Computes bounds and sensitivity parameters as part of sensitivity 
    analysis for selection bias. Different bounds are provided: the SV (Smith 
    and VanderWeele), sharp bounds,  AF (assumption-free) bound, GAF (generalized 
    AF), and CAF (counterfactual AF) bounds. The calculation of the sensitivity 
    parameters for the SV, sharp, and GAF bounds assume an additional dependence 
    structure in form of a generalized M-structure. The bounds can be
    calculated for any structure as long as the necessary assumptions hold. See 
    Smith and VanderWeele (2019) <doi:10.1097/EDE.0000000000001032>,
    Zetterstrom, Sjölander, and Waernabum (2025) <doi:10.1177/09622802251374168>,
    Zetterstrom and Waernbaum (2022) <doi:10.1515/em-2022-0108>, and
    Zetterstrom (2024) <doi:10.1515/em-2023-0033>.

Multi-stage selection is practiced in numerous fields of life
    and social sciences and particularly in breeding. A special characteristic of
    multi-stage selection is that candidates are evaluated in successive stages
    with increasing intensity and effort, and only a fraction of the superior
    candidates is selected and promoted to the next stage. For the optimum design
    of such selection programs, the selection gain plays a crucial role. It can be
    calculated by integration of a truncated multivariate normal (MVN) distribution.
    While mathematical formulas for calculating the selection gain and the variance
    among selected candidates were developed long time ago, solutions for numerical
    calculation were not available. This package can also be used for optimizing
    multi-stage selection programs for a given total budget and different costs of
    evaluating the candidates in each stage.

The aim of most plant breeding programmes is simultaneous improvement of several characters. An objective method involving simultaneous selection for several attributes then becomes necessary. It has been recognised that most rapid improvements in the economic value is expected from selection applied simultaneously to all the characters which determine the economic value of a plant, and appropriate assigned weights to each character according to their economic importance, heritability and correlations between characters. So the selection for economic value is a complex matter. If the component characters are combined together into an index in such a way that when selection is applied to the index, as if index is the character to be improved, most rapid improvement of economic value is expected. Such an index was first proposed by Smith (1937 <doi:10.1111/j.1469-1809.1936.tb02143.x>) based on the Fisher's (1936 <doi:10.1111/j.1469-1809.1936.tb02137.x>) "discriminant function" Dabholkar (1999 <https://books.google.co.in/books?id=mlFtumAXQ0oC&lpg=PA4&ots=Xgxp1qLuxS&dq=elements%20of%20biometrical%20genetics&lr&pg=PP1#v=onepage&q&f=false>). In this package selection index is calculated based on the Smith (1937) selection index method.