Proportion Functions

Description

An example Bernoulli proportion function.

Usage

Blocks(x)

Arguments

Details

A proportion function based on the blocks function of Donoho, or that of Antoniadis and LeBlanc (2000). The extra “r" versions of these functions are reflected at the right endpoint.

Value

Author(s)

Matt Nunes (m.nunes@ucl.ac.uk)

References

Antoniadis, A. and LeBlanc, F. (2000) Nonparametric wavelet regression for binary response. Statistics, 34, 183–213.

Examples

t<-seq(0,1,length=256)

y<-Blocks(t)

plot(t,y, type="l")

NN and Anscombe samples

Description

Samples binomial Fisz and Anscombe transformed random variables on a grid of binomial probabilities.

Usage

afgen(xgrid = seq(0, 1, length = 21), ygrid = seq(0, 1, length = 21), samples = 1000, 
binsize = 32)

Arguments

Details

The function produces sampled values from the random variable:

\zeta(X_1,X_2)=\frac{X_1-X_2}{ \sqrt{ (X_1+X_2)(2*binsize-X_1-X_2)/ 2*binsize }} ,

where X_i are Bin(binsize,p_i) random variables, for all combinations of values of p_1 in xgrid and p_2 in ygrid. For Anscombe's transformation, A=sin^{-1}\sqrt{(x+3/8)/(binsize+3/4)}, the values correspond to the random variable with the larger binomial probability.

Value

Author(s)

Matt Nunes (m.nunes@ucl.ac.uk)

References

Anscombe, F.J. (1948) The transformation of poisson, binomial and negative binomial Data, Biometrika,35, 246–254.
Nunes, M. and Nason, G.P. (2009) A multiscale variance stabilization for binomial sequence proportion estimation. Statistica Sinica, 19 (1491–1510).

See Also

ansc

Examples

##
varvalues<-afgen(xgrid=seq(0,1,length=21),ygrid=seq(0,1,length=21),samples=1000,binsize=32)

##creates 1000 samples of the two random variables zeta_B and A for each point 
##(x,y) for x and y regularly-spaced probability vectors of length 21.
##

Anscombe transformation

Description

Does Anscombe's inverse sine transformation on a vector input.

Usage

ansc(x, binsize)

Arguments

Details

Performs the Anscombe calculation: A=sin^{-1}\sqrt{(x+3/8)/(binsize+3/4)}.

Value

Author(s)

Matt Nunes (m.nunes@ucl.ac.uk)

References

Anscombe, F.J. (1948) The transformation of poisson, binomial and negative binomial data. Biometrika, 35, 246-254.

See Also

afgen, hfdenoise, hfdenoise.wav, link{invansc}

Examples

#generate binomial data:

x<-rbinom(100,10,.5)

y<-ansc(x,10)

#this is now the transformed data.

Asymptotic mean calculation

Description

This function gives values for the asymptotic mean of the new binomial Fisz random variable for a grid of bivariate proportion values.

Usage

asymean(xgrid = seq(0, 1, length = 21), ygrid = seq(0, 1, length = 21), binsize = 32)

Arguments

Details

See afgen for an explanation of the computation.

Value

Author(s)

Matt Nunes (m.nunes@ucl.ac.uk)

References

Fisz, M. (1955), The Limiting Distribution of a Function of Two Independent Random Variables and its Statistical Application, Colloquium Mathematicum, 3, 138–146.

See Also

asyvar, afgen

Examples

means<-asymean(xgrid=seq(0,1,length=21),ygrid=seq(0,1,length=21),binsize=32)

## this produces a 21x21 matrix for an equally-spaced grid of binomial proportions. 

Asymptotic variance function

Description

This function gives values for the asymptotic mean of the new binomial Fisz random variable.

Usage

asyvar(xgrid = seq(0, 1, length = 21), ygrid = seq(0, 1, length = 21))

Arguments

Details

Due to the form of the asymptotic variance for equal binomial sizes, this does not need a specification of the binomial size binsize (see asymean).

Value

Author(s)

Matt Nunes (m.nunes@ucl.ac.uk)

References

Fisz, M. (1955), The Limiting Distribution of a Function of Two Independent Random Variables and its Statistical Application, Colloquium Mathematicum, 3, 138–146.

See Also

asymean, statgen

Examples

variance<-asyvar(xgrid=seq(0,1,length=21),ygrid=seq(0,1,length=21))

## this produces a 21x21 matrix for an equally-spaced grid of binomial proportions. 

Binomial Haar-Fisz wavelet transform

Description

Forward Haar-Fisz transform for binomial random variables.

