBO, sigma, gamma, and convergence deltas across VB engines.

• Conservative automatic warmup defaults for the most failure-prone shared blocks: RHS-family tau scheduling plus exAL ⁠(sigma, gamma)⁠ warmup in VB and MCMC entry points, with explicit controls available only when users need to override the defaults.

• Optional C++ acceleration for selected state-space computations.

Runtime options

• options(exdqlm.use_cpp_kf = TRUE|FALSE) – C++ Kalman bridge (optional; default TRUE).

• options(exdqlm.compute_elbo = TRUE|FALSE) – Compute ELBO (optional; default TRUE).

• options(exdqlm.tol_elbo = numeric) – Positive ELBO convergence tolerance used when exdqlm.compute_elbo = TRUE; smaller values enforce stricter ELBO stabilization checks (default 1e-6).

• options(exdqlm.use_cpp_builders = TRUE|FALSE) – C++ model builders (optional; default FALSE).

• options(exdqlm.use_cpp_samplers = TRUE|FALSE) – C++ samplers (optional; default FALSE).

• options(exdqlm.use_cpp_postpred = TRUE|FALSE) – C++ posterior predictive sampler (optional; default FALSE).

• options(exdqlm.use_cpp_mcmc = TRUE|FALSE) – MCMC backend routing (optional; default TRUE).

• options(exdqlm.cpp_mcmc_mode = "strict"|"fast") – strict keeps legacy R-kernel parity; fast enables C++ FFBS in MCMC (default "fast").

• options(exdqlm.cpp_threads = numeric) – Positive integer thread cap for eligible OpenMP-enabled C++ paths (1L forces single-thread; default 1L).

Author(s)

Maintainer: Raquel Barata raquel.a.barata@gmail.com

Authors:

• Antonio Aguirre

Other contributors:

• Raquel Prado [thesis advisor]

• Bruno Sanso [thesis advisor]

See Also

Useful links:

• https://github.com/AntonioAPDL/exdqlm

• Report bugs at https://github.com/AntonioAPDL/exdqlm/issues

Addition for exdqlm objects

Description

Combines two state space blocks into a single state space model for an exDQLM.

Usage

## S3 method for class 'exdqlm'
m1 + m2

Arguments

Value

An object of class "exdqlm" containing the new combined state space model components:

• FF - Observational vector.

• GG - Evolution matrix.

• m0 - Prior mean of the state vector.

• C0 - Prior covariance of the state vector.

Examples

trend.comp = polytrendMod(2, rep(0, 2), 10*diag(2))
seas.comp = seasMod(365, c(1,2,4), C0 = 10*diag(6))
model = trend.comp + seas.comp

Monthly streamflow at the Big Trees gauge

Description

Observed monthly mean streamflow, in cubic feet per second, at the Big Trees gauge on the San Lorenzo River in Santa Cruz County, California. The monthly values were obtained by averaging the daily USGS streamflow observations within each calendar month.

Usage

BTflow

Format

A monthly time series (ts) of length 471, spanning January 1987 through March 2026.

Source

U.S. Geological Survey, National Water Information System (USGS Water Data for the Nation), https://waterdata.usgs.gov/.

References

U.S. Geological Survey (2016). National Water Information System data available on the World Wide Web (USGS Water Data for the Nation). https://waterdata.usgs.gov/.

Daily time-series of ELI anomalies.

Description

ELI anomalies on the daily time-scale from January 1, 1979 to December 31, 2019 with all February 29ths omitted.

Usage

ELIanoms

Format

A time series of length 14965.

Source

https://portal.nersc.gov/archive/home/projects/cascade/www/ELI

References

Patricola, C.M., O’Brien, J.P., Risser, M.D. et al. Maximizing ENSO as a source of western US hydroclimate predictability. Clim Dyn 54, 351–372 (2020). doi:10.1007/s00382-019-05004-8

exdqlm objects

Description

as.exdqlm attempts to turn a list into an exdqlm object. Works for time-invariant dlm objects created using the dlm package.

Usage

as.exdqlm(m)

Arguments

Value

An object of class "exdqlm" containing the state space model components:

• FF - Observational vector.

• GG - Evolution matrix.

• m0 - Prior mean of the state vector.

• C0 - Prior covariance of the state vector.

Monthly climate indices for streamflow examples

Description

Monthly atmospheric and oceanic climate indices used as external predictors in the Big Trees streamflow examples. Values are stored on their original scales; examples that combine indices standardize the relevant columns within the analysis code.

Usage

climateIndices

Format

A data frame with 516 rows and 3 variables:

date

First day of the calendar month.

noi

Northern Oscillation Index.

amo

Atlantic Multidecadal Oscillation index.

The data frame spans January 1980 through December 2022.

Source

Compiled from the NOAA Physical Sciences Laboratory monthly climate indices collection, https://psl.noaa.gov/data/climateindices/.

Plot a component of an exDQLM

Description

The function plots the dynamic MAP estimates and 95% credible intervals (CrIs) of a specified component of an exDQLM. Alternatively, if just.theta=TRUE the MAP estimates and 95% credible intervals (CrIs) of a single element of the dynamic state vector are plotted.

Usage

compPlot(
  m1,
  index,
  add = FALSE,
  col = "purple",
  just.theta = FALSE,
  cr.percent = 0.95
)

Arguments

Value

A list of the following is returned:

• map.comp - MAP estimate of the dynamic component (or element of the state vector).

• lb.comp - Lower bound of the 95% CrIs of the dynamic component (or element of the state vector).

• ub.comp - Upper bound of the 95% CrIs of the dynamic component (or element of the state vector).

Examples

data("scIVTmag", package = "exdqlm")
old = options(exdqlm.max_iter = 15L)
y = scIVTmag[1:80]
trend.comp = polytrendMod(2, rep(0, 2), 10*diag(2))
seas.comp = seasMod(365, c(1, 2), C0 = 10*diag(4))
model = trend.comp + seas.comp
M0 = exdqlmLDVB(y, p0 = 0.85, model, df = c(0.98, 1), dim.df = c(2, 4),
                   gam.init = -3.5, sig.init = 15,
                   n.samp = 20, tol = 0.2, verbose = FALSE)
# plot first harmonic component
compPlot(M0, index = c(3, 4), col = "blue")
options(old)

Density Function for the Extended Asymmetric Laplace (exAL) Distribution

Description

Computes the PDF of the Extended Asymmetric Laplace (exAL) distribution. Vectorized over x.

Usage

dexal(x, p0 = 0.5, mu = 0, sigma = 1, gamma = 0, log = FALSE)

Arguments

Value

Numeric vector of densities (same length as x).

Examples

dexal(0)
dexal(1, p0 = 0.75, mu = 0, sigma = 2, gamma = 0.25)
dexal(seq(-3, 3, by = 0.1), p0 = 0.3, mu = 0, sigma = 1, gamma = -0.45)

exAL Diagnostics

Description

Static diagnostics companion for exalStaticLDVB() and exalStaticMCMC(). The function summarizes fitted quantiles on a shared design matrix, reports mean check loss against observed responses when available, and can optionally compare the fitted quantile curve against a known reference quantile function.

Usage

exalStaticDiagnostics(
  m1,
  m2 = NULL,
  X = NULL,
  y = NULL,
  ref = NULL,
  plot = TRUE,
  cols = c("red", "blue"),
  cr.percent = 0.95
)

Arguments

Details

Unlike exdqlmDiagnostics, which is built around one-step-ahead dynamic forecast diagnostics, exalStaticDiagnostics() is designed for the static regression setting. It reports fitted quantile summaries on a common design matrix, optional mean check loss against observed responses, optional truth/reference errors, and compact comparison plots.

Value

An object of class "exalStaticDiagnostic" containing fitted-quantile summaries, residual summaries (when y is provided), optional reference-curve error metrics, and run-time metadata for m1 and m2 (if supplied).

Examples

set.seed(1)
x <- seq(-2, 2, length.out = 60)
X <- cbind(1, x)
y <- 0.5 * x + (1.2 + 0.35 * x) * stats::rnorm(length(x))
q_true <- 0.5 * x + (1.2 + 0.35 * x) * stats::qnorm(0.25)

fit_ldvb <- exalStaticLDVB(
  y = y, X = X, p0 = 0.25,
  max_iter = 60, tol = 1e-3,
  verbose = FALSE
)
fit_mcmc <- exalStaticMCMC(
  y = y, X = X, p0 = 0.25,
  n.burn = 60, n.mcmc = 60,
  mh.proposal = "slice",
  verbose = FALSE
)
out <- exalStaticDiagnostics(fit_ldvb, fit_mcmc, ref = q_true, plot = FALSE)
print(out)

Static exAL Regression - LDVB Approximation

Description

The function applies a mean-field variational approximation to static Extended Asymmetric Laplace (exAL) regression. Closed-form block updates are combined with a Laplace-Delta approximation for the joint (\sigma,\gamma) block, yielding the package's static LDVB routine.

Usage

exalStaticLDVB(
  y,
  X,
  p0,
  max_iter = 1000,
  tol = 1e-04,
  b0 = NULL,
  V0 = NULL,
  beta_prior = c("ridge", "rhs", "rhs_ns"),
  beta_prior_controls = NULL,
  a_sigma = 1,
  b_sigma = 1,
  gamma_bounds = c(L.fn(p0), U.fn(p0)),
  log_prior_gamma = NULL,
  init = NULL,
  dqlm.ind = FALSE,
  al.ind = NULL,
  n.samp = 200,
  n_samp_xi = 200,
  ld_controls = NULL,
  vb_control = NULL,
  verbose = TRUE
)

Arguments

Details

Mean-field factorization:

q(\beta)\ \prod_{i=1}^n q(v_i)\ q(s_i)\ q(\sigma,\gamma).

