The conivol package provides functions for the chi-bar-squared distribution, the bivariate chi-bar-squared distribution, and the conic intrinsic volumes.
conivol supports standard functions for the density/cdf/sampling of the (bivariate)
chi-bar-squared distribution, calculations and known formulas for special classes
of intrinsic volumes of cones, sampling functions for ellipsoidal cones and
general polyhedral cones, as well as functions for estimating intrinsic volumes
either from direct samples of the intrinsic volumes distribution
(in the case of polyhedral cones) or from samples of the corresponding
bivariate chi-bar-squared distribution. The package supports point estimates
as well as Bayesian estimates via JAGS and Stan.
dchibarsq / pchibarsq /
rchibarsq: evaluates the density /
evaluates the cumulative distribution function / produces samples
of the chi-bar-squared distribution
dbichibarsq / pbichibarsq /
rbichibarsq: evaluates the density /
evaluates the cumulative distribution function / produces samples
of the bivariate chi-bar-squared distribution
prod_ivols: computes the intrinsic volumes of a product cone
by convolving the intrinsic volumes of
its elements
circ_ivols: computes the intrinsic volumes of (a product of)
circular cones
ellips_semiax / ellips_rbichibarsq:
computes the semiaxes / produces samples from the bivariate
chi-bar-squared distribution of an ellipsoidal cone
weyl_matrix / weyl_ivols:
computes a matrix representation / computes the
intrinsic volumes of (a product of) Weyl chambers
polyh_reduce_gen / polyh_reduce_ineq:
compute a reduced representation
of a polyhedral cone given by generators / inequalities
polyh_rivols_gen / polyh_rivols_ineq:
produce samples from the intrinsic volumes distribution of
a polyhedral cone given by generators / inequalities
polyh_rbichibarsq_gen / polyh_rbichibarsq_ineq:
produce samples from the bivariate chi-bar-squared distribution
with weights given by the conic intrinsic volumes of
a polyhedral cone given by generators / inequalities
polyh_bayes: generates functions for computing quantiles of marginals
of the posterior distribution and for sampling
from the posterior distribution,
given samples of the intrinsic volumes distribution
(based on analytic solution)
polyh_stan: generates inputs for Stan
(data list and model string or external file)
for sampling from the posterior distribution,
given samples of the intrinsic volumes distribution
using a model that naturally implies log-concavity
(and cannot be solved analytically)
estim_statdim_var: estimates the statistical dimension and
the variance of the intrinsic volumes from samples of the
corresponding bivariate chi-bar-squared distribution
init_ivols: finds an initial estimate of the weights, potentially
based on first and/or second moment
loglike_ivols: computes the log-likelihood of a weight vector
for specific sample data
prepare_em: evaluates the sample data of the bivariate chi-bar-squared
data (find the corresponding chi-squared density values)
estim_em: produces EM-type iterates that may or may not converge
to the maximum likelihood estimate for the weights
of the bivariate chi-bar-squared distribution
from sample data
estim_jags / estim_stan:
generate inputs for JAGS / Stan (data list and model
string or external file) for sampling from the posterior distribution
of the intrinsic volumes,
given samples of the bivariate chi-bar-squared distribution
Conic intrinsic volumes and (bivariate) chi-bar-squared distribution: introduces conic intrinsic volumes and (bivariate) chi-bar-squared distributions, as well as the computations involving polyhedral cones
Estimating conic intrinsic volumes from bivariate chi-bar-squared data: describes the details of the algorithm for finding the intrinsic volumes of closed convex cones from samples of the associated bivariate chi-bar-squared distribution
Bayesian estimates for conic intrinsic volumes: describes the Bayesian approach for reconstructing intrinsic volumes from sampling data, which can either be samples from the intrinsic volumes distribution (in the case of polyhedral cones), or from the bivariate chi-bar-squared distribution, and which can be with or without enforcing log-concavity of the intrinsic volumes