Usage

binhf.wd(x, binsize = 1,print.info=FALSE)

Arguments

Details

The procedure performs the Haar wavelet transform on the data x, and then modifies the wavelet coefficients by f_jk=d_jk/\sqrt{c_jk*(N-c_jk)/2N}. The inverse Haar transform is then performed. This modification will stabilize the variance of the resulting vector.

Value

Author(s)

Matt Nunes (m.nunes@ucl.ac.uk)

References

Nunes, M.A. and Nason, G.P. (2009) A Multiscale Variance Stabilization for binomial sequence proportion estimation, Statistica Sinica, 19(4), 1491-1510.

See Also

invbinhf.wd

Examples

x<-rbinom(256,32,.35)

y<-binhf.wd(x,32)

DNA datasets

Description

Example DNA sequences.

Usage

data(chr20)

Details

The datasets are the chromosome 20 sequence of the human genome, and the mhc dataset available from the Human Genome Project website, binary-coded by base pair content and curtailed to a power of two.

Source

http://www.sanger.ac.uk

Modified EbayesThresh wavelet thresholding function

Description

Modified EbayesThresh functions.

Details

For help on these function, see the original help file supplied with the WaveThresh package. There is a modification to try and avoid zero noise standard deviation estimation.

Freeman-Tukey transform

Description

Does Freeman-Tukey average inverse sine transformation on a vector input.

Usage

free(x, n)

Arguments

Value

Author(s)

Matt Nunes (m.nunes@ucl.ac.uk)

References

Freeman, M. F. and Tukey, J. W. (1950) Transformations related to the angular and the square root. Ann. Math. Stat., 21, 607–611.

See Also

freeinv

Examples

#generate binomial data:

x<-rbinom(100,10,.5)

y<-free(x,10)

#this is now the transformed data.

Inverse Freeman-Tukey transform

Description

Does the inverse of the Freeman-Tukey inverse sine transformation on a vector input.

Usage

freeinv(y, n)

Arguments

Value

Author(s)

Matt Nunes (m.nunes@ucl.ac.uk)

References

Freeman, M. F. and Tukey, J. W. (1950) Transformations related to the angular and the square root. Ann. Math. Stat., 21, 607–611.

See Also

free

Examples

#generate binomial data:

x<-rbinom(100,10,.5)

y<-free(x,10)

x1<-freeinv(y,10)

#this should be the original data.

Haar-NN inverse transform

Description

Inverse Haar-NN transform for binomial random variables ("in-place").

Usage

hf.inv2(data, binsize = 1)

Arguments

Details

The procedure performs the inverse "in-place" Haar-NN wavelet transform on the data x.

Author(s)

Matt Nunes (m.nunes@ucl.ac.uk)

References

Nunes, M.A. and Nason, G.P. (2009) A Multiscale Variance Stabilization for binomial sequence proportion estimation, Statistica Sinica,19 (4), 1491–1510.

See Also

invbinhf.wd

Simulation function

Description

Proportion estimation procedure for simulations.

Usage

hfdenoise(n = 256, proportion = P2, binsize = 1, thrule = "ebayesthresh",
    van = 8, fam = "DaubLeAsymm", pl = 3, prior = "laplace", vscale = "independent", 
plotstep = FALSE, truncate = FALSE, ...)

Arguments

Details

This function creates a regularly-spaced vector on the unit interval of length length, and uses these values to create corresponding values using the proportion function. These values are then used as binomial probabilities to sample "observed" binomial random variables. The observation vector is then denoised using a wavelet transform defined by the arguments pl, van, fam with thresholding method thrule. This denoising is done for both Anscombe and the Haar-Fisz method for binomial random variables. The procedure is repeated times times, and the resulting proportion estimates averaged.

Value

Author(s)

Matt Nunes (m.nunes@ucl.ac.uk)

See Also

simsij

Examples

sim<-hfdenoise()

plot(sim$x,sim$truep,type="l", xlab="",ylab="Binomial Proportion")

##^^ shows original proportion to estimate.

lines(sim$x,sim$fhat,col=2)
lines(sim$x,sim$fhata,col=3)

##^^shows the estimates of the proportion from the two transforms.

Denoising function

Description

Denoise algorithm for thresholding methods supplied with wavethresh.

Usage

hfdenoise.wav(x, binsize, transform = "binhf", meth = "u", van = 1, fam = "DaubExPhase", 
min.level = 3,coarse=FALSE)

Arguments

Details

The function pre and post-processes the observed data with either Anscombe's transform or the binomial Haar-Fisz transform, using a wavelet denoiser to smooth the data, specified by the inputs min.level, van and fam combined with the thresholding rule meth.If coarse is set to true, the first finest 11 coefficient levels are set to zero, corresponding to coefficients produced from 2^11= 2048 nucleotide bases.