This factorization induces a blockwise coordinate-ascent variational inference scheme. The (\sigma,\gamma) block is the only nonconjugate component, so LDVB approximates it in transformed coordinates \eta=\mathrm{logit}((\gamma-L)/(U-L)) and \ell=\log\sigma. The xi expectations needed by the remaining block updates are then computed with a second-order Delta approximation. The xi expectations used in the updates can be computed either from a deterministic second-order Delta approximation in (\eta,\ell) or from a Gaussian Monte Carlo sample. The Laplace-Delta controls also allow bounded optimization in the transformed (\eta,\ell) block to better mimic the stabilized RHS-family readout implementation. For RHS-family priors, the prior block uses tau warmup/freeze scheduling to avoid the early-collapse regime where global shrinkage drives all slope coefficients toward zero before the likelihood-side variational factors stabilize.

Value

An object of class "exalStaticLDVB" containing:

• qbeta: list with m, V.

• samp.beta: posterior sample from q(\beta) with n.samp rows.

• qv: list with chi (length n), psi (scalar), E_v and E_inv_v (moments).

• qs: list with mu (length n), tau2 (length n), E_s, E_s2.

• qsiggam: list with eta_hat, ell_hat, Sigma (2x2), approximate means gamma_mean, sigma_mean, and the xi expectations.

• samp.sigma, samp.gamma: posterior samples from the variational approximation for the scale and skewness parameters. In the AL special case (dqlm.ind = TRUE), samp.gamma is a vector of zeros.

• converged, iter, run.time, and misc (including p0, bounds L,U, dimensions, and ELBO trace).

• beta_prior: prior metadata and, for RHS-family priors, posterior summaries of the shrinkage hyperparameters, including warmup/freeze-aware tau summaries and collapse diagnostics (collapse_flag, tau_near_zero, beta_collapse, and warning when triggered). For "rhs_ns", the state also tracks lambda2, nu, tau2, xi, and zeta2 with the corresponding inverse moments.

• diagnostics: ELBO and joint-convergence diagnostics including a standardized VB iteration trace at diagnostics$vb_trace (iteration-wise ELBO / sigma / gamma / convergence deltas), state/sigma/gamma/ELBO deltas, stopping reason, and Laplace-Delta block trace diagnostics, including replicated-xi controls, automatic stabilization / cycle-detection fields, and final local-mode quality checks. For RHS fits this also includes diagnostics$rhs with the resolved preflight configuration and collapse diagnostics.

Examples

set.seed(123)
n <- 60
X <- cbind(1, seq(-1, 1, length.out = n))
y <- as.numeric(X %*% c(0.2, -0.1) + rnorm(n, sd = 0.15))
fit <- exalStaticLDVB(y = y, X = X, p0 = 0.5, max_iter = 60, tol = 1e-3, verbose = FALSE)
fit$converged
head(fit$diagnostics$vb_trace)

fit_rhs <- exalStaticLDVB(
  y = y, X = X, p0 = 0.5,
  beta_prior = "rhs",
  beta_prior_controls = list(tau0 = 0.5, nu = 3, s2 = 1, shrink_intercept = FALSE),
  max_iter = 50, tol = 5e-3, verbose = FALSE
)
fit_rhs$beta_prior$type

fit_rhs_ns <- exalStaticLDVB(
  y = y, X = X, p0 = 0.5,
  beta_prior = "rhs_ns",
  beta_prior_controls = list(tau0 = 0.5, a_zeta = 1.5, b_zeta = 1, zeta2_fixed = 1),
  max_iter = 50, tol = 5e-3, verbose = FALSE
)
fit_rhs_ns$beta_prior$type

fit_al <- exalStaticLDVB(
  y = y, X = X, p0 = 0.5,
  al.ind = TRUE,
  max_iter = 50, tol = 5e-3, verbose = FALSE
)
fit_al$dqlm.ind

exAL (static) - MCMC algorithm

Description

The function applies a Gibbs sampler for static Extended Asymmetric Laplace regression (exAL). We update \beta, v, s from their full conditionals, then update (\sigma,\gamma) either jointly on transformed coordinates (\ell,\eta)=(\log \sigma,\mathrm{logit}((\gamma-L)/(U-L))) (for "rw" and "laplace_rw") or with univariate gamma kernels ("slice", "slice_eta", "laplace_local"). Optional multi-refresh and global-jump controls are available to improve exAL mixing in hard cases.

Usage

exalStaticMCMC(
  y,
  X,
  p0,
  b0 = NULL,
  V0 = NULL,
  beta_prior = c("ridge", "rhs", "rhs_ns"),
  beta_prior_controls = NULL,
  a_sigma = 1,
  b_sigma = 1,
  gamma_bounds = c(L.fn(p0), U.fn(p0)),
  log_prior_gamma = NULL,
  init = NULL,
  dqlm.ind = FALSE,
  al.ind = NULL,
  n.burn = 2000,
  n.mcmc = 1500,
  thin = 1,
  init.from.vb = FALSE,
  vb_init_controls = NULL,
  vb_init_fit = NULL,
  mcmc_control = NULL,
  sigmagam_controls = NULL,
  mh.proposal = c("slice", "laplace_rw", "rw", "slice_eta", "laplace_local"),
  mh.adapt = TRUE,
  mh.adapt.interval = 50L,
  mh.target.accept = c(0.2, 0.45),
  mh.scale.bounds = c(0.1, 10),
  mh.max_scale.step = 0.35,
  mh.min_burn_adapt = 50L,
  slice.width = 0.1,
  slice.max.steps = Inf,
  gamma.substeps = 1L,
  p.global.eta.jump = 0,
  global.eta.jump.scale = 1,
  trace.diagnostics = TRUE,
  trace.every = 1L,
  verbose = TRUE,
  progress_callback = NULL
)

Arguments

Value

An object of class "exalStaticMCMC" containing:

• run.time - total wall time in seconds.

• X, p0, bounds - design, quantile, and (L, U).

• samp.beta - posterior sample of beta as coda::mcmc (n.mcmc x p).

• samp.sigma - posterior sample of sigma as coda::mcmc.

• samp.gamma - posterior sample of gamma as coda::mcmc.

• samp.v - latent v draws as coda::mcmc (n.mcmc x n).

• samp.s - latent s draws as coda::mcmc (n.mcmc x n).

• samp.lambda, samp.tau, samp.c2 - RHS latent draws when an RHS-family prior is used; otherwise NULL.

• beta_prior - prior metadata and, for RHS-family priors, posterior summaries of the shrinkage block. For "rhs_ns", the state tracks lambda2, nu, tau2, xi, and zeta2.

• mh.diagnostics - proposal kernel diagnostics for the exAL gamma update, including whether the saved kernel is exact/signoff-ready.

• rhs.diagnostics - RHS latent summaries and optional trace metadata when an RHS-family prior is used, including the resolved preflight configuration used at fit start.

• last - last state of the chain (useful for restarts).

Examples

set.seed(123)
n <- 60; p <- 3
X <- cbind(1, rnorm(n), rnorm(n))
beta0 <- c(0.5, -1, 0.8); sigma0 <- 1.2
y <- as.numeric(X %*% beta0 + rnorm(n, 0, sigma0))
fit <- exalStaticMCMC(
  y, X, p0 = 0.5, n.burn = 60, n.mcmc = 60, thin = 1, verbose = FALSE
)
summary(fit$samp.beta)

fit_rhs <- exalStaticMCMC(
  y, X, p0 = 0.5,
  beta_prior = "rhs",
  beta_prior_controls = list(tau0 = 0.5, nu = 3, s2 = 1, shrink_intercept = FALSE),
  n.burn = 50, n.mcmc = 50, thin = 1, mh.proposal = "slice", verbose = FALSE
)
fit_rhs$beta_prior$type

fit_rhs_ns <- exalStaticMCMC(
  y, X, p0 = 0.5,
  beta_prior = "rhs_ns",
  beta_prior_controls = list(tau0 = 0.5, a_zeta = 1.5, b_zeta = 1, zeta2_fixed = 1),
  n.burn = 40, n.mcmc = 40, thin = 1, mh.proposal = "slice", verbose = FALSE
)
fit_rhs_ns$beta_prior$type

fit_al <- exalStaticMCMC(
  y, X, p0 = 0.5,
  al.ind = TRUE,
  n.burn = 50, n.mcmc = 50, thin = 1, verbose = FALSE
)
fit_al$dqlm.ind

Build advanced MCMC control

Description

Returns a readable mcmc_control list for exalStaticMCMC() and exdqlmMCMC(). This keeps the warmup surface explicit instead of relying on ad hoc nested lists.

Usage

exal_make_mcmc_control(
  n_burn = 2000L,
  n_mcmc = 1500L,
  thin = 1L,
  verbose = FALSE,
  progress_every = NULL,
  init_from_vb = TRUE,
  vb_warm_start_control = NULL,
  sigmagam = NULL,
  theta = NULL,
  latent_state = NULL,
  dqlm_sigma = NULL,
  control = NULL
)

Arguments

Value

A normalized list suitable for mcmc_control.

Build DQLM sigma-only MCMC warmup control

Description

Returns a normalized mcmc_control$dqlm_sigma block for exdqlmMCMC() in the reduced AL / DQLM branch.

Usage

exal_make_mcmc_dqlm_sigma_control(
  freeze_burnin_iters = 0L,
  freeze_only_during_burn = TRUE,
  force_after_warmup = TRUE,
  trace = TRUE
)

Arguments

Value

A normalized list suitable for mcmc_control$dqlm_sigma.

Build dynamic MCMC latent-state warmup control

Description

Returns a normalized mcmc_control$latent_state block for exdqlmMCMC().

Usage

exal_make_mcmc_latent_state_control(
  mode = c("u_only", "u_st_pair"),
  freeze_burnin_iters = 0L,
  freeze_only_during_burn = TRUE,
  force_after_warmup = TRUE,
  min_postwarmup_updates = 0L,
  trace = TRUE
)

Arguments

Value

A normalized list suitable for mcmc_control$latent_state.

