Type: Package
Title: Wavelet Functional ANOVA Through Markov Groves
Version: 1.1.1
Date: 2023-12-09
Author: Jacopo Soriano and Li Ma
Maintainer: Li Ma <li.ma@duke.edu>
Description: Functional denoising and functional ANOVA through wavelet-domain Markov groves. Fore more details see: Ma L. and Soriano J. (2018) Efficient functional ANOVA through wavelet-domain Markov groves. <doi:10.48550/arXiv.1602.03990>.
License: GPL (≥ 3)
Imports: methods, Rcpp (≥ 0.11.2), wavethresh
LinkingTo: Rcpp, RcppArmadillo
NeedsCompilation: yes
Packaged: 2023-12-10 01:41:20 UTC; lm186
Repository: CRAN
Date/Publication: 2023-12-10 08:30:02 UTC

grove: A package for functional denoising and functional ANOVA

Description

The grove package implements a wavelet-domain Bayesian hierarchical model for functional analysis of variance.

Discrete wavelet transform

Description

This function performs the discrete wavelet transform (DWT) according to Mallat's pyramidal algorithm (Mallat, 1989).

Usage

DWT(data, filter.number = 10, family = "DaubLeAsymm")

Arguments

data

A matrix of data, where each row is an observation. The number of columns must be a power of two.

filter.number

The smoothness of the wavelet to use in the decomposition.

family

The family of wavelets. The two most common options are DaubExPhase and DaubLeAsymm.

Details

See function wd from package wavethresh for more details.

Value

A DWT object. This object is a list with the following components:

Examples

data <- GenerateSyntheticAnova(st.dev = 5, n.replicates = 10)
W <- DWT(data$noisy.Y)

Bayesian wavelet denoising

Description

This function carries out Bayesian wavelet denoising using the Normal Inverse Gamma Markov Tree method of Ma and Soriano (2016).

Usage

Denoise(W, alpha = 0.5, nu = 5, n.samples = 500,
  transition.mode = "Markov", method = "Nelder-Mead")

Arguments

W

An object of class DWT.

alpha

Hyperparameter controlling the global smoothness.

nu

Hyperparameter controlling variance heterogeneity. If Inf, then the variance is identical for all nodes.

n.samples

Number of posterior draws.

transition.mode

Type of transition. The two options are Markov or Independent.

method

Method used for find maxmimum of marginal likelihood.

Value

An object of class grove.

References

Ma L. and Soriano J. (2016) Efficient functional ANOVA through wavelet-domain Markov groves. arXiv:1602.03990v2 [stat.ME] (https://arxiv.org/abs/1602.03990v2).

Examples

data <- wavethresh::DJ.EX(n = 512, noisy = TRUE, rsnr = 5)$doppler
W <- DWT(data)
ans <- Denoise(W)

Bayesian functional ANOVA

Description

This function carries out Bayesian functional ANOVA using the Normal Inverse Gamma Markov Grove method of Ma and Soriano (2016).

Usage

FAnova(W, X, formula, nu = 5, is.kappa.fixed = FALSE, gamma.kappa = 0.3,
  eta.kappa = 0.1, n.samples = 500, transition.mode = "Markov",
  method = "Nelder-Mead")

Arguments

W

An object of class DWT.

X

Design matrix.

formula

An object of class formula.

nu

Hyperparameter controlling the heterogeneity in the noise variance.

is.kappa.fixed

If TRUE, gamma.kappa and eta.kappa are fixed. If FALSE gamma_kappa and eta_kappa are determined using Empirical Bayes.

gamma.kappa

Hyperparameter for the MT transition matrix.

eta.kappa

Hyperparameter for the MT transition matrix.

n.samples

Number of posterior draws.

transition.mode

Type of transition. The two options are Markov or Independent.

method

Method used for find maxmimum of marginal likelihood.

Value

An object of class grove.

References

Ma L. and Soriano J. (2016) Efficient functional ANOVA through wavelet-domain Markov groves. arXiv:1602.03990v2 [stat.ME] (https://arxiv.org/abs/1602.03990v2).

Examples

## Not run: 
data <- GenerateSyntheticAnova(st.dev = 5, n.replicates = 5)
W <- DWT(data$noisy.Y)
X <- data$X
ans <- FAnova(W, X, ~ 1 + factorA + factorB)
denoised.data <- InvDWT(ans, x = c(0, 0, 1, 0))
PlotFun(denoised.data)
## End(Not run)

Generate synthetic functional ANOVA dataset

Description

This function generates a synthetic 3-factor functional ANOVA dataset.

Usage

GenerateSyntheticAnova(st.dev = 10, n.replicates = 5)

Arguments

st.dev

The standard deviation of the error.

n.replicates

The number of replicates for each factor combination.

Value

A list containing the data without noise, the data with noise, and the design matrix.

Examples

data <- GenerateSyntheticAnova(st.dev = 5, n.replicates = 10)
ix <- 1
plot(data$clean.Y[ix, ], type = "l", col = "red", ylab = "")
lines(data$noisy.Y[ix, ], col = "blue")

Inverse discrete wavelet transform

Description

This function performs the inverse discrete wavelet transform.

Usage

InvDWT(grove.obj, x = NULL, include.C = TRUE, sample.C = FALSE)

Arguments

grove.obj

An object of class grove.

x

A vector of the values of a predictor.

include.C

If TRUE, C is used for reconstructing the function.

sample.C

If TRUE, draws from C are used for recontructing the function.

Value

A matrix with each row representing a draw from the reconstructed signal.

Examples

data <- wavethresh::DJ.EX(n = 512, noisy = TRUE, rsnr = 5)$doppler
W <- DWT(data)
ans <- Denoise(W)
denoised.data <- InvDWT(ans)
plot(data, type = "l")
lines(denoised.data[1, ], col = "red")

Function to plot the denoised signal

Description

This function plots the credible bounds of the denoised signal.

Usage

PlotFun(data, p = c(0.025, 0.5, 0.975), band.type = "pointwise",
  main = "", col = "blue", type = "l", ylab = "", xlab = "",
  ylim = NULL)

Arguments

data

Matrix of posterior samples.

p

Vector with the lower, center and upper quantile.

band.type

Type of credible intervals. The options are: pointwise, gloabl or global.

main

The main title of the plot.

col

The color of the point estimate.

type

The type of line of the point estimate.

ylab

The label of the y-axis.

xlab

The label of the x-axis.

ylim

The range of the y-axis.

Value

A plot.

Examples

data <- wavethresh::DJ.EX(n = 512, noisy = TRUE, rsnr = 5)$doppler
W <- DWT(data)
ans <- Denoise(W)
denoised.data <- InvDWT(ans)
PlotFun(denoised.data)
PlotFun(denoised.data, band.type = "both")

Function to plot the hidden states

Description

This function plots on a tree the state of each latent variables.

Usage

PlotStates(grove.obj, block = "Intercept", legend = FALSE, main = NULL,
  prior = FALSE)

Arguments

grove.obj

Output from function FAnova.

block

Which block to plot.

legend

If TRUE, show legend.

main

Main title.

prior

If TRUE, plot prior state probabilities. If FALE, plot posterior state probabilities.

Value

A plot.

Examples

## Not run: 
data <- GenerateSyntheticAnova(st.dev = 5, n.replicates = 5)
W <- DWT(data$noisy.Y)
X <- data$X
ans <- FAnova(W, X, ~ 1 + factorA + factorB)
PlotStates(ans)
PlotStates(ans, block = "factorA")
PlotStates(ans, block = "factorB")
## End(Not run)