Package 'grove' reference manual

Package 'grove'

Title:	Wavelet Functional ANOVA Through Markov Groves
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. <arXiv:1602.03990v2 [stat.ME]>.
Authors:	Jacopo Soriano and Li Ma
Maintainer:	Li Ma <[email protected]>
License:	GPL (>= 3)
Version:	1.1.1
Built:	2024-11-05 03:56:14 UTC
Source:	https://github.com/cran/grove

Title:

Wavelet Functional ANOVA Through Markov Groves

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. <arXiv:1602.03990v2 [stat.ME]>.

Authors:

Jacopo Soriano and Li Ma

Maintainer:

Li Ma <[email protected]>

License:

GPL (>= 3)

Version:

1.1.1

Built:

2024-11-05 03:56:14 UTC

Source:

https://github.com/cran/grove

Help Index

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

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

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")
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)
## 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)
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")
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")

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.

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