Build MCMC sigmagam warmup control

Description

Returns a normalized mcmc_control$sigmagam block for exalStaticMCMC() and exdqlmMCMC().

Usage

exal_make_mcmc_sigmagam_control(
  freeze_burnin_iters = NULL,
  freeze_only_during_burn = NULL,
  force_after_warmup = NULL,
  delay_adapt_until_after_warmup = NULL,
  delay_laplace_refresh_until_after_warmup = NULL
)

Arguments

Value

A normalized list suitable for mcmc_control$sigmagam.

When called with no arguments, this returns the package's conservative default exAL ⁠(sigma, gamma)⁠ MCMC warmup profile.

Build MCMC theta warmup control

Description

Returns a normalized mcmc_control$theta block for exdqlmMCMC().

Usage

exal_make_mcmc_theta_control(
  enabled = FALSE,
  freeze_burnin_iters = 0L,
  freeze_only_during_burn = TRUE,
  sparse_update_every = 1L,
  sparse_update_until_iter = 0L,
  force_first_postwarmup_update = TRUE,
  trace = TRUE
)

Arguments

Value

A normalized list suitable for mcmc_control$theta.

Build advanced VB control

Description

Returns a readable vb_control list for exalStaticLDVB() and exdqlmLDVB(). This keeps the warmup surface explicit instead of relying on ad hoc nested lists.

Usage

exal_make_vb_control(
  max_iter = 150L,
  tol = 1e-04,
  n_samp_xi = 200L,
  verbose = FALSE,
  sigmagam = NULL,
  sts = NULL,
  control = NULL
)

Arguments

Value

A normalized list suitable for vb_control.

Build VB sigmagam warmup control

Description

Returns a normalized sigmagam block for vb_control lists used by exalStaticLDVB(), exdqlmLDVB(), and VB warm-start paths in exalStaticMCMC() and exdqlmMCMC().

Usage

exal_make_vb_sigmagam_control(
  freeze_warmup_iters = NULL,
  force_after_warmup = NULL,
  postwarmup_damping = NULL,
  postwarmup_damping_iters = NULL,
  min_postwarmup_updates = NULL
)

Arguments

Value

A normalized list suitable for vb_control$sigmagam.

When called with no arguments, this returns the package's conservative default exAL ⁠(sigma, gamma)⁠ warmup profile.

Build dynamic VB latent-state warmup control

Description

Returns a normalized sts block for vb_control lists used by exdqlmLDVB().

Usage

exal_make_vb_sts_control(
  freeze_warmup_iters = 0L,
  force_after_warmup = TRUE,
  min_postwarmup_updates = 0L
)

Arguments

Value

A normalized list suitable for vb_control$sts.

exDQLM Diagnostics

Description

The function computes the following for the model(s) provided: the posterior predictive loss criterion based off the check loss, the CRPS from posterior predictive draws, the one-step-ahead distribution sequence, and both the forward and reversed KL divergences from normality. The function also plots the following: the qq-plot and ACF plot corresponding to the one-step-ahead distribution sequence, and a time series plot of the MAP standard forecast errors.

Usage

exdqlmDiagnostics(
  m1,
  m2 = NULL,
  plot = TRUE,
  cols = c("red", "blue"),
  ref = NULL
)

Arguments

Value

An object of class "exdqlmDiagnostic" containing the following:

• m1.uts - The one-step-ahead distribution sequence of m1.

• m1.KL - The KL divergence of m1.uts and a standard normal.

• m1.KL.flip - The reversed ("flipped") KL divergence of m1.uts and a standard normal.

• m1.CRPS - The mean CRPS computed from posterior predictive draws.

• m1.pplc - The posterior predictive loss criterion of m1 based off the check loss function.

• m1.qq - The ordered pairs of the qq-plot comparing m1.uts with a standard normal distribution.

• m1.acf - The autocorrelations of m1.uts by lag.

• m1.rt - Run-time of the original model m1 in seconds.

• m1.msfe - MAP standardized one-step-ahead forecast errors from the original model m1.

• y - The original time-series used to fit m1.

If m2 is provided, analogous results for m2 are also included in the list.

Examples

data("scIVTmag", package = "exdqlm")
old = options(exdqlm.max_iter = 15L)
y = scIVTmag[1:60]
model = polytrendMod(1, stats::quantile(y, 0.85), 10)
M0 = exdqlmLDVB(y, p0 = 0.85, model, df = c(0.95), dim.df = c(1),
                  gam.init = -3.5, sig.init = 15,
                  n.samp = 20, tol = 0.2, verbose = FALSE)
M0.diags = exdqlmDiagnostics(M0, plot = FALSE)
options(old)

k-step-ahead quantile forecasts

Description

Computes filtered and k-step-ahead forecast quantiles from a fitted dynamic quantile model and optionally adds them to an existing plot.

Usage

exdqlmForecast(
  start.t,
  k,
  m1,
  fFF = NULL,
  fGG = NULL,
  plot = TRUE,
  add = FALSE,
  cols = c("purple", "magenta"),
  cr.percent = 0.95,
  return.draws = FALSE,
  n.samp = NULL,
  seed = NULL
)

Arguments

Value

An object of class "exdqlmForecast" containing the following:

• start.t Integer index at which forecasts start (within the span of the fitted model in m1).

• k Integer number of steps ahead forecasted.

• m1 The fitted exDQLM model object used to initialize the forecast.

• cr.percent The probability mass for the credible intervals (e.g., 0.95).

• fa Forecast state mean vectors (q \times k matrix).

• fR Forecast state covariance matrices (q \times q \times k array).

• ff Forecast quantile means (length-k numeric).

• fQ Forecast quantile variances (length-k numeric).

• samp.fore Optional posterior predictive forecast draws (k x n.samp) returned when return.draws = TRUE.

Examples

 # Toy example
 data("scIVTmag", package = "exdqlm")
 old = options(exdqlm.max_iter = 20L)
 y = scIVTmag[1:100]
 model = polytrendMod(1, stats::quantile(y, 0.85), 10)
 M0 = exdqlmLDVB(y, p0 = 0.85, model, df = c(0.98), dim.df = c(1),
                  gam.init = -3.5, sig.init = 15, n.samp = 30,
                  verbose = FALSE)
 exdqlmForecast(start.t = 90, k = 10, m1 = M0)
 M0.forecast = exdqlmForecast(start.t = 90, k = 10, m1 = M0,
                              return.draws = TRUE, n.samp = 50, seed = 123)
 dim(M0.forecast$samp.fore)
 options(old)

exDQLM - legacy ISVB algorithm

Description

The function applies an Importance Sampling Variational Bayes (ISVB) algorithm to estimate the posterior of an exDQLM. This legacy VB engine is retained for backward compatibility and historical comparisons; for standard exDQLM VB fits, exdqlmLDVB() is the main default technique.

Usage

exdqlmISVB(
  y,
  p0,
  model,
  df,
  dim.df,
  fix.gamma = FALSE,
  gam.init = NA,
  fix.sigma = FALSE,
  sig.init = NA,
  dqlm.ind = FALSE,
  exps0,
  tol = 0.1,
  n.IS = 500,
  n.samp = 200,
  PriorSigma = NULL,
  PriorGamma = NULL,
  verbose = TRUE,
  debug_shapes = FALSE,
  debug_every = 5
)

Arguments

Details

Advanced options (set via options()):

• exdqlm.use_cpp_kf: use the C++ Kalman filter bridge (default TRUE).

• exdqlm.compute_elbo: compute ELBO every iteration (default TRUE).

• exdqlm.tol_elbo: ELBO convergence tolerance (default 1e-6).

• exdqlm.tol_sigma: sigma-delta convergence tolerance (default: tol).

• exdqlm.tol_gamma: gamma-delta convergence tolerance (default: tol).

• exdqlm.vb.min_iter: minimum iterations before convergence can trigger (default 10).

• exdqlm.vb.patience: number of consecutive joint-converged iterations required (default 3).

• exdqlm.use_cpp_samplers: use C++ samplers for s_t, u_t, theta (default FALSE). The GIG-based u_t sampler always uses the package C++ Devroye implementation; when FALSE, the remaining samplers fall back to R implementations.

• exdqlm.use_cpp_postpred: use C++ posterior predictive sampler (default FALSE).

Value

An object of class "exdqlmISVB" containing the following:

• y - Time-series data used to fit the model.

• run.time - Algorithm run time in seconds.

• iter - Number of iterations until convergence was reached.

• dqlm.ind - Logical value indicating whether gamma was fixed at 0, reducing the exDQLM to the special case of the DQLM.

• model - List of the state-space model including GG, FF, prior parameters m0 and C0.

• p0 - The quantile which was estimated.

• df - Discount factors used for each block.

• dim.df - Dimension used for each block of discount factors.

• sig.init - Initial value for sigma, or value at which sigma was fixed if fix.sigma=TRUE.

• seq.sigma - Sequence of sigma estimated by the algorithm until convergence.

• samp.theta - Posterior sample of the state vector variational distribution.

• samp.post.pred - Sample of the posterior predictive distributions.

• map.standard.forecast.errors - MAP standardized one-step-ahead forecast errors.

• samp.sigma - Posterior sample of scale parameter sigma variational distribution.

• samp.vts - Posterior sample of latent parameters, v_t, variational distributions.

• theta.out - List containing the variational distribution of the state vector including filtered distribution parameters (fm and fC) and smoothed distribution parameters (sm and sC).

• vts.out - List containing the variational distributions of latent parameters v_t.

• fix.sigma Logical value indicating whether sigma was fixed at sig.init.

• diagnostics - List containing ELBO trace, standardized VB iteration trace diagnostics$vb_trace (iteration-wise ELBO / sigma / gamma / convergence deltas), and convergence diagnostics (joint stopping status, deltas for state/sigma/gamma/ELBO, and criteria used).

