A sampling algorithm for HBEST

HBEST is an MCMC algorithm that samples parameter values for HBEST.

Usage

HBEST(
  ts_list,
  B,
  iter,
  burnin,
  sigmasquared_glob = 100,
  sigmasquared_loc = 0.1,
  nu_tau = 2,
  tausquared = 10,
  nu_zeta = 5,
  zeta_min = 1.001,
  zeta_max = 15,
  tau_min = 0.001,
  tau_max = 100,
  num_gpts = 1000
)

Arguments

ts_list: A list R long containing the vectors of the stationary time series of potentially different lengths.
B: An integer specifying the number of basis coefficients (not including the intercept basis coefficient \(\beta_0\)).
iter: An integer specifying the number of iterations for the MCMC algorithm embedded in this function.
burnin: An integer specifying the burn-in to be removed at the end of the sampling algorithm.
sigmasquared_glob: A scalar specifying the variance of the prior (N(0,sigmasquared_glob)) intercept term for \(\beta^{glob}_0\). (default is 100 to ensure a diffuse prior).
sigmasquared_loc: A scalar specifying the variance of the prior (N(0,sigmasquared_loc)) intercept term for \(\beta^{loc}_0\). (default is 0.1).
nu_tau: A scalar indicating the degrees of freedom for the prior on \(\tau\). (default is 2).
tausquared: A scalar used as the initial value of tausquared that controls the global smoothing effect. (default is 10).
nu_zeta: A scalar indicating the degrees of freedom for the prior on \(\zeta\). (default is 5).
zeta_min: A scalar controlling the smallest value \(\zeta\) can take. So, zeta_min^2 is the smallest value zetasquared can take. (default is 1.001).
zeta_max: A scalar controlling the largest value \(\zeta\) can take. So, zeta_max^2 is the largest value that zetasquared can take. (default is 15).
tau_min: A scalar controlling the smallest value \(\tau\) can take. So, tau_min^2 is the smallest value tausquared can take. (default is 0.001).
tau_max: A scalar controlling the largest value \(\tau\) can take. So, tau_max^2 is the largest value tausquared can take. (default is 100).
num_gpts: A scalar controlling the denseness of the grid during the sampling of both tausquared and zetasquared. (default is 1000).

Value

A list object with components:

`beta_loc_est`	returns a `(iter - burnin` \(\times\) `B+1` \(\times\) `R)` array of \(\beta^{loc}_{br}\) estimates.
`beta_glob_est`	returns a `(iter - burnin` \(\times\) `B+1)` array of \(\beta^{glob}_{b}\) estimates.
`zetasquared_est`	returns a `(iter - burnin` \(\times\) `R)` array of \(\zeta^{2}_{r}\) estimates.
`tausquared_est`	returns a `(iter - burnin` \(\times\) `1)` array of \(\tau^{2}\) estimates.
`perio_list`	returns an `R` list of column matrices each storing a truncated/half periodogram.
`omega`	returns an `R` list of column matrices each storing \(\omega_{j}\) see paper in references for details.
`D`	returns a `B` vector that stores the prior variance for \(\beta_{1}\) through \(\beta_{B}\).

References

Lee R, Coulter A, Siegle GJ, Bruce SA, Bhattacharya A (2025). “Hierarchical Bayesian spectral analysis of multiple stationary time series.” doi:10.48550/ARXIV.2511.19406 , Version Number: 1, https://arxiv.org/abs/2511.19406.

Examples

# To view the full explanation and examples, run:
if (FALSE) { # \dontrun{
vignette("HBEST_tutorial", package = "HBEST")} # }