Dempsterian-Shaferian Belief