Value

Note

This function requires the package wavethresh.

Author(s)

Matt Nunes (m.nunes@ucl.ac.uk)

See Also

hfdenoise

Examples

library(wavethresh)

#create a sample intensity vector:

int<-sinlog(seq(0,1,length=256))
x<-NULL
for(i in 1:256){
x[i]<-rbinom(1,1,int[i])
}


est<-hfdenoise.wav(x,1,transform="ansc","u",6,"DaubLeAsymm",3,FALSE) 

Forward Haar wavelet transform

Description

Forward Haar transform.

Usage

ht(x)

Arguments

Details

The procedure performs the Haar wavelet transform on the data x.

See Also

ht.inv

Examples

x<-rbinom(256,32,.35)
ht(x)

Inverse Haar-NN

Description

Inverse Haar transform for binomial random variables.

Usage

ht.inv(data)

Arguments

Details

The procedure performs the inverse Haar wavelet transform.

Value

References

Nunes, M.A. and Nason, G.P. (2009) A Multiscale Variance Stabilization for binomial sequence proportion estimation, Statistica Sinica,19 (4), 1491–1510.

See Also

ht2

Examples

x<-rbinom(256,32,.35)
hx<-ht2(x)
y<-ht.inv(x)

Inverse Anscombe transformation

Description

Does the inverse of Anscombe's inverse sine transformation on a vector input.

Usage

invansc(y, n)

Arguments

Value

Author(s)

Matt Nunes (m.nunes@ucl.ac.uk)

References

Anscombe, F.J. (1948) The transformation of poisson, binomial and negative binomial data. Biometrika, 35, 246-254.

See Also

ansc, hfdenoise, hfdenoise.wav

Examples

#generate binomial data:

x<-rbinom(100,10,.5)

y<-ansc(x,10)

x1<-invansc(y,10)

#this should be the original data.

Inverse Haar-NN transform

Description

Performs the inverse Haar-NN transform for binomial random variables.

Usage

invbinhf.wd(transformed, binsize = 1,print.info=FALSE)

Arguments

Details

The procedure performs the Haar wavelet transform on the data transformed, and then modifies the wavelet coefficients by d'_jk=d_jk*sqrt(c_jk(N-c_jk)/2N). The inverse Haar transform is then performed. This modification will stabilize the variance of the resulting vector.

Value

Note

This function requires the package wavethresh.

Author(s)

Matt Nunes (m.nunes@ucl.ac.uk)

References

Nunes, M.A. and Nason, G.P. (2009) “A Multiscale Variance Stabilization for binomial sequence proportion estimation", Statistica Sinica,19 (4), 1491–1510.

See Also

binhf.wd

Examples

x<-rbinom(256,32,.35)

y<-binhf.wd(x,32)

x1<-invbinhf.wd(y,32)

Euclidean norm

Description

Calculates the root squared error of two vectors.

Usage

norm(x,y)

Arguments

Value

Author(s)

Matt Nunes (m.nunes@ucl.ac.uk)

Examples

#generate data:

x<-y<-runif(100)

error<-norm(x,y)


#this is the difference between the vectors.

pintens

Description

An example binomial intensity vector.

Usage

data(pintens)

Format

The format is: num [1:1024] 0.278 0.278 0.278 0.278 0.278 ...

Details

The intensity is a vector of length 1024, based on a scaled ‘bumps’ function of Donoho and Johnstone.

Examples

data(pintens)
plot(pintens,type="l")

Plotting function

Description

Plotting function for proportion estimates procedure.

Usage

plotest(l, plot.it = FALSE, verbose = FALSE)

Arguments

Details

This function uses norm to compute errors for estimates produced by doall.

Value

Author(s)

Matt Nunes (m.nunes@ucl.ac.uk)

See Also

norm

Examples

sim<-hfdenoise()

plotest(sim)

Proportion estimation function

Description

Proportion estimation procedure for simulations.

Usage

propest.wav(proportion = P2, binsize=1,length = 256, times = 100, meth = "u", van = 6, 
fam = "DaubLeAsymm", min.level = 3)

Arguments

Details

This function creates a regularly-spaced vector on the unit interval of length length, and uses these values to create corresponding values using the proportion function. These values are then used as binomial probabilities to sample "observed" binomial random variables. The observation vector is then denoised using a wavelet transform defined by the arguments van, fam, min.level with thresholding method meth. This denoising is done for both Anscombe and the Haar-Fisz method for binomial random variables. The procedure is repeated times times, and the resulting proportion estimates averaged.

