The purpose of the functions implemented in this package is to find a subset containing the weakest species with some acceptable certainty. Suppose we have sampled some quality measures T_{k,j} (>=0) from K species (k=1,...,K, j=1,...,m_k= sample size of kth species), and wish to find the species with the smallest alpha quantile (say, 5th percentile) of T (namely the weakest species). Due to the small sample size (m_k) or large number of species to be considered (K), we might not be able to select a single species as a weakest one with acceptably large certainty. Instead of selecting a single species with a low certainty, we propose to select a subset of species which contains the weakest species with predetermined certainty.

Semi- and nonparametric Bayesian Subset Selection Procedures
Implement the Bayesian subset selection procedure proposed in the paper titled "Bayesian Subset Selection Procedures with an Application to Lumber Strength Properties" by Yumi Kondo, James V. Zidek, Carolyn Taylor, and Constance van Eeden. This procedure models the lumber strengths with Dirichlet processes (DP) with the Weibull components and finds, with pre-specified certainty, the smallest subset that contains those species having the smallest alpha-th quantile of strength (i.e., the weakest species). We consider two models for the strengths: [1] A semi-parametric model which assumes that strengths are from the DP mixture of Weibulls; [2] the nonparametric model which assumes that probability measures of strengths are from DP with Weibull base distribution. Either model can be used to estimate the posterior probability that a subset contains the weakest species.

The purpose of the functions implemented in this package
is to find the subset containing the weakest species with some
acceptable certainty; Suppose we have sampled some quality
measures T_{k,j} (>=0) from K species (k=1...K, j=1,...,m_j=
sample size of jth species), and wish to find the species with
the smallest alpha quantile (say, 5th quantile) of T (namely
the weakest species).Due to the smalle sample size (m_k) or
large number of species to be considered (K), we might not be
able to select a single species as a weakest species with
acceptably large certainty. Instead of selecting a single
species with a low certainty, we propose to select a subset of
species which contains the weakest species with predetermined
certainty.