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#' Bayesian wavelet denoising
#'
#' This function carries out Bayesian wavelet denoising using the Normal
#' Inverse Gamma Markov Tree method of Ma and Soriano (2016).
#'
#' @param W An object of class \code{DWT}.
#' @param alpha Hyperparameter controlling the global smoothness.
#' @param nu Hyperparameter controlling variance heterogeneity. If \code{Inf},
#' then the variance is identical for all nodes.
#' @param n.samples Number of posterior draws.
#' @param transition.mode Type of transition.
#' The two options are \code{Markov} or \code{Independent}.
#' @param method Method used for find maxmimum of marginal likelihood.
#'
#' @return An object of class \code{grove}.
#' @references Ma L. and Soriano J. (2016) Efficient functional ANOVA
#' through wavelet-domain Markov groves. arXiv:1602.03990v2 [stat.ME]
#' (\url{https://arxiv.org/abs/1602.03990v2}).
#' @export
#' @examples
#' data <- wavethresh::DJ.EX(n = 512, noisy = TRUE, rsnr = 5)$doppler
#' W <- DWT(data)
#' ans <- Denoise(W)
Denoise <- function(W,
alpha = 0.5,
nu = 5,
n.samples = 500,
transition.mode = "Markov",
method = "Nelder-Mead") {
frml <- formula(~ 1)
X <- data.frame(rep(1, nrow(W$D)))
output <- .groveEB.all.random(W = W,
formula = frml,
X = X,
alpha = alpha,
nu = nu,
eta.rho = .InitEtaRhoPar(),
eta.kappa = .InitEtaKappaPar(),
gamma.rho = .InitGammaRhoPar(),
gamma.kappa = .InitGammaKappaPar(),
n.samples = n.samples,
verbose = FALSE,
transition.mode = transition.mode,
method = method)
return(output)
}
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