variofitCMB: Estimates parameters of variograms
In rcosmo: Cosmic Microwave Background Data Analysis

Description Usage Arguments Details Value References Examples

This function estimates variogram parameters by fitting a parametric model from covmodelCMB to a sample variogram. The function extends variofit from the package geoR to additional covariance models on spheres.

variofitCMB(
  vario,
  ini.cov.pars,
  cov.model,
  fix.nugget = FALSE,
  nugget = 0,
  fix.kappa = TRUE,
  kappa = 0.5,
  simul.number = NULL,
  max.dist = vario$max.dist,
  weights,
  minimisation.function,
  limits = geoR::pars.limits(),
  messages,
  ...
)

`vario`	An object of the class `variogram` obtained as an output of the function `variogramCMB`.
`ini.cov.pars`	A vector with initial values for the variogram parameters. The first parameter corresponds to the variance sigma^2. The second parameter corresponds to the range phi of the correlation function.
`cov.model`	A type of the variogram function. Available choices are: "matern", "exponential","spherical", "powered.exponential", "cauchy", "gencauchy", "pure.nugget", "askey", "c2wendland", "c4wendland", "sinepower", "multiquadric". The default is "matern"
`fix.nugget`	logical. Indicates whether the nugget variance should be regarded as fixed or be estimated. The default is FALSE.
`nugget`	A value for the nugget parameter. Regarded as a fixed values if `fix.nugget = TRUE` or as a initial value for the minimization algorithm if `fix.nugget = FALSE`. The default is zero.
`fix.kappa`	logical. Indicates whether the parameter kappa should be regarded as fixed or be estimated. The default is TRUE.
`kappa`	A value for the smoothness parameter. Regarded as a fixed values if `fix.kappa = TRUE` or as a initial value for the minimization algorithm if `fix.kappa = FALSE`. Required not in all covariance models, see `covmodelCMB`. The default is 0.5.
`simul.number`	number of simulation. Used if `vario` has empirical variograms for more than one data-set (simulations). The default is NULL
`max.dist`	A maximum distance to fit a variogram model. The default is `x$max.dist`.
`weights`	Weights used in the loss function in the minimization algorithm.
`minimisation.function`	Minimization function ("optim", "nlm", "nls") to estimate the parameters.
`limits`	Lower and upper limits for the model parameters used in the numerical minimisation by `minimisation.function = "optim"`.
`messages`	logical. Indicates whether or not status messages are printed on the screen.
`...`	other minimisation parameters

The parameter values of a variogram function from covmodelCMB are found by numerical optimization using one of the functions: optim, nlm and nls.

The function extends variofit from the package geoR to additional variogram models on spheres. Available models are: "matern", "exponential", "spherical", "powered.exponential", "cauchy", "gencauchy", "pure.nugget", "askey", "c2wendland", "c4wendland", "sinepower", "multiquadric".

Additionally it rescales an empirical variogram to the range [0,1] before numerical optimisation and then transforms all obtained results to the original scale. If ini.cov.pars are not provided then the 5x5 grid (seq(0,max(vario$v),l=5), seq(0,vario$max.dist,l=5)) of initial values of sigma^2 and phi is used.

An object of the class variomodel and variofit, see variofit

geoR package, variofit, covmodelCMB

#
# df <- CMBDataFrame("../CMB_map_smica1024.fits")
# cmbdf <- sampleCMB(df, sample.size = 10000)
# varcmb <- variogramCMB(cmbdf, max.dist = 0.1, num.bins = 30)
# varcmb
#
# ols <- variofitCMB(varcmb,  fix.nug=FALSE, wei="equal", cov.model= "matern")
# plot(varcmb)
# lines(ols, lty=2)
# str(ols)
#
# ols <- variofitCMB(varcmb, fix.nug = TRUE, kappa = 3, wei = "equal",
# cov.model = "askey")
# plot(varcmb, main = ols$cov.model)
# linesCMB(ols, lty = 2)
# str(ols)