If dqlm.ind=FALSE, the object also contains:

• gam.init - Initial value for gamma, or value at which gamma was fixed if fix.gamma=TRUE.

• seq.gamma - Sequence of gamma estimated by the algorithm until convergence.

• samp.gamma - Posterior sample of skewness parameter gamma variational distribution.

• samp.sts - Posterior sample of latent parameters, s_t, variational distributions.

• gammasig.out - List containing the IS estimate of the variational distribution of sigma and gamma.

• sts.out - List containing the variational distributions of latent parameters s_t.

• fix.gamma Logical value indicating whether gamma was fixed at gam.init.

Or if dqlm.ind=TRUE, the object also contains:

• sig.out - As above but for the DQLM case (gamma = 0); list containing the IS estimate of the variational distribution of sigma.

Examples

data("scIVTmag", package = "exdqlm")
old = options(exdqlm.max_iter = 20L)
y = scIVTmag[1:120]
trend.comp = polytrendMod(1, stats::quantile(y, 0.85), 10)
seas.comp = seasMod(365, c(1,2), C0 = 10*diag(4))
model = trend.comp + seas.comp
# Legacy ISVB fit retained for backward-compatible comparisons
M0 = exdqlmISVB(y, p0 = 0.85, model, df = c(1,1), dim.df = c(1,4),
                 gam.init = -3.5, sig.init = 15, tol = 0.2,
                 n.IS = 20, n.samp = 20, verbose = FALSE)
head(M0$diagnostics$vb_trace)

M0_al = exdqlmISVB(y, p0 = 0.85, model, df = c(1,1), dim.df = c(1,4),
                   dqlm.ind = TRUE, sig.init = 15, tol = 0.2,
                   n.IS = 20, n.samp = 20, verbose = FALSE)
tail(M0_al$diagnostics$vb_trace$elbo, 2)
options(old)

exDQLM - LDVB algorithm (Laplace-Delta)

Description

The function applies a Laplace-Delta Variational Bayes (LDVB) algorithm to estimate the posterior of an exDQLM.

Arguments

Details

Advanced options (set via options()):

• exdqlm.use_cpp_kf: use the C++ Kalman filter bridge (default TRUE).

• exdqlm.compute_elbo: compute ELBO every iteration (default TRUE).

• exdqlm.tol_elbo: ELBO convergence tolerance (default 1e-6).

• exdqlm.tol_sigma: sigma-delta convergence tolerance (default: tol).

• exdqlm.tol_gamma: gamma-delta convergence tolerance (default: tol).

• exdqlm.vb.min_iter: minimum iterations before convergence can trigger (default 10).

• exdqlm.vb.patience: number of consecutive joint-converged iterations required (default 3).

• exdqlm.use_cpp_samplers: use C++ samplers for s_t, u_t, theta (default FALSE). The GIG-based u_t sampler always uses the package C++ Devroye implementation; when FALSE, the remaining samplers fall back to R implementations.

• exdqlm.use_cpp_postpred: use C++ posterior predictive sampler (default FALSE).

• exdqlm.dynamic.ldvb.sts: optional warmup/freeze controls for the exDQLM latent s_t VB block. Supported fields are freeze_warmup_iters, force_after_warmup, and min_postwarmup_updates.

Value

An object of class "exdqlmLDVB" containing the following:

• y - Time-series data used to fit the model.

• run.time - Algorithm run time in seconds.

• iter - Number of iterations until convergence was reached.

• dqlm.ind - Logical value indicating whether gamma was fixed at 0, reducing the exDQLM to the special case of the DQLM.

• model - List of the state-space model including GG, FF, prior parameters m0 and C0.

• p0 - The quantile which was estimated.

• df - Discount factors used for each block.

• dim.df - Dimension used for each block of discount factors.

• sig.init - Initial value for sigma, or value at which sigma was fixed if fix.sigma=TRUE.

• seq.sigma - Sequence of sigma estimated by the algorithm until convergence.

• samp.theta - Posterior sample of the state vector variational distribution.

• samp.post.pred - Sample of the posterior predictive distributions.

• map.standard.forecast.errors - MAP standardized one-step-ahead forecast errors.

• samp.sigma - Posterior sample of scale parameter sigma variational distribution.

• samp.vts - Posterior sample of latent parameters, v_t, variational distributions.

• theta.out - List containing the variational distribution of the state vector including filtered distribution parameters (fm and fC) and smoothed distribution parameters (sm and sC).

• vts.out - List containing the variational distributions of latent parameters v_t.

• fix.sigma Logical value indicating whether sigma was fixed at sig.init.

• diagnostics - List containing ELBO trace, standardized VB iteration trace diagnostics$vb_trace (iteration-wise ELBO / sigma / gamma / convergence deltas), and convergence diagnostics (joint stopping status, deltas for state/sigma/gamma/ELBO, and criteria used).

If dqlm.ind=FALSE, the list also contains:

• gam.init - Initial value for gamma, or value at which gamma was fixed if fix.gamma=TRUE.

• seq.gamma - Sequence of gamma estimated by the algorithm until convergence.

• samp.gamma - Posterior sample of skewness parameter gamma variational distribution.

• samp.sts - Posterior sample of latent parameters, s_t, variational distributions.

• gammasig.out - List containing the LD (Laplace-Delta) approximation for the variational distribution of sigma and gamma (means, transformed Hessian, and ELBO components).

• sts.out - List containing the variational distributions of latent parameters s_t.

• fix.gamma Logical value indicating whether gamma was fixed at gam.init.

Or if dqlm.ind=TRUE, the list also contains:

• sig.out - As above but for the DQLM case (gamma = 0), the LD approximation for sigma.

Examples

data("scIVTmag", package = "exdqlm")
old = options(exdqlm.max_iter = 20L)
y = scIVTmag[1:80]
trend.comp = polytrendMod(1, stats::quantile(y, 0.85), 10)
seas.comp = seasMod(365, c(1,2), C0 = 10*diag(4))
model = trend.comp + seas.comp
M0 = exdqlmLDVB(y, p0 = 0.85, model, df = c(1,1), dim.df = c(1,4),
                 gam.init = -3.5, sig.init = 15, tol = 0.2,
                 n.samp = 20, verbose = FALSE)

M0_al = exdqlmLDVB(y, p0 = 0.85, model, df = c(1,1), dim.df = c(1,4),
                   dqlm.ind = TRUE, sig.init = 15, tol = 0.2,
                   n.samp = 20, verbose = FALSE)
options(old)

exDQLM - MCMC algorithm

Description

The function applies a Markov chain Monte Carlo (MCMC) algorithm to sample the posterior of an exDQLM.

Arguments

Value

An object of class "exdqlmMCMC" containing the following:

• y - Time-series data used to fit the model.

• run.time - Algorithm run time in seconds.

• dqlm.ind - Logical value indicating whether gamma was fixed at 0, reducing the exDQLM to the special case of the DQLM.

• model - List of the state-space model including GG, FF, prior parameters m0 and C0.

• p0 - The quantile which was estimated.

• df - Discount factors used for each block.

• dim.df - Dimension used for each block of discount factors.

• samp.theta - Posterior sample of the state vector.

• samp.post.pred - Sample of the posterior predictive distributions.

• map.standard.forecast.errors - MAP standardized one-step-ahead forecast errors.

• samp.sigma - Posterior sample of scale parameter sigma.

• samp.vts - Posterior sample of latent parameters, v_t.

• theta.out - List containing the distributions of the state vector including filtered distribution parameters (fm and fC) and smoothed distribution parameters (sm and sC).

• n.burn Number of MCMC iterations that were burned.

• n.mcmc Number of MCMC iterations that were sampled.

If dqlm.ind=FALSE, the object also contains the following:

• samp.gamma - Posterior sample of skewness parameter gamma.

• samp.sts - Posterior sample of latent parameters, s_t.

• init.log.sigma - Burned samples of log sigma from the random walk MH joint sampling of sigma and gamma.

• init.logit.gamma - Burned samples of logit gamma from the random walk MH joint sampling of sigma and gamma.

• accept.rate - Acceptance rate of the MH step.

• accept.rate.burn - MH acceptance rate during burn-in.

• accept.rate.keep - MH acceptance rate in kept MCMC samples.

• Sig.mh - Covariance matrix used in MH step to jointly sample sigma and gamma.

• mh.diagnostics - MH tuning diagnostics (proposal mode, scaling path, adaptation summary).

• diagnostics - ESS and chain-ready summaries for sigma/gamma.

Examples

data("scIVTmag", package = "exdqlm")
y = scIVTmag[1:80]
trend.comp = polytrendMod(order = 1, m0 = stats::quantile(y, 0.85), C0 = 10)
seas.comp = seasMod(p = 365, h = c(1,2), C0 = 10*diag(4))
model = trend.comp + seas.comp
M2 = exdqlmMCMC(y, p0=0.85, model, df = c(1,1), dim.df = c(1,4),
                gam.init = -3.5, sig.init = 15,
                n.burn = 40, n.mcmc = 40,
                init.from.vb = FALSE, verbose = FALSE)

M2_al = exdqlmMCMC(y, p0=0.85, model, df = c(1,1), dim.df = c(1,4),
                   dqlm.ind = TRUE, sig.init = 15,
                   n.burn = 30, n.mcmc = 30,
                   init.from.vb = FALSE, verbose = FALSE)

Plot exDQLM

Description

The function plots the MAP estimates and 95% credible intervals (CrIs) of the dynamic quantile of an exDQLM.

Usage

exdqlmPlot(m1, add = FALSE, col = "purple", cr.percent = 0.95)

Arguments

Value

A list of the following is returned:

• map.quant - MAP estimate of the dynamic quantile.

• lb.quant - Lower bound of the 95% CrIs of the dynamic quantile.

• ub.quant - Upper bound of the 95% CrIs of the dynamic quantile.

