Package 'HTDV'

Bridge-Sampling Bayes Factor

Description

Computes the Bayes factor between two fitted htdv_fit objects via bridge sampling. Requires the bridgesampling package.

Usage

htdv_bf(fit1, fit0, ...)

Arguments

fit1	Model in the numerator.
fit0	Model in the denominator.
...	Additional arguments passed to bridgesampling::bridge_sampler.

Value

A list with bf10, log_bf10, logml1, logml0, and error_percentage.

References

Meng, X.-L., & Wong, W.H. (1996). Simulating Ratios of Normalizing Constants. Statistica Sinica 6(4): 831-860. Gronau, Q.F. et al. (2017). A Tutorial on Bridge Sampling. JMP 81: 80-97.

Examples

if (requireNamespace("bridgesampling", quietly = TRUE)) {
  x <- rnorm(50)
  f1 <- htdv_fit(x, model = "tac", chains = 2, iter = 500,
                 refresh = 0, seed = 1)
  f0 <- htdv_fit(x, model = "tac", chains = 2, iter = 500,
                 refresh = 0, seed = 2)
  htdv_bf(f1, f0)$bf10
}

---

Block Bootstrap with Automatic Block Length

Description

Implements circular and stationary block bootstraps (Politis-Romano 1992, 1994) with Patton-Politis-White (2009) automatic block length selection.

Usage

htdv_boot(
  x,
  statistic,
  R = 1999L,
  type = c("circular", "stationary"),
  block_length = "auto",
  level = 0.95,
  seed = NULL
)

Arguments

x	Numeric vector.
statistic	Function function(x) returning a scalar or numeric vector.
R	Number of bootstrap replicates.
type	"circular" or "stationary".
block_length	Either "auto" (Patton-Politis-White) or a positive integer.
level	Confidence level for intervals.
seed	Optional integer seed.

Value

A list with t0 (statistic on original data), t_star (bootstrap distribution), ci_percentile, ci_basic, ci_studentized, and block_length.

References

Politis, D.N., & Romano, J.P. (1994). The Stationary Bootstrap. JASA 89(428): 1303-1313. Patton, A., Politis, D.N., & White, H. (2009). Correction to Automatic Block-Length Selection for the Dependent Bootstrap. Econometric Reviews 28(4): 372-375.

Examples

x <- arima.sim(model = list(ar = 0.5), n = 200, rand.gen = rnorm)
out <- htdv_boot(as.numeric(x), mean, R = 500, type = "stationary", seed = 1)
out$ci_percentile

---

Composite Log-Likelihood for Dependent Data

Description

Pairwise or k-tuple composite log-likelihood (Varin, Reid and Firth 2011) for strictly stationary sequences.

Usage

htdv_composite(x, density_fun, theta, k = 1L, log = FALSE)

Arguments

x	Numeric vector.
density_fun	Function function(block, theta) returning the joint density of a (k+1)-block of consecutive observations.
theta	Numeric parameter vector.
k	Window width (pairwise if k = 1).
log	Logical; if TRUE, density_fun already returns log densities.

Value

A list with loglik (scalar), n_blocks, and block_values.

References

Varin, C., Reid, N., & Firth, D. (2011). An overview of composite likelihood methods. Statistica Sinica, 21(1), 5-42.

Examples

x <- arima.sim(model = list(ar = 0.4), n = 200, rand.gen = rnorm)
gauss_ar1 <- function(block, theta) {
  phi <- theta[1]; sigma2 <- theta[2]
  a <- block[1]; b <- block[2]
  dnorm(a, 0, sqrt(sigma2 / (1 - phi^2)), log = TRUE) +
    dnorm(b, phi * a, sqrt(sigma2), log = TRUE)
}
htdv_composite(as.numeric(x), gauss_ar1, c(0.4, 1), k = 1, log = TRUE)$loglik

---

Adaptive Conformal Inference for Dependent Data

Description

Online adaptive conformal prediction intervals with gradient update on the miscoverage rate (Gibbs-Candes 2021). Provides long-run marginal coverage without exchangeability.

