R: Estimate background

do.fit {BBEST}

R Documentation

Estimate background

Description

do.fit estimates the background using the Bayesian approach and Differential Evolution algorithm.

Usage

do.fit(data, bounds.lower, bounds.upper, scale=c(1,1), knots.x=NA,
       knots.n=NA, analytical=FALSE, stdev=TRUE, control=list(), p.bkg=.5,
	   save.to="")

Arguments

`data`	an object of type `data`. See `set.data` for details.
`bounds.lower`, `bounds.upper`	numerics specifying the lower and upper bounds for the fitted spline values.
`scale`	numeric vector which, if applicable, determines the bounds for the fitted scale parameter. The default value of `c(1,1)` means a no-scale fit. See details.
`knots.x`	numeric vector which, if not `NA`, specifies the knot positions.
`knots.n`	numeric, the number of knots. If `knots.x` is `NA` then `knots.n` equidistant knots will be created.
`analytical`	logical. If `TRUE` background is approximated by an analytical function `f(x)=P_1\exp(-P_2x)x^{P_3} + P_4/[(x-P_5)^2+P_6^2]`.
`stdev`	logical, whether to calculate the uncertainty for the estimated background. Should be set to `FALSE` if `analytical=TRUE`.
`control`	list, the return value of `set.control`. Specifies various parameters of the Differential Evolution optimization algorithm implemented in `DEoptim`.
`p.bkg`	numeric, the probability that a single pixel contains "only" a background.
`save.to`	character, a filename for saving the results.

Details

If information on the low-r behavior of G(r) is provided, the global intensity scale and atomic displacement parameters can be fitted along with the positions of the knots, (set.Gr). To fit normalization parameter set bounds in scale for the desired values. To fit Atomic Displacement Parameters see set.SB.

In most cases p.bkg should be set to its default value 0.5.

For further details see BBEST-package.

Value

A list with elements:

`x`	numeric vector of grid points
`curves`	list, see below.
`uncrt`	list, see below.
`knots`	list with elements `x` and `y` that specify the positions of the knots and the corresponding fitted intensity values, respectively.
`pars`	numeric vector. If the background is approximated using the analytical function, contains all the relevant parameters `P`.
`scale`	fitted value of the `scale` parameter, if used.
`ADP`	fitted values of the atomic displacement parameters, if applicable.
`fit.details`	list, see below.

Element curves is a list with sub-elements:

`y`	numeric vector of the (normalized) function values.
`bkg`	numeric vector, the estimated background.
`SB`	numeric vector, the (fitted) coherent baseline.

Element uncrt is a list with sub-elements:

`stdev`	numeric vector, indicates estimated standard deviations for the reconstructed signal.
`stdev.r`	numeric vector, indicates estimated standard deviations for a reconstructed signal in r-space.
`hess`	Hessian matrix for a `\psi(c)` function.
`cov.matrix`	covariance matrix, i.e. the inverse of the Hessian.
`cov.matrix.r`	covariance matrix in r-space.

Element fit.details is a list with sub-elements:

`lambda`	numeric vector, the estimated mean magnitude of the signal.
`sigma`	numeric vector, the estimated Gaussian noise.
`knots.n`	the number of knots used in the fit.
`knots.x`	knot positions used in the fit.
`control`	see the `control` argument.
`Gr`	list contacting information on the low-r behaviour of G(r) . See `set.Gr` for details.
`n.atoms`	numeric vector, number of different atoms per unit cell.
`scatter.length`	numeric vector, atomic scattering factors.

References

Ardia, D., Mullen, K., Peterson, B. & Ulrich, J. (2011): DEoptim. R Package Version 2.2-2. https://CRAN.R-project.org/package=DEoptim.

Mullen, K.M., Ardia, D., Gil, D., Windover, D., Cline, J. (2011): DEoptim: An R Package for Global Optimization by Differential Evolution. J. Stat. Softw., 40(6), 1-26. https://www.jstatsoft.org/article/view/v040i06.

[Package BBEST version 0.1-8 Index]