Examples

data("scIVTmag", package = "exdqlm")
old = options(exdqlm.max_iter = 15L)
y = scIVTmag[1:60]
model = polytrendMod(1, stats::quantile(y, 0.85), 10)
M0 = exdqlmLDVB(y, p0 = 0.85, model, df = c(0.98), dim.df = c(1),
                   gam.init = -3.5, sig.init = 15,
                   n.samp = 20, tol = 0.2, verbose = FALSE)
exdqlmPlot(M0, col = "blue")
options(old)

Transfer Function exDQLM - legacy ISVB algorithm

Description

The function applies an Importance Sampling Variational Bayes (ISVB) algorithm to estimate the posterior of an exDQLM with exponential-decay transfer function component. This transfer wrapper is retained as a legacy path; exdqlmTransferLDVB() is the main VB transfer entry point.

Usage

exdqlmTransferISVB(
  y,
  p0,
  model,
  X,
  df,
  dim.df,
  lam,
  tf.df,
  fix.gamma = FALSE,
  gam.init = NA,
  fix.sigma = FALSE,
  sig.init = NA,
  dqlm.ind = FALSE,
  exps0,
  tol = 0.1,
  n.IS = 500,
  n.samp = 200,
  PriorSigma = NULL,
  PriorGamma = NULL,
  tf.m0 = NULL,
  tf.C0 = NULL,
  verbose = TRUE
)

Arguments

Details

Advanced options (set via options()):

• exdqlm.use_cpp_kf: use the C++ Kalman filter bridge (default TRUE).

• exdqlm.compute_elbo: compute ELBO every iteration (default TRUE).

• exdqlm.tol_elbo: ELBO convergence tolerance (default 1e-6).

• exdqlm.use_cpp_samplers: use C++ samplers for s_t, u_t, theta (default FALSE). The GIG-based u_t sampler always uses the package C++ Devroye implementation; when FALSE, the remaining samplers fall back to R implementations.

• exdqlm.use_cpp_postpred: use C++ posterior predictive sampler (default FALSE).

Value

An object of class "exdqlmISVB" containing the following:

• run.time - Algorithm run time in seconds.

• iter - Number of iterations until convergence was reached.

• dqlm.ind - Logical value indicating whether gamma was fixed at 0, reducing the exDQLM to the special case of the DQLM.

• model - List of the augmented state-space model including GG, FF, prior parameters m0 and C0.

• p0 - The quantile which was estimated.

• df - Discount factors used for each block, including transfer function component.

• dim.df - Dimension used for each block of discount factors, including transfer function component.

• lam - Transfer function rate parameter lambda.

• sig.init - Initial value for sigma, or value at which sigma was fixed if fix.sigma=TRUE.

• seq.sigma - Sequence of sigma estimated by the algorithm until convergence.

• samp.theta - Posterior sample of the state vector variational distribution.

• samp.post.pred - Sample of the posterior predictive distributions.

• map.standard.forecast.errors - MAP standardized one-step-ahead forecast errors.

• samp.sigma - Posterior sample of scale parameter sigma variational distribution.

• samp.vts - Posterior sample of latent parameters, v_t, variational distributions.

• theta.out - List containing the variational distribution of the state vector including filtered distribution parameters (fm and fC) and smoothed distribution parameters (sm and sC).

• vts.out - List containing the variational distributions of latent parameters v_t.

• median.kt - Median number of time steps until the aggregated transfer effect |x_t^\top \psi_{t-1}| is less than or equal to 1e-3.

If dqlm.ind=FALSE, the object also contains:

• gam.init - Initial value for gamma, or value at which gamma was fixed if fix.gamma=TRUE.

• seq.gamma - Sequence of gamma estimated by the algorithm until convergence.

• samp.gamma - Posterior sample of skewness parameter gamma variational distribution.

• samp.sts - Posterior sample of latent parameters, s_t, variational distributions.

• gammasig.out - List containing the IS estimate of the variational distribution of sigma and gamma.

• sts.out - List containing the variational distributions of latent parameters s_t.

Or if dqlm.ind=TRUE, the object also contains:

• sig.out - As above but for the DQLM case (gamma = 0); list containing the IS estimate of the variational distribution of sigma.

Examples

data("scIVTmag", package = "exdqlm")
data("ELIanoms", package = "exdqlm")
old = options(exdqlm.max_iter = 20L)
y = scIVTmag[1:120]
X = ELIanoms[1:120]
trend.comp = polytrendMod(1, stats::quantile(y, 0.85), 10)
seas.comp = seasMod(365, c(1,2), C0 = 10*diag(4))
model = trend.comp + seas.comp
# Legacy ISVB transfer fit retained for backward-compatible comparisons
M1 = exdqlmTransferISVB(y, p0 = 0.85, model = model,
                          X, df = c(1,1), dim.df = c(1,4),
                          gam.init = -3.5, sig.init = 15,
                          lam = 0.38, tf.df = c(0.97,0.97),
                          n.IS = 20, n.samp = 20, tol = 0.2,
                          verbose = FALSE)
X_multi = cbind(ELIanoms[1:120], scale(scIVTmag[1:120])[, 1])
M2 = exdqlmTransferISVB(y, p0 = 0.85, model = model,
                          X_multi, df = c(1,1), dim.df = c(1,4),
                          gam.init = -3.5, sig.init = 15,
                          lam = 0.38, tf.df = c(0.97, 0.99),
                          n.IS = 20, n.samp = 20, tol = 0.2,
                          verbose = FALSE)
options(old)

Transfer Function exDQLM - LDVB algorithm

Description

The function applies a Laplace-Delta Variational Bayes (LDVB) algorithm to estimate the posterior of an exDQLM with an exponential-decay transfer function component. For multivariate transfer inputs, each column of X has its own instantaneous coefficient state in \psi_t, while a single scalar decay rate lam controls persistence of the accumulated transfer effect \zeta_t.

Usage

exdqlmTransferLDVB(
  y,
  p0,
  model,
  X,
  df,
  dim.df,
  lam,
  tf.df,
  fix.gamma = FALSE,
  gam.init = NA,
  fix.sigma = FALSE,
  sig.init = NA,
  dqlm.ind = FALSE,
  exps0,
  tol = 0.1,
  n.samp = 200,
  PriorSigma = NULL,
  PriorGamma = NULL,
  tf.m0 = NULL,
  tf.C0 = NULL,
  verbose = TRUE,
  debug_shapes = FALSE,
  debug_every = 5
)

Arguments

Value

An object of class "exdqlmLDVB" containing the following:

• y - Time-series data used to fit the model.

• run.time - Algorithm run time in seconds.

• iter - Number of iterations until convergence was reached.

• dqlm.ind - Logical value indicating whether gamma was fixed at 0, reducing the exDQLM to the special case of the DQLM.

• model - List of the state-space model including GG, FF, prior parameters m0 and C0.

• p0 - The quantile which was estimated.

• df - Discount factors used for each block.

• dim.df - Dimension used for each block of discount factors.

• sig.init - Initial value for sigma, or value at which sigma was fixed if fix.sigma=TRUE.

• seq.sigma - Sequence of sigma estimated by the algorithm until convergence.

• samp.theta - Posterior sample of the state vector variational distribution.

• samp.post.pred - Sample of the posterior predictive distributions.

• map.standard.forecast.errors - MAP standardized one-step-ahead forecast errors.

• samp.sigma - Posterior sample of scale parameter sigma variational distribution.

• samp.vts - Posterior sample of latent parameters, v_t, variational distributions.

• theta.out - List containing the variational distribution of the state vector including filtered distribution parameters (fm and fC) and smoothed distribution parameters (sm and sC).

• vts.out - List containing the variational distributions of latent parameters v_t.

• fix.sigma Logical value indicating whether sigma was fixed at sig.init.

• diagnostics - List containing ELBO trace, standardized VB iteration trace diagnostics$vb_trace (iteration-wise ELBO / sigma / gamma / convergence deltas), and convergence diagnostics (joint stopping status, deltas for state/sigma/gamma/ELBO, and criteria used).

If dqlm.ind=FALSE, the list also contains:

• gam.init - Initial value for gamma, or value at which gamma was fixed if fix.gamma=TRUE.

• seq.gamma - Sequence of gamma estimated by the algorithm until convergence.

• samp.gamma - Posterior sample of skewness parameter gamma variational distribution.

• samp.sts - Posterior sample of latent parameters, s_t, variational distributions.

• gammasig.out - List containing the LD (Laplace-Delta) approximation for the variational distribution of sigma and gamma (means, transformed Hessian, and ELBO components).

• sts.out - List containing the variational distributions of latent parameters s_t.

• fix.gamma Logical value indicating whether gamma was fixed at gam.init.

Or if dqlm.ind=TRUE, the list also contains:

• sig.out - As above but for the DQLM case (gamma = 0), the LD approximation for sigma.

Transfer-function return fields

In addition to the standard exdqlmLDVB() return values, the returned model, df, and dim.df entries correspond to the transfer-function-augmented state-space model, with appended \zeta_t and \psi_t states. The object also contains:

• lam - Single transfer-function decay-rate parameter \lambda.

• median.kt - Median number of time steps until the aggregated transfer effect |x_t^\top \psi_{t-1}| is less than or equal to 1e-3.

• transfer_input_names - Column names of the transfer inputs after normalization of X.