Usage

htdv_conformal(
  x,
  predictor,
  residual_fun = function(e) abs(e),
  alpha_target = 0.1,
  lambda = 0.05,
  burn_in = 20L
)

Arguments

x	Numeric vector of sequential observations.
predictor	Function function(history) returning a scalar one-step point prediction.
residual_fun	Function of residuals to calibrate the score; default absolute residual.
alpha_target	Target miscoverage rate.
lambda	Step size for the gradient update.
burn_in	Integer; the first burn_in observations are used only to warm up the predictor.

Value

A list with intervals (matrix of lower/upper), coverage (empirical), alpha_path, and point_predictions.

References

Gibbs, I., & Candes, E. (2021). Adaptive Conformal Inference under Distribution Shift. NeurIPS 34: 1660-1672.

Examples

x <- arima.sim(model = list(ar = 0.6), n = 200, rand.gen = rnorm)
pred <- function(hist) if (length(hist) >= 1) hist[length(hist)] else 0
out <- htdv_conformal(as.numeric(x), pred, alpha_target = 0.1,
                      lambda = 0.05, burn_in = 20)
out$coverage

---

MCMC Diagnostics for htdv_fit Objects

Description

Computes split-Rhat, bulk and tail ESS, E-BFMI, divergence count, and treedepth saturation; all standard HMC diagnostics (Vehtari et al. 2021, Betancourt 2016).

Usage

htdv_diagnostics(
  fit,
  rhat_threshold = 1.01,
  ess_threshold = 400,
  bfmi_threshold = 0.3
)

Arguments

fit	An htdv_fit object.
rhat_threshold	Convergence threshold for Rhat.
ess_threshold	Minimum effective sample size.
bfmi_threshold	Minimum acceptable energy-BFMI.

Value

A list with rhat, ess_bulk, ess_tail, bfmi, divergences, max_treedepth, passed (logical), and failures (character vector).

References

Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Buerkner, P.-C. (2021). Rank-normalization, folding, and localization: An improved Rhat for assessing convergence of MCMC. Bayesian Analysis 16(2): 667-718. Betancourt, M. (2016). Diagnosing Suboptimal Cotangent Disintegrations. <doi:10.48550/arXiv.1604.00695>.

Examples

x <- rnorm(50)
fit <- htdv_fit(x, model = "tac", chains = 2, iter = 500,
                refresh = 0, seed = 1)
htdv_diagnostics(fit)$passed

---

HTDV Empirical Benchmarks Against Published References

Description

Output of the three-dataset external validation protocol of Section 12-ter of the companion paper. Each dataset is run against a pre-existing reference result from the published literature on the same vintage, with the three HTDV inferential layers (HAR, bootstrap, hierarchical Bayesian) reporting their point estimate, 95% interval, and a Bayesian diagnostic-pass flag.

Usage

htdv_empirical_benchmarks

Format

A data frame with three rows (one per dataset) and the following columns:

dataset

Name of the benchmark dataset.

reference

Citation of the reference paper.

n

Sample size after preprocessing.

sample

Sample window (string).

reference_value

Reference point value.

reference_se

Reference standard error (NA when the reference does not provide one).

har_point, har_ci_lo, har_ci_hi

HAR-Wald point and 95% CI.

bayes_point, bayes_ci_lo, bayes_ci_hi

Bayesian point and 95% credible interval.

bayes_diag_pass, bayes_rhat_max, bayes_ess_min, bayes_divergences

Bayesian HMC diagnostics.

boot_point, boot_ci_lo, boot_ci_hi

Stationary block bootstrap point and 95% percentile CI.

agreement_har, agreement_bayes, agreement_boot

Per-layer agreement verdict: "agreement", "htdv-strict (above ref)", or "htdv-strict (below ref)".

Details

The three benchmarks (E1, E2, E3) and their references are:

• E1. Post-1984 US CPI inflation against Stock and Watson (2007). FRED-MD vintage 2026-03, variable CPIAUCSL transformed to annualized monthly inflation.

• E2. Long-run mean of log-CAPE against Campbell and Shiller (1998). Robert Shiller's online historical dataset.

• E3. US vs. Canada 10-year government bond yield differential against the iid Welch baseline. FRED series GS10 and IRLTLT01CAM156N, common sample 1990-01 to latest.

Source

Generated by run_benchmarks.R of the companion paper repository. See vignette("HTDV-validation") for the methodological narrative and the persistence-ladder reading.

