smash.gaus: Estimate underlying mean function from noisy Gaussian data.
In zrxing/smash: Smoothing by Adaptive Shrinkage in R

Description Usage Arguments Details Value Examples

This function performs non-parametric regression (signal denoising) using Empirical Bayes wavelet-based methods.

smash.gaus(
  x,
  sigma = NULL,
  v.est = FALSE,
  joint = FALSE,
  v.basis = FALSE,
  post.var = FALSE,
  filter.number = 1,
  family = "DaubExPhase",
  return.loglr = FALSE,
  jash = FALSE,
  SGD = TRUE,
  weight = 0.5,
  min.var = 1e-08,
  ashparam = list(),
  homoskedastic = FALSE,
  reflect = FALSE
)

`x`	A vector of observations. Reflection is done automatically if length of `x` is not a power of 2.
`sigma`	A vector of standard deviations. Can be provided if known or estimated beforehand.
`v.est`	Boolean indicating if variance estimation should be performed instead.
`joint`	Boolean indicating if results of mean and variance estimation should be returned together.
`v.basis`	Boolean indicating if the same wavelet basis should be used for variance estimation as mean estimation. If false, defaults to Haar basis for variance estimation (this is much faster than other bases).
`post.var`	Boolean indicating if the posterior variance should be returned for the mean and/or variance estiamtes.
`filter.number`	Choice of wavelet basis to be used, as in `wavethresh`.
`family`	Choice of wavelet basis to be used, as in `wavethresh`.
`return.loglr`	Boolean indicating if a logLR should be returned.
`jash`	Indicates if the prior from method JASH should be used. This will often provide slightly better variance estimates (especially for nonsmooth variance functions), at the cost of computational efficiency. Defaults to FALSE.
`SGD`	Boolean indicating if stochastic gradient descent should be used in the EM. Only applicable if jash=TRUE.
`weight`	Optional parameter used in estimating overall variance. Only works for Haar basis. Defaults to 0.5. Setting this to 1 might improve variance estimation slightly.
`min.var`	The minimum positive value to be set if the variance estimates are non-positive.
`ashparam`	A list of parameters to be passed to `ash`; default values are set by function `setAshParam.gaus`.
`homoskedastic`	indicates whether to assume constant variance (if v.est is true)
`reflect`	A logical indicating if the signals should be reflected.

We assume that the data come from the model Y_t = μ_t + ε_t for t=1,...,T, where μ_t is an underlying mean, assumed to be spatially structured (or treated as points sampled from a smooth continous function), and ε_t \sim N(0, σ_t), and are independent. Smash provides estimates of μ_t and σ_t^2 (and their posterior variances if desired).

By default smash.gaus simply returns a vector of estimated means. However, if more outputs are requested (eg if return.loglr or v.est is TRUE) then the output is a list with one or more of the following elements:

mu.res

A list with the mean estimate, its posterior variance if post.var is TRUE, the logLR if return.loglr is TRUE, or a vector of mean estimates if neither post.var nor return.loglr are TRUE.

If v.est is TRUE, then smash.gaus returns the following:

var.res

A list with the variance estimate, its posterior variance if post.var is TRUE, or a vector of variance estimates if post.var is FALSE In addition, if joint is TRUE, then both mu.res and var.res are returned.

n=2^10
t=1:n/n
spike.f = function(x) (0.75*exp(-500*(x-0.23)^2) +
  1.5*exp(-2000*(x-0.33)^2) + 3*exp(-8000*(x-0.47)^2) +
  2.25*exp(-16000*(x-0.69)^2)+0.5*exp(-32000*(x-0.83)^2))
mu.s = spike.f(t)

# Gaussian case
mu.t = (1+mu.s)/5
plot(mu.t,type='l')
var.fn = (0.0001 + 4*(exp(-550*(t-0.2)^2) + exp(-200*(t-0.5)^2) +
  exp(-950*(t-0.8)^2)))/1.35
plot(var.fn,type='l')
rsnr=sqrt(5)
sigma.t=sqrt(var.fn)/mean(sqrt(var.fn))*sd(mu.t)/rsnr^2
X.s=rnorm(n,mu.t,sigma.t)
mu.est=smash.gaus(X.s)
plot(mu.t,type='l')
lines(mu.est,col=2)