Examples

data("scIVTmag", package = "exdqlm")
data("ELIanoms", package = "exdqlm")
old = options(exdqlm.max_iter = 20L)
y = scIVTmag[1:120]
X = ELIanoms[1:120]
trend.comp = polytrendMod(1, stats::quantile(y, 0.85), 10)
seas.comp = seasMod(365, c(1,2), C0 = 10*diag(4))
model = trend.comp + seas.comp
M1 = exdqlmTransferLDVB(
  y, p0 = 0.85, model = model, X = X,
  df = c(1,1), dim.df = c(1,4),
  gam.init = -3.5, sig.init = 15,
  lam = 0.38, tf.df = c(0.97,0.97),
  n.samp = 20, tol = 0.2, verbose = FALSE
)
X_multi = cbind(ELIanoms[1:120], scale(scIVTmag[1:120])[, 1])
M2 = exdqlmTransferLDVB(
  y, p0 = 0.85, model = model, X = X_multi,
  df = c(1,1), dim.df = c(1,4),
  gam.init = -3.5, sig.init = 15,
  lam = 0.38, tf.df = c(0.97, 0.99),
  n.samp = 20, tol = 0.2, verbose = FALSE
)
options(old)

Transfer Function exDQLM - MCMC algorithm

Description

The function applies a Markov chain Monte Carlo (MCMC) algorithm to sample the posterior of an exDQLM with an exponential-decay transfer function component for a fixed transfer rate parameter lam. For multivariate transfer inputs, each column of X has its own instantaneous coefficient state in \psi_t, while a single scalar decay rate lam controls persistence of the accumulated transfer effect \zeta_t.

Usage

exdqlmTransferMCMC(
  y,
  p0,
  model,
  X,
  df,
  dim.df,
  lam,
  tf.df,
  fix.gamma = FALSE,
  gam.init = NA,
  fix.sigma = FALSE,
  sig.init = NA,
  dqlm.ind = FALSE,
  Sig.mh,
  joint.sample = FALSE,
  n.burn = 2000,
  n.mcmc = 1500,
  init.from.isvb = FALSE,
  PriorSigma = NULL,
  PriorGamma = NULL,
  verbose = TRUE,
  init.from.vb = TRUE,
  vb_init_controls = NULL,
  vb_init_fit = NULL,
  mh.proposal = c("slice", "laplace_rw", "rw"),
  mh.adapt = TRUE,
  mh.adapt.interval = 50L,
  mh.target.accept = c(0.2, 0.45),
  mh.scale.bounds = c(0.1, 10),
  mh.max_scale.step = 0.35,
  mh.min_burn_adapt = 50L,
  slice.width = 0.1,
  slice.max.steps = Inf,
  trace.diagnostics = TRUE,
  trace.every = 1L,
  verbose.every = 500L,
  progress_callback = NULL,
  tf.m0 = NULL,
  tf.C0 = NULL
)

Arguments

Value

An object of class "exdqlmMCMC" containing the following:

• y - Time-series data used to fit the model.

• run.time - Algorithm run time in seconds.

• dqlm.ind - Logical value indicating whether gamma was fixed at 0, reducing the exDQLM to the special case of the DQLM.

• model - List of the state-space model including GG, FF, prior parameters m0 and C0.

• p0 - The quantile which was estimated.

• df - Discount factors used for each block.

• dim.df - Dimension used for each block of discount factors.

• samp.theta - Posterior sample of the state vector.

• samp.post.pred - Sample of the posterior predictive distributions.

• map.standard.forecast.errors - MAP standardized one-step-ahead forecast errors.

• samp.sigma - Posterior sample of scale parameter sigma.

• samp.vts - Posterior sample of latent parameters, v_t.

• theta.out - List containing the distributions of the state vector including filtered distribution parameters (fm and fC) and smoothed distribution parameters (sm and sC).

• n.burn Number of MCMC iterations that were burned.

• n.mcmc Number of MCMC iterations that were sampled.

If dqlm.ind=FALSE, the object also contains the following:

• samp.gamma - Posterior sample of skewness parameter gamma.

• samp.sts - Posterior sample of latent parameters, s_t.

• init.log.sigma - Burned samples of log sigma from the random walk MH joint sampling of sigma and gamma.

• init.logit.gamma - Burned samples of logit gamma from the random walk MH joint sampling of sigma and gamma.

• accept.rate - Acceptance rate of the MH step.

• accept.rate.burn - MH acceptance rate during burn-in.

• accept.rate.keep - MH acceptance rate in kept MCMC samples.

• Sig.mh - Covariance matrix used in MH step to jointly sample sigma and gamma.

• mh.diagnostics - MH tuning diagnostics (proposal mode, scaling path, adaptation summary).

• diagnostics - ESS and chain-ready summaries for sigma/gamma.

Transfer-function return fields

In addition to the standard exdqlmMCMC() return values, the returned model, df, and dim.df entries correspond to the transfer-function-augmented state-space model, with appended \zeta_t and \psi_t states. The object also contains:

• lam - Single transfer-function decay-rate parameter \lambda.

• median.kt - Median number of time steps until the aggregated transfer effect |x_t^\top \psi_{t-1}| is less than or equal to 1e-3.

• transfer_input_names - Column names of the transfer inputs after normalization of X.

Examples

data("scIVTmag", package = "exdqlm")
data("ELIanoms", package = "exdqlm")
y = scIVTmag[1:120]
X = ELIanoms[1:120]
trend.comp = polytrendMod(1, stats::quantile(y, 0.85), 10)
seas.comp = seasMod(365, c(1,2), C0 = 10*diag(4))
model = trend.comp + seas.comp
M1 = exdqlmTransferMCMC(
  y, p0 = 0.85, model = model, X = X,
  df = c(1,1), dim.df = c(1,4),
  gam.init = -3.5, sig.init = 15,
  lam = 0.38, tf.df = c(0.97,0.97),
  n.burn = 40, n.mcmc = 40,
  init.from.vb = FALSE, verbose = FALSE
)
X_multi = cbind(ELIanoms[1:120], scale(scIVTmag[1:120])[, 1])
M2 = exdqlmTransferMCMC(
  y, p0 = 0.85, model = model, X = X_multi,
  df = c(1,1), dim.df = c(1,4),
  gam.init = -3.5, sig.init = 15,
  lam = 0.38, tf.df = c(0.97, 0.99),
  n.burn = 40, n.mcmc = 40,
  init.from.vb = FALSE, verbose = FALSE
)

Bounds for the exAL shape parameter gamma

Description

Returns valid lower/upper bounds (L, U) for the shape parameter gamma of the standardized extended Asymmetric Laplace (exAL), given p0 in (0,1).

Usage

get_gamma_bounds(p0)

Arguments

Details

This is a user-facing convenience wrapper around the C++ routine get_gamma_bounds_cpp(), which performs the actual computation.

Value

A numeric vector of length 2 named c("L","U").

Examples

get_gamma_bounds(0.5)
get_gamma_bounds(0.9)

exalStaticDiagnostic objects

Description

is.exalStaticDiagnostic tests if its argument is an exalStaticDiagnostic object.

Usage

is.exalStaticDiagnostic(x)

Arguments

exalStaticLDVB objects

Description

is.exalStaticLDVB tests if its argument is an exalStaticLDVB object.

Usage

is.exalStaticLDVB(m)

Arguments

exalStaticMCMC objects

Description

is.exalStaticMCMC tests if its argument is an exalStaticMCMC object.

Usage

is.exalStaticMCMC(m)

Arguments

exdqlm objects

Description

is.exdqlm tests if its argument is a exdqlm object.

Usage

is.exdqlm(m)

Arguments

exdqlmDiagnostic objects

Description

is.exdqlmDiagnostic tests if its argument is a exdqlmDiagnostic object.

Usage

is.exdqlmDiagnostic(x)

Arguments

exdqlmForecast objects

Description

is.exdqlmForecast tests if its argument is a exdqlmForecast object.

Usage

is.exdqlmForecast(x)

Arguments

exdqlmISVB objects

Description

is.exdqlmISVB tests if its argument is a exdqlmISVB object.

Usage

is.exdqlmISVB(m)

Arguments

exdqlmLDVB objects

Description

is.exdqlmLDVB tests if its argument is a exdqlmLDVB object.

Usage

is.exdqlmLDVB(m)

Arguments

exdqlmMCMC objects

Description

is.exdqlmMCMC tests if its argument is a exdqlmMCMC object.

Usage

is.exdqlmMCMC(m)

Arguments

exdqlmSynthesis objects

Description

is.exdqlmSynthesis tests if its argument is an exdqlmSynthesis object returned by quantileSynthesis.

Usage

is.exdqlmSynthesis(x)

Arguments

Cumulative Distribution Function (CDF) for the exAL Distribution

Description

Vectorized over q.

Usage

pexal(
  q,
  p0 = 0.5,
  mu = 0,
  sigma = 1,
  gamma = 0,
  lower.tail = TRUE,
  log.p = FALSE
)

Arguments

Value

Numeric vector of CDF values (same length as q).

Examples

pexal(0)
pexal(c(-1, 0, 1), p0 = 0.5, mu = 0, sigma = 1, gamma = 0.1)

Plot Method for exalStaticDiagnostic Objects

Description

Plot Method for exalStaticDiagnostic Objects

Usage

## S3 method for class 'exalStaticDiagnostic'
plot(x, cols = c("red", "blue"), ...)

Arguments

Plot Method for exalStaticLDVB Objects

Description

Plot Method for exalStaticLDVB Objects

Usage

## S3 method for class 'exalStaticLDVB'
plot(x, X = NULL, add = FALSE, col = "purple", cr.percent = 0.95, ...)

Arguments

Value

A list with map.quant, lb.quant, and ub.quant.

Plot Method for exalStaticMCMC Objects

Description

Plot Method for exalStaticMCMC Objects

Usage

## S3 method for class 'exalStaticMCMC'
plot(x, add = FALSE, col = "purple", cr.percent = 0.95, ...)

Arguments

Value

A list with map.quant, lb.quant, and ub.quant.