---

Berger-Robust Envelope Posterior

Description

Builds an envelope posterior over a list of htdv_fit objects by entropy-maximizing mixture weights subject to predictive consistency (Berger 1994).

Usage

htdv_envelope(fits, target = "theta")

Arguments

fits	List of htdv_fit objects on the same data.
target	Name of the Stan parameter over which to build the envelope.

Value

A list with draws (envelope draws for the target parameter), weights, intervals, and component_intervals.

References

Berger, J.O. (1994). An Overview of Robust Bayesian Analysis. Test 3(1): 5-124.

Examples

x <- rnorm(50)
f1 <- htdv_fit(x, model = "tac", chains = 2, iter = 500,
               refresh = 0, seed = 1)
f2 <- htdv_fit(x, model = "wsc", chains = 2, iter = 500,
               refresh = 0, seed = 2)
htdv_envelope(list(f1, f2), target = "theta")$intervals

---

Numerical Constants for TAC/WSC/MPC Metric Equivalence

Description

Computes the explicit finite-sample constants K_TAC(gamma, q), K_MPC(gamma) and the unified two-sided envelope (c_L, c_U) from Theorems 5-8 of the companion paper.

Usage

htdv_equivalence_constants(gamma, q = 6, n = 100, C_alpha = 1)

Arguments

gamma	Mixing decay rate; must satisfy gamma > 1.
q	Moment order used in Ibragimov-Rio covariance bound; must satisfy q > 2 and gamma * (1 - 2/q) > 1.
n	Sample size used for the two-sided envelope.
C_alpha	Strong-mixing constant (default 1).

Value

A list with components K_TAC, K_MPC, c_L, c_U, b_optimal, m_optimal, and regime (a short label describing which method is favored).

Examples

htdv_equivalence_constants(gamma = 2, q = 6, n = 60)

---

Hierarchical Bayesian Fit for Dependent Variables

Description

Fits the hierarchical Bayesian model described in the companion paper via Hamiltonian Monte Carlo (NUTS) using rstan. Nuisance parameters sigma_inf, gamma_mix, and (for WSC) b carry priors and are integrated over.

Usage

htdv_fit(
  x,
  model = c("tac", "wsc", "mpc", "whittle", "composite"),
  chains = 4L,
  iter = 4000L,
  warmup = iter%/%2L,
  refresh = max(iter%/%10L, 1L),
  adapt_delta = 0.99,
  max_treedepth = 12L,
  seed = NULL,
  ...
)

htdv_tac(x, ...)

htdv_wsc(x, ...)

htdv_mpc(x, ...)

Arguments

x	Numeric vector of observations.
model	One of "tac", "wsc", "mpc", "whittle", "composite".
chains	Number of HMC chains.
iter	Total iterations per chain (warmup plus sampling).
warmup	Number of warmup iterations.
refresh	Stan progress refresh rate (0 suppresses output).
adapt_delta	HMC adaptation target acceptance.
max_treedepth	Maximum NUTS treedepth.
seed	Optional integer seed forwarded to rstan.
...	Additional arguments forwarded to rstan::sampling.

Value

An object of class htdv_fit, a list with components stanfit, model, data, n, call.

References

Hoffman, M.D., & Gelman, A. (2014). The No-U-Turn Sampler. JMLR 15(1): 1593-1623. Betancourt, M. (2016). Diagnosing Suboptimal Cotangent Disintegrations in HMC. <doi:10.48550/arXiv.1604.00695>.

Examples

x <- rnorm(50)
fit <- htdv_fit(x, model = "tac", chains = 2, iter = 500,
                refresh = 0, seed = 1)
class(fit)

---

Fixed-Bandwidth HAR Inference (Kiefer-Vogelsang 2005)

Description

Fixed-b HAR Wald test where the bandwidth is a fixed fraction of the sample size. Critical values are obtained by simulation from the asymptotic functional distribution.

Usage

htdv_fixedb(
  x,
  theta0 = 0,
  B = 0.1,
  kernel = c("bartlett", "parzen", "qs"),
  sims = 5000L,
  alpha = 0.05,
  seed = NULL
)

Arguments

x	Numeric vector.
theta0	Null value for the mean (default 0).
B	Fixed bandwidth fraction in (0, 1].
kernel	Kernel choice (see htdv_lrv).
sims	Number of Monte Carlo draws for the critical-value simulation.
alpha	Significance level.
seed	Optional integer seed for reproducibility. NULL leaves the user's RNG state untouched.

