pgs (version 0.4-0)

vol.mse: MSE approximation for volume predictors

Description

Compute a MSE approximation for volume predictors. The structure of interest is an isotropic 3D random compact set. The sampling device is a uniform random lattice of figures (point patterns, line segments, sections...). The approximation depends only on sampling parameters and on the mean surface (to be provided) of the structure.

Usage

vol.mse(x, S = 1, L = 3)

Arguments

x

a lattice of figures, object of class FigLat-class.

S

the mean surface. Default: 1.

L

an integer, the criterion for stopping summation of the Epstein zeta function. Argument of the function Ezeta. Default: 3.

Value

The MSE approximation as a numeric.

References

Kieu, K. and Mora, M. (2005). Stereological estimation of mean volume: precision of three sampling designs. Technical report 2005-1, Unite de Mathematiques et informatique appliquees, INRA. http://www.inra.fr/bia/J/nosdoc/rapport_miaj_2005_1.pdf.

See Also

area.mse, dvol.mse.

Examples

# Sampling by a unit cubic point lattice
vol.mse(FigLat(3,VecLat(diag(3)),PointPattern(rep(0,3))))
# Sampling by serial sections
vol.mse(FigLat(3,VecLat(c(0,0,1)),PointPattern(rep(0,3)),lmat=rbind(diag(2),rep(0,2))))