Plot Method for exdqlmDiagnostic Objects

Description

Plot Method for exdqlmDiagnostic Objects

Usage

## S3 method for class 'exdqlmDiagnostic'
plot(x, ...)

Arguments

Examples

data("scIVTmag", package = "exdqlm")
old = options(exdqlm.max_iter = 15L)
y = scIVTmag[1:60]
model = polytrendMod(1, stats::quantile(y, 0.85), 10)
M0 = exdqlmLDVB(y, p0 = 0.85, model, df = c(0.95), dim.df = c(1),
                  gam.init = -3.5, sig.init = 15,
                  n.samp = 20, tol = 0.2, verbose = FALSE)
M0.diags = exdqlmDiagnostics(M0, plot = FALSE)
plot(M0.diags)
options(old)

Plot Method for exdqlmForecast Objects

Description

Plot Method for exdqlmForecast Objects

Usage

## S3 method for class 'exdqlmForecast'
plot(x, ...)

Arguments

Examples

 data("scIVTmag", package = "exdqlm")
 old = options(exdqlm.max_iter = 15L)
 y = scIVTmag[1:60]
 model = polytrendMod(1, stats::quantile(y, 0.85), 10)
 M0 = exdqlmLDVB(y, p0 = 0.85, model, df = c(0.98), dim.df = c(1),
                  gam.init = -3.5, sig.init = 15,
                  n.samp = 20, tol = 0.2, verbose = FALSE)
 M0.forecast = exdqlmForecast(start.t = 50, k = 5, m1 = M0)
 plot(M0.forecast)
 options(old)

Plot Method for exdqlmISVB Objects

Description

Plot Method for exdqlmISVB Objects

Usage

## S3 method for class 'exdqlmISVB'
plot(x, ...)

Arguments

Examples

data("scIVTmag", package = "exdqlm")
old = options(exdqlm.max_iter = 15L)
y = scIVTmag[1:60]
model = polytrendMod(1, stats::quantile(y, 0.85), 10)
# Legacy ISVB object retained for backward-compatible plotting methods
M0 = exdqlmISVB(y, p0 = 0.85, model, df = c(0.98), dim.df = c(1),
                   gam.init = -3.5, sig.init = 15,
                   n.IS = 20, n.samp = 20, tol = 0.2,
                   verbose = FALSE)
plot(M0)
options(old)

Plot Method for exdqlmLDVB Objects

Description

Plot Method for exdqlmLDVB Objects

Usage

## S3 method for class 'exdqlmLDVB'
plot(x, ...)

Arguments

Examples

data("scIVTmag", package = "exdqlm")
old = options(exdqlm.max_iter = 15L)
y = scIVTmag[1:60]
model = polytrendMod(1, stats::quantile(y, 0.85), 10)
M0 = exdqlmLDVB(y, p0 = 0.85, model, df = c(0.98), dim.df = c(1),
                   gam.init = -3.5, sig.init = 15,
                   n.samp = 20, tol = 0.2, verbose = FALSE)
plot(M0)
options(old)

Plot Method for exdqlmMCMC Objects

Description

Plot Method for exdqlmMCMC Objects

Usage

## S3 method for class 'exdqlmMCMC'
plot(x, ...)

Arguments

Examples

data("scIVTmag", package = "exdqlm")
y = scIVTmag[1:60]
model = polytrendMod(1, stats::quantile(y, 0.85), 10)
M2 = exdqlmMCMC(y, p0=0.85, model, df = c(0.98), dim.df = c(1),
                gam.init = -3.5, sig.init = 15,
                n.burn = 20, n.mcmc = 20,
                init.from.vb = FALSE, verbose = FALSE)
plot(M2)                

Plot Method for exdqlmSynthesis Objects

Description

Plot the pointwise posterior predictive interval produced by quantileSynthesis. The method is intentionally separate from quantileSynthesis() so the synthesis step remains a computation, while the returned object still has a standard plotting interface.

Usage

## S3 method for class 'exdqlmSynthesis'
plot(
  x,
  y = NULL,
  time = NULL,
  add = FALSE,
  interval = 0.95,
  show.median = TRUE,
  show.mean = FALSE,
  band.col = grDevices::adjustcolor("lightblue", alpha.f = 0.35),
  median.col = "blue",
  mean.col = "darkblue",
  y.col = "dark grey",
  border = NA,
  xlab = "time",
  ylab = "posterior predictive synthesis",
  main = NULL,
  xlim = NULL,
  ylim = NULL,
  ...
)

Arguments

Create an n-th order polynomial exDQLM component

Description

The function creates an n-th order polynomial exDQLM component.

Usage

polytrendMod(order, m0, C0, backend = c("auto", "R", "cpp"))

Arguments

Value

An object of class "exdqlm" containing the following:

• FF - n \times 1 observational vector.

• GG - n \times n evolution matrix.

• m0 - n \times 1 prior mean of the state vector.

• C0 - n \times n prior covariance matrix of the state vector.

Examples

# create a second order polynomial component
trend.comp = polytrendMod(2, rep(0, 2), 10*diag(2))

Print Method for exalStaticDiagnostic Objects

Description

Print Method for exalStaticDiagnostic Objects

Usage

## S3 method for class 'exalStaticDiagnostic'
print(x, ...)

Arguments

Print Method for exalStaticLDVB Objects

Description

Print Method for exalStaticLDVB Objects

Usage

## S3 method for class 'exalStaticLDVB'
print(x, ...)

Arguments

Print Method for exalStaticMCMC Objects

Description

Print Method for exalStaticMCMC Objects

Usage

## S3 method for class 'exalStaticMCMC'
print(x, ...)

Arguments

Print exDQLM model details

Description

Print the details of the exDQLM model.

Usage

## S3 method for class 'exdqlm'
print(x, ...)

Arguments

Print Method for exdqlmDiagnostic Objects

Description

Print Method for exdqlmDiagnostic Objects

Usage

## S3 method for class 'exdqlmDiagnostic'
print(x, ...)

Arguments

Examples

data("scIVTmag", package = "exdqlm")
old = options(exdqlm.max_iter = 15L)
y = scIVTmag[1:60]
model = polytrendMod(1, stats::quantile(y, 0.85), 10)
M0 = exdqlmLDVB(y, p0 = 0.85, model, df = c(0.95), dim.df = c(1),
                  gam.init = -3.5, sig.init = 15,
                  n.samp = 20, tol = 0.2, verbose = FALSE)
M0.diags = exdqlmDiagnostics(M0, plot=FALSE)
print(M0.diags)
options(old)

Print Method for exdqlmForecast Objects

Description

Print Method for exdqlmForecast Objects

Usage

## S3 method for class 'exdqlmForecast'
print(x, ...)

Arguments

Examples

 data("scIVTmag", package = "exdqlm")
 old = options(exdqlm.max_iter = 15L)
 y = scIVTmag[1:60]
 model = polytrendMod(1, stats::quantile(y, 0.85), 10)
 M0 = exdqlmLDVB(y, p0 = 0.85, model, df = c(0.98), dim.df = c(1),
                  gam.init = -3.5, sig.init = 15,
                  n.samp = 20, tol = 0.2, verbose = FALSE)
 M0.forecast = exdqlmForecast(start.t = 50, k = 5, m1 = M0)
 print(M0.forecast)
 options(old)

Print Method for exdqlmISVB Objects

Description

Print Method for exdqlmISVB Objects

Usage

## S3 method for class 'exdqlmISVB'
print(x, ...)

Arguments

Examples

data("scIVTmag", package = "exdqlm")
old = options(exdqlm.max_iter = 15L)
y = scIVTmag[1:60]
model = polytrendMod(1, stats::quantile(y, 0.85), 10)
# Legacy ISVB object retained for backward-compatible inspection methods
M0 = exdqlmISVB(y, p0 = 0.85, model, df = c(0.98), dim.df = c(1),
                   gam.init = -3.5, sig.init = 15,
                   n.IS = 20, n.samp = 20, tol = 0.2,
                   verbose = FALSE)
print(M0)
options(old)

Print Method for exdqlmLDVB Objects

Description

Print Method for exdqlmLDVB Objects

Usage

## S3 method for class 'exdqlmLDVB'
print(x, ...)

Arguments

Examples

data("scIVTmag", package = "exdqlm")
old = options(exdqlm.max_iter = 15L)
y = scIVTmag[1:60]
model = polytrendMod(1, stats::quantile(y, 0.85), 10)
M0 = exdqlmLDVB(y, p0 = 0.85, model, df = c(0.98), dim.df = c(1),
                   gam.init = -3.5, sig.init = 15,
                   n.samp = 20, tol = 0.2, verbose = FALSE)
print(M0)
options(old)

Print Method for exdqlmMCMC Objects

Description

Print Method for exdqlmMCMC Objects

Usage

## S3 method for class 'exdqlmMCMC'
print(x, ...)

Arguments

Examples

data("scIVTmag", package = "exdqlm")
y = scIVTmag[1:60]
model = polytrendMod(1, stats::quantile(y, 0.85), 10)
M2 = exdqlmMCMC(y, p0 = 0.85, model, df = c(0.98), dim.df = c(1),
                gam.init = -3.5, sig.init = 15,
                n.burn = 20, n.mcmc = 20,
                init.from.vb = FALSE, verbose = FALSE)
print(M2)                

Print Method for exdqlmSynthesis Objects

Description

Print Method for exdqlmSynthesis Objects

Usage

## S3 method for class 'exdqlmSynthesis'
print(x, ...)

Arguments

Quantile Function for the exAL Distribution

Description

Vectorized over p.

Usage

qexal(
  p,
  p0 = 0.5,
  mu = 0,
  sigma = 1,
  gamma = 0,
  lower.tail = TRUE,
  log.p = FALSE
)

Arguments

Value

Numeric vector of quantiles (same length as p).