Value

A list with statistic, critical_value, p_value, reject, bandwidth, and kernel.

References

Kiefer, N.M., & Vogelsang, T.J. (2005). A New Asymptotic Theory for Heteroskedasticity-Autocorrelation Robust Tests. Econometric Theory 21(6): 1130-1164.

Examples

x <- arima.sim(model = list(ar = 0.5), n = 200, rand.gen = rnorm)
htdv_fixedb(as.numeric(x), theta0 = 0, B = 0.2, sims = 1000, seed = 1)$p_value

---

Long-Run Variance Estimation (HAC)

Description

Heteroskedasticity-and-autocorrelation-consistent long-run variance with data-driven Andrews (1991) optimal bandwidth, Bartlett, Parzen, and Quadratic-Spectral kernels.

Usage

htdv_lrv(
  x,
  kernel = c("bartlett", "parzen", "qs"),
  bandwidth = "andrews",
  prewhiten = FALSE
)

Arguments

x	Numeric vector of observations.
kernel	Kernel choice: "bartlett", "parzen", or "qs" (Quadratic-Spectral).
bandwidth	Either "andrews" (data-driven) or a positive numeric scalar.
prewhiten	Logical; if TRUE, AR(1) prewhiten-recolor (Andrews-Monahan 1992).

Value

A list with components lrv (long-run variance estimate), bandwidth, kernel, and ar_coef (only if prewhitened).

References

Andrews, D.W.K. (1991). Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation. Econometrica 59(3): 817-858. Newey, W.K. & West, K.D. (1987). A Simple, Positive Semi-Definite Heteroskedasticity and Autocorrelation Consistent Covariance Matrix. Econometrica 55(3): 703-708.

Examples

set_seed_user <- 42
x <- arima.sim(model = list(ar = 0.6), n = 200, rand.gen = rnorm)
out <- htdv_lrv(as.numeric(x), kernel = "qs", bandwidth = "andrews")
out$lrv

---

Posterior-Predictive Checks on Dependence Statistics

Description

Replicates autocorrelation, Ljung-Box, spectral discrepancy, and a detrended-fluctuation Hurst exponent under the posterior and computes posterior-predictive p-values.

Usage

htdv_ppc(fit, x_obs, lag_max = 10L)

Arguments

fit	An htdv_fit object whose posterior-predictive replicates are stored as parameter x_rep.
x_obs	The observed data vector.
lag_max	Maximum lag for autocorrelation.

Value

A list with p_acf, p_ljung_box, p_spectral, p_hurst.

Examples

x <- rnorm(50)
fit <- htdv_fit(x, model = "tac", chains = 2, iter = 500,
                refresh = 0, seed = 1)
htdv_ppc(fit, x)

---

Region-of-Practical-Equivalence (ROPE) Decision

Description

Posterior decision under Kruschke's (2018) Region of Practical Equivalence.

Usage

htdv_rope(draws, rope, level = 0.95)

Arguments

draws	Numeric vector of posterior draws of the parameter of interest.
rope	Length-2 numeric vector c(lower, upper) defining the practical-equivalence region.
level	Credibility level for the highest-density interval.

Value

A list with decision ("accept", "reject", "undecided"), hdi, rope, and prob_in_rope.

References

Kruschke, J.K. (2018). Rejecting or Accepting Parameter Values in Bayesian Estimation. Advances in Methods and Practices in Psychological Science 1(2): 270-280.

Examples

draws <- rnorm(4000, mean = 0.05, sd = 0.1)
htdv_rope(draws, rope = c(-0.1, 0.1), level = 0.95)$decision

---

Aggregated Output of the HTDV Factorial Simulation Study

Description

Sign-corrected aggregated results of the factorial Monte Carlo study described in Section 12-bis of the companion paper. The study crosses five factors at four levels each (sample size, AR(1) coefficient, innovation tail, imbalance ratio, location shift) for 1024 cells, each replicated 500 times against three inferential layers (HAR, bootstrap, hierarchical Bayesian). One cell (n=500, phi=0.85, t3, imb=1, delta=0) was lost to an I/O collision and is excluded; the table contains 1023 cells x 3 layers = 3069 rows.