Value

Author(s)

Matt Nunes (m.nunes@ucl.ac.uk)

Examples

## Not run: 
sim<-propest.wav(proportion = P2, binsize=1,length = 256, times = 1000, meth = "u", 
van = 6, fam = "DaubLeAsymm", min.level = 4)

plot(sim$x,sim$y,type="l",xlab="",ylab="Binomial mean function")

##^^ shows original proportion to estimate.

lines(sim$x,sim$meanfhat,col=2)
lines(sim$x,sim$meanfhata,col=3)

##^^shows the estimates of the proportion from the two transforms.

## End(Not run)

Quantile generator

Description

A Q-Q value generator.

Usage

qqnormy(y)

Arguments

Details

This is an equivalent to qqnorm, but returning sorted values. See qqnorm.

Value

Author(s)

Matt Nunes (m.nunes@ucl.ac.uk)

See Also

qqstuff

Quantile-quantile information about Haar-NN and Anscombe samples

Description

A function to generate Q-Q plots (from simulations) for the Anscombe and (binomial) Haar-Fisz transforms.

Usage

qqstuff(intensity, binsize = 4, paths = 100, respaths = 1000, plot.q = FALSE, 
plot.sq = FALSE)

Arguments

Details

respaths paths are sampled from the mean intensity vector. From these, the first paths are used to generate Q-Q data, which are then averaged for the Q-Q plots. The original paths are used to calculate a squared residual vector corresponding to the mean intensity vector.

Value

qqinfo. A 8 component list of quantile and residual plot information.

Note

This function requires the package wavethresh. N.B. Since this function returns a lot of information, assign the output to a variable, to avoid printing endless information in the console.

Author(s)

Matt Nunes (m.nunes@ucl.ac.uk)

See Also

qqnormy

Examples

data(pintens)

a<-qqstuff(intensity=pintens,binsize=4,paths=100,respaths=100,plot.q=TRUE,plot.sq=TRUE)

#plots some interesting graphs.

Shift function

Description

This function shifts a vector input a certain number of places in the direction desired.

Usage

shift(v, places, dir = "right")

Arguments

Details

The function shifts the vector v by places in the direction of direction, using wrapping at the boundaries. Used for cycle spinning.

Value

Author(s)

Matt Nunes (m.nunes@ucl.ac.uk)

Examples

v<-runif(10)

#have a look at v:

v

#now shift the values 4 places to the right...

shift(v,4,dir="right")

Simulation function

Description

Proportion estimation procedure for simulations.

Usage

simsij(nsims = 100, n = 256, proportion = P2, binsize = 1,
    thrule = "ebayesthresh", van = 8, fam = "DaubLeAsymm", pl = 3,
    prior = "laplace",
    vscale = "independent", plotstep = FALSE, a = NA,truncate = FALSE, ...)

Arguments

Details

This function creates a regularly-spaced vector on the unit interval of length length, and uses these values to create corresponding values using the proportion function. These values are then used as binomial probabilities to sample "observed" binomial random variables. The observation vector is then denoised using a wavelet transform defined by the arguments van, fam, min.level with thresholding method meth. This denoising is done for both Anscombe and the Haar-Fisz method for binomial random variables. The procedure is repeated times times, and the resulting proportion estimates averaged.

Value

Author(s)

Matt Nunes (m.nunes@ucl.ac.uk)

See Also

hfdenoise

Examples

## Not run: 
a<-simsij(nsims=100)

plot(a$est[1,,1])


##^^ shows 1st binomial Haar-Fisz estimate.

## End(Not run)

Statistics generator

Description

This function generates useful simulation statistics for NN and Anscombe transforms.

Usage

statgen(valuelist, xgrid = seq(0, 1, length = 21), ygrid = seq(0, 1, length = 21), 
binsize = 32, plot.m = FALSE, plot.v = FALSE, plot.ks = FALSE, ptype = "persp")

Arguments

Details

The function does several sample variance plots, Kolmogorov-Smirnov and mean plots for the data in the variable valuelist (for both Anscombe and binomial Haar-Fisz transforms).

Value

Author(s)

Matt Nunes (m.nunes@ucl.ac.uk)

See Also

afgen

Examples

a<-afgen(xgrid = seq(0, 1, length = 21), ygrid = seq(0, 1, length = 21), 
samples = 1000, binsize = 32)

b<-statgen(a,xgrid=seq(0,1,length=21),ygrid=seq(0,1,length=21),binsize=32,plot.m=FALSE,
plot.v=TRUE,plot.ks=FALSE,ptype="persp")