Examples

p <- seq(0.1, 0.9, by = 0.2)
q <- qexal(p, p0 = 0.5, mu = 0, sigma = 1, gamma = 0)
all.equal(p, pexal(q, p0 = 0.5, mu = 0, sigma = 1, gamma = 0), tol = 1e-4)

Synthesize a unified posterior predictive distribution from multiple quantile-model draws

Description

The function synthesizes posterior predictive draws from multiple fitted quantile models into a single posterior predictive distribution. It uses a two-step correction: (i) isotonic regression at the grid of target quantiles to align the fitted quantile levels, and (ii) distributional alignment (shift each model's draws so its tau-quantile matches the isotone anchor). It then builds a single predictive quantile function per time by piecewise-linear blending across adjacent quantile models with optional global monotone rearrangement.

Usage

quantileSynthesis(
  draws_list,
  p,
  enforce_isotonic = TRUE,
  rearrange = TRUE,
  grid_M = 1001L,
  n_samp = 1000L,
  seed = NULL,
  T_expected = NULL
)

Arguments

Value

An object of class "exdqlmSynthesis", which is a list containing:

• draws - Numeric matrix T x n_samp of synthesized draws.

• levels - Sorted copy of p (length L).

• quantiles - Numeric matrix T x L of isotone anchors m^*_{i,t}.

• summary - List with row-wise summaries of draws (mean, q025, q250, q500, q750, q975).

• method - List of synthesis settings used (name, isotonic, rearrange, grid_M, T_inferred).

Examples

# short example
data("scIVTmag", package = "exdqlm")
old = options(exdqlm.max_iter = 10L)
TT = 50
y = scIVTmag[1:TT]

# create a compact trend model
trend.comp = polytrendMod(1, stats::quantile(y, 0.85), 10)
model = trend.comp

# fit quantiles using LDVB and save posterior predictive samples
fits <- draws <- NULL
p0s = c(0.10, 0.50, 0.90)
for(i in 1:length(p0s)){
  fits[[i]] = exdqlmLDVB(
    y, p0 = p0s[i], model, df = 0.98, dim.df = 1,
    sig.init = 15, n.samp = 20, tol = 0.2, verbose = FALSE
  )
  draws[[i]] = fits[[i]]$samp.post.pred
}

# synthesize posterior predictive from all quantiles
syn = quantileSynthesis(
  draws_list = draws,
  p = p0s,
  T_expected = TT)

# alternatively, pass fitted dynamic objects directly
syn2 = quantileSynthesis(
  draws_list = fits,
  p = p0s,
  T_expected = TT)

# plot the synthesized 95% posterior predictive interval
plot(syn2, y = y)
options(old)

Create a standard regression component for an exDQLM

Description

The function constructs a regression block where the observation vector at time t is F_t = X_t (row of the design matrix), and the state evolves as \theta_t = \theta_{t-1} (i.e., G_t = I_n).

Usage

regMod(X, m0, C0)

Arguments

Details

Input X is a T \times n matrix of regressors; the returned FF is an n \times T matrix (i.e., t(X)), consistent with component composition via +.exdqlm.

Value

An object of class "exdqlm" with elements:

• FF - n \times T matrix with column t equal to F_t = X_t.

• GG - n \times n identity matrix (static coefficients).

• m0, C0 - Prior mean/covariance for regression coefficients.

Examples

data("climateIndices", package = "exdqlm")

T <- 150
bt_dates <- seq(as.Date("1987-01-01"), by = "month", length.out = T)
idx <- match(bt_dates, climateIndices$date)
X <- scale(climateIndices[idx, c("noi", "amo")])

# Single regressor (T x 1)
reg1 = regMod(X[, "noi"])
# Multiple regressors (T x n)
reg2 = regMod(X)

# Combine with trend/seasonal components
trend.comp = polytrendMod(order = 3, m0 = rep(0,3), C0 = diag(3))
seas.comp  = seasMod(p = 12, h = 1, C0 = diag(1, 2))
base.mod   = trend.comp + seas.comp
model.std  = base.mod + reg2

Random Sample Generation for the exAL Distribution

Description

Random Sample Generation for the exAL Distribution

Usage

rexal(n, p0 = 0.5, mu = 0, sigma = 1, gamma = 0)

Arguments

Value

Numeric vector of length n.

Examples

set.seed(1)
rexal(3, p0 = 0.5, mu = c(-1, 0, 1))

Time series of daily average magnitude IVT in Santa Cruz, CA.

Description

ECMWF Re-Analysis 5 (ERA5) daily average magnitude IVT in Santa Cruz, CA (approximately 22 N, 122 W) from January 1, 1979 to December 31, 2019 with all February 29ths omitted.

Usage

scIVTmag

Format

A time series of length 14965.

Source

https://cds.climate.copernicus.eu

References

Hersbach, H, Bell, B, Berrisford, P, et al. The ERA5 global reanalysis. Q J R Meteorol Soc. 2020; 146: 1999– 2049. doi:10.1002/qj.3803

Create Fourier representation of a periodic exDQLM component

Description

The function creates a Fourier form periodic component for given period and harmonics.

Usage

seasMod(p, h, m0, C0, backend = c("auto", "R", "cpp"))

Arguments

Value

An object of class "exdqlm" containing the following:

• FF - q \times 1 observational vector.

• GG - q \times q evolution matrix.

• m0 - q \times 1 prior mean of the state vector.

• C0 - q \times q prior covariance matrix of the state vector.

Examples

# create a seasonal component with first, second and fourth harmonics of a period of 365
seas.comp = seasMod(365, c(1, 2, 4), C0 = 10*diag(6))

Summary Method for exalStaticDiagnostic Objects

Description

Summary Method for exalStaticDiagnostic Objects

Usage

## S3 method for class 'exalStaticDiagnostic'
summary(object, ...)

Arguments

Summary Method for exalStaticLDVB Objects

Description

Summary Method for exalStaticLDVB Objects

Usage

## S3 method for class 'exalStaticLDVB'
summary(object, ...)

Arguments

Summary Method for exalStaticMCMC Objects

Description

Summary Method for exalStaticMCMC Objects

Usage

## S3 method for class 'exalStaticMCMC'
summary(object, ...)

Arguments

Summary exDQLM model details

Description

Print the details of the exDQLM model.

Usage

## S3 method for class 'exdqlm'
summary(object, ...)

Arguments

Summary Method for exdqlmDiagnostic Objects

Description

Summary Method for exdqlmDiagnostic Objects

Usage

## S3 method for class 'exdqlmDiagnostic'
summary(object, ...)

Arguments

Examples

data("scIVTmag", package = "exdqlm")
old = options(exdqlm.max_iter = 15L)
y = scIVTmag[1:60]
model = polytrendMod(1, stats::quantile(y, 0.85), 10)
M0 = exdqlmLDVB(y, p0 = 0.85, model, df = c(0.95), dim.df = c(1),
                  gam.init = -3.5, sig.init = 15,
                  n.samp = 20, tol = 0.2, verbose = FALSE)
M0.diags = exdqlmDiagnostics(M0, plot = FALSE)
summary(M0.diags)
options(old)

Summary Method for exdqlmForecast Objects

Description

Summary Method for exdqlmForecast Objects

Usage

## S3 method for class 'exdqlmForecast'
summary(object, ...)

Arguments

Examples

 data("scIVTmag", package = "exdqlm")
 old = options(exdqlm.max_iter = 15L)
 y = scIVTmag[1:60]
 model = polytrendMod(1, stats::quantile(y, 0.85), 10)
 M0 = exdqlmLDVB(y, p0 = 0.85, model, df = c(0.98), dim.df = c(1),
                  gam.init = -3.5, sig.init = 15,
                  n.samp = 20, tol = 0.2, verbose = FALSE)
 M0.forecast = exdqlmForecast(start.t = 50, k = 5, m1 = M0)
 summary(M0.forecast)
 options(old)

Summary Method for exdqlmISVB Objects

Description

Summary Method for exdqlmISVB Objects

Usage

## S3 method for class 'exdqlmISVB'
summary(object, ...)

Arguments

Examples

data("scIVTmag", package = "exdqlm")
old = options(exdqlm.max_iter = 15L)
y = scIVTmag[1:60]
model = polytrendMod(1, stats::quantile(y, 0.85), 10)
# Legacy ISVB object retained for backward-compatible inspection methods
M0 = exdqlmISVB(y, p0 = 0.85, model, df = c(0.98), dim.df = c(1),
                   gam.init = -3.5, sig.init = 15,
                   n.IS = 20, n.samp = 20, tol = 0.2,
                   verbose = FALSE)
summary(M0)
options(old)

Summary Method for exdqlmLDVB Objects

Description

Summary Method for exdqlmLDVB Objects

Usage

## S3 method for class 'exdqlmLDVB'
summary(object, ...)

Arguments

Examples

data("scIVTmag", package = "exdqlm")
old = options(exdqlm.max_iter = 15L)
y = scIVTmag[1:60]
model = polytrendMod(1, stats::quantile(y, 0.85), 10)
M0 = exdqlmLDVB(y, p0 = 0.85, model, df = c(0.98), dim.df = c(1),
                   gam.init = -3.5, sig.init = 15,
                   n.samp = 20, tol = 0.2, verbose = FALSE)
summary(M0)
options(old)

Summary Method for exdqlmMCMC Objects

Description

Summary Method for exdqlmMCMC Objects

Usage

## S3 method for class 'exdqlmMCMC'
summary(object, ...)

Arguments

Examples

data("scIVTmag", package = "exdqlm")
y = scIVTmag[1:60]
model = polytrendMod(1, stats::quantile(y, 0.85), 10)
M2 = exdqlmMCMC(y, p0 = 0.85, model, df = c(0.98), dim.df = c(1),
                gam.init = -3.5, sig.init = 15,
                n.burn = 20, n.mcmc = 20,
                init.from.vb = FALSE, verbose = FALSE)
summary(M2)                

Summary Method for exdqlmSynthesis Objects

Description

Summary Method for exdqlmSynthesis Objects

Usage

## S3 method for class 'exdqlmSynthesis'
summary(object, time = NULL, ...)

Arguments

Value

A data frame containing pointwise summaries of the synthesized posterior predictive draws.