Usage

htdv_sim_summary

Format

A data frame with one row per (cell, layer) and the following columns:

n

Per-group primary sample size (40, 80, 200, 500).

phi

AR(1) coefficient (0, 0.3, 0.6, 0.85).

tail

Innovation distribution: "normal", "t5", "t3", "t2_1".

imb

Imbalance ratio n1/n2 (1, 1.5, 3, 6).

delta

Location shift in units of sigma_inf (0, 0.1, 0.25, 0.5).

layer

Inferential layer: "har", "boot", "bayes".

n_reps

Number of replications aggregated (500 for all cells).

reject_rate

Empirical rejection rate at nominal alpha = 0.05.

coverage

Fraction of replications whose 95% interval covered the true parameter (sign-corrected for HAR and bootstrap).

mean_ci_length

Average length of the 95% interval.

mean_runtime

Mean per-replication runtime in seconds.

diag_pass_rate

Fraction of replications passing all HMC diagnostic gates (Bayesian layer only; NA otherwise).

Source

Generated by run_simstudy.R of the companion paper repository on master seed 20260422, with sign-corrected coverage produced by recover_coverage.R. Total wall-clock 31.1 hours on a 16-core Linux workstation. See vignette("HTDV-validation") for the full report.

---

Factorial Monte Carlo Simulation Study for Dependent-Unbalanced Data

Description

Runs the pre-registered factorial Monte Carlo study of Section 12-bis of the companion paper. The study crosses four factors (per-group sample size, AR(1) coefficient, innovation tail, imbalance ratio) and evaluates three inferential layers (HAR-Wald, stationary block bootstrap, hierarchical Bayesian HMC) on each replication.

Usage

htdv_simstudy(
  n_grid = c(40L, 80L, 200L, 500L),
  phi_grid = c(0, 0.3, 0.6, 0.85),
  tail_grid = c("normal", "t5", "t3", "t2_1"),
  imb_grid = c(1, 1.5, 3, 6),
  delta_grid = c(0, 0.1, 0.25, 0.5),
  R = 500L,
  seed = 20260422L,
  n_cores = 1L,
  layers = c("har", "boot", "bayes"),
  bayes_chains = 2L,
  bayes_iter = 600L,
  bayes_warmup = 300L,
  boot_R = 999L,
  rope = c(-0.1, 0.1),
  alpha = 0.05,
  out_dir = NULL,
  progress = TRUE
)

Arguments

n_grid	Integer vector of primary sample sizes $n_1$.
phi_grid	Numeric vector of AR(1) coefficients in $(-1,1)$.
tail_grid	Character vector; any subset of "normal", "t5", "t3", "t2_1".
imb_grid	Numeric vector of imbalance ratios $n_1/n_2$.
delta_grid	Numeric vector of location shifts in units of $\sigma_\infty$.
R	Integer number of Monte Carlo replications per cell.
seed	Integer master seed.
n_cores	Integer number of workers for cell-level parallelism. On non-Unix platforms parallelism falls back to serial.
layers	Character vector; any subset of c("har","boot","bayes").
bayes_chains	Number of HMC chains per Bayesian fit.
bayes_iter	Total HMC iterations (warmup + sampling).
bayes_warmup	HMC warmup iterations.
boot_R	Bootstrap replicates per call.
rope	Length-2 numeric vector; ROPE for the Bayesian decision on the raw (non-standardized) delta.
alpha	Significance level (nominal size of tests; $1-\alpha$ is the coverage target for intervals).
out_dir	Optional directory for per-cell incremental RDS results. Each cell is written to its own cell_<id>.rds so that concurrent workers cannot collide on a shared file. Final aggregation reads the directory back, so successful cells are preserved even if some workers later die. If NULL, no per-cell artifacts are written and the only result is the in-memory return value.
progress	Logical; print a one-line status per completed cell.

Value

A data frame with one row per (cell, replication, layer). Columns: cell_id, n, phi, tail, imb, n1, n2, delta, sigma_inf, layer, replicate, reject, ci_lo, ci_hi, estimate, covered, ci_length, rhat_max, ess_min, divergences, diag_pass, runtime_sec.

