do.fit: Estimate background In BBEST: Bayesian Estimation of Incoherent Neutron Scattering Backgrounds

Description

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

Usage

 ```1 2 3``` ```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 ψ(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.

BBEST documentation built on Jan. 8, 2021, 2:22 a.m.