Data-generating process

Two independent AR(1) series $x^{(1)}_t$ of length $n_1=n$ and $x^{(2)}_t$ of length $n_2 = \max(2, \mathrm{round}(n / \mathrm{imb}))$ are generated. The innovations are drawn from rnorm, scaled Student-$t_{(5)}$, scaled Student-$t_{(3)}$ or scaled Student-$t_{(2.1)}$ so that the nominal innovation variance is one when the law has a finite second moment. Group one has mean zero; group two has mean $\Delta\cdot\sigma_\infty$ where $\sigma_\infty = 1/\sqrt{1 - \phi^2}$.

Inferential layers

• HAR-Wald ("har"). Welch-style two-sample statistic $z = (\bar x_1 - \bar x_2) / \sqrt{\hat\sigma_1^2/n_1 + \hat\sigma_2^2/n_2}$ with long-run variances estimated via htdv_lrv (QS kernel, Andrews bandwidth) on each group's demeaned series. Rejection at asymptotic $\chi^2_1$ critical value.

• Stationary block bootstrap ("boot"). Each group resampled independently using htdv_boot with block_length = "auto" (Patton- Politis-White). Percentile interval on $\bar x_1^* - \bar x_2^*$.

• Hierarchical Bayesian ("bayes"). Two-sample AR(1) Stan model (simstudy_two_sample.stan); posterior interval on $\delta = \alpha_2 - \alpha_1$. A run is flagged diag_pass = TRUE only if $\hat R < 1.01$, bulk and tail ESS above $200$, and zero divergences.

References

Kiefer, N.M., & Vogelsang, T.J. (2005). Econometric Theory 21(6): 1130-1164. Patton, A., Politis, D.N., & White, H. (2009). Econometric Reviews 28(4): 372-375. Kruschke, J.K. (2018). Advances in Methods and Practices in Psychological Science 1(2): 270-280.

Examples

res <- htdv_simstudy(n_grid = c(40, 80),
                     phi_grid = c(0, 0.6),
                     tail_grid = c("normal"),
                     imb_grid = c(1, 3),
                     delta_grid = c(0, 0.25),
                     R = 5L, n_cores = 1L,
                     layers = c("har", "boot"))
head(htdv_simstudy_summary(res))

---

Aggregate a Simulation-Study Output

Description

Computes empirical size (or rejection rate), coverage, and mean interval length per (cell x layer) from the raw output of htdv_simstudy.

Usage

htdv_simstudy_summary(res, alpha = 0.05)

Arguments

res	Data frame returned by htdv_simstudy.
alpha	Nominal size used in the study (must match what htdv_simstudy was called with).

Value

A data frame with one row per (cell, layer) and columns n, phi, tail, imb, delta, layer, n_reps, reject_rate, coverage, mean_ci_length, mean_runtime, diag_pass_rate.

Examples

res <- htdv_simstudy(n_grid = c(40), phi_grid = c(0.3),
                     tail_grid = "normal", imb_grid = 1,
                     delta_grid = c(0, 0.3), R = 5,
                     layers = c("har"))
htdv_simstudy_summary(res)

---

Flag Simulation-Study Cells in the Limit-of-Identification Zone

Description

Reads an aggregated htdv_simstudy_summary output and returns the subset of cells where the Bayesian diagnostic-pass rate falls below a user-set threshold. Such cells are typically located in the corner of the design where strong autocorrelation meets a small sample (high $\phi$ and low $n$); the AR(1) likelihood there approaches its limit of identification, MCMC diagnostics flag the resulting posterior, and practitioners should treat the cell with extra caution—either by increasing HMC iterations, tightening the priors on $\phi$, or falling back to the conformal anchor whose validity does not require identifiability.

Usage

htdv_simstudy_warnings(summ, threshold = 0.7)

Arguments

summ	Data frame from htdv_simstudy_summary.
threshold	Minimum acceptable Bayesian diag_pass_rate. Default 0.7.

Value

A data frame with the columns n, phi, tail, imb, delta, layer, diag_pass_rate, restricted to Bayesian rows whose pass rate is below threshold, plus an integer column flag_index (sequential identifier of flagged cells, useful for cross-referencing in reports and in vignettes).

Examples

res <- htdv_simstudy(n_grid = c(40, 200),
                     phi_grid = c(0, 0.85),
                     tail_grid = "normal",
                     imb_grid = c(1, 6),
                     delta_grid = c(0, 0.25),
                     R = 50L)
summ <- htdv_simstudy_summary(res)
htdv_simstudy_warnings(summ, threshold = 0.7)

---

Predictive Stacking of Bayesian Models

Description

Computes stacking weights (Yao, Vehtari, Simpson, Gelman 2018) across a list of fitted models by LOO-log-score maximization.

Usage

htdv_stack(fits, method = c("log_score"))

Arguments

fits	Named list of htdv_fit objects.
method	Stacking objective. Only "log_score" supported in this release.

Value

A list with weights, model_names, and elpd_per_model.

Examples

if (requireNamespace("loo", quietly = TRUE)) {
  x <- rnorm(50)
  f1 <- htdv_fit(x, model = "tac", chains = 2, iter = 500,
                 refresh = 0, seed = 1)
  f2 <- htdv_fit(x, model = "wsc", chains = 2, iter = 500,
                 refresh = 0, seed = 2)
  htdv_stack(list(tac = f1, wsc = f2))$weights
}

---

Print-Friendly Summary for an HTDV Fit

Description

Print-Friendly Summary for an HTDV Fit

Usage

htdv_summary(fit, rope = NULL, target = "theta")

Arguments

fit	An htdv_fit object.
rope	Optional two-element vector for ROPE decision on the target.
target	Parameter name to summarize.

Value

A data frame with posterior mean, sd, 2.5%, 50%, 97.5%, Rhat, bulk and tail ESS for target, plus the ROPE decision if requested.

Examples

x <- rnorm(50)
fit <- htdv_fit(x, model = "tac", chains = 2, iter = 500,
                refresh = 0, seed = 1)
htdv_summary(fit, target = "theta")

---

WAIC and Leave-Future-Out Cross-Validation

Description

Computes the Widely Applicable Information Criterion (Watanabe 2010) and leave-future-out expected log predictive density (Buerkner-Gabry-Vehtari 2020) from a fitted htdv_fit object.

Usage

htdv_waic_lfo(fit, L = NULL, k_threshold = 0.7)

Arguments

fit	An htdv_fit object with pointwise log-likelihood stored as parameter log_lik.
L	Block-prefix length; leave-future-out starts at time L+1. Default floor(n/5).
k_threshold	Pareto-k refresh threshold; when exceeded, importance sampling is refreshed.

Value

A list with waic, elpd_lfo, elpd_se, pareto_k, and refresh_times.

References

Watanabe, S. (2010). Asymptotic Equivalence of Bayes Cross Validation and Widely Applicable Information Criterion. JMLR 11: 3571-3594. Buerkner, P.-C., Gabry, J., & Vehtari, A. (2020). Approximate Leave-Future-Out Cross-Validation for Bayesian Time Series Models. Journal of Statistical Computation and Simulation 90(14): 2499-2523.

Examples

if (requireNamespace("loo", quietly = TRUE)) {
  x <- rnorm(50)
  fit <- htdv_fit(x, model = "tac", chains = 2, iter = 500,
                  refresh = 0, seed = 1)
  htdv_waic_lfo(fit)$waic
}

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Whittle Likelihood for Stationary Series

Description

Computes the Whittle pseudo-log-likelihood at Fourier frequencies for a user-supplied spectral density.

Usage

htdv_whittle(x, spec_fun, theta, taper = FALSE)

Arguments

x	Numeric vector.
spec_fun	Function function(lambda, theta) returning spectral density values at angular frequencies lambda.
theta	Numeric parameter vector passed to spec_fun.
taper	Logical; if TRUE, a 10-percent cosine taper is applied.

Value

A list with loglik (scalar), frequencies, periodogram, and fitted_spectrum.

References

Whittle, P. (1953). Estimation and Information in Stationary Time Series. Arkiv foer Matematik, 2(5), 423-434. Dzhaparidze, K. (1986). Parameter Estimation and Hypothesis Testing in Spectral Analysis of Stationary Time Series. Springer.

Examples

x <- arima.sim(model = list(ar = 0.5), n = 200, rand.gen = rnorm)
ar1_spec <- function(lambda, theta) {
  phi <- theta[1]; sigma2 <- theta[2]
  sigma2 / (2 * pi * (1 - 2 * phi * cos(lambda) + phi^2))
}
htdv_whittle(as.numeric(x), ar1_spec, c(0.5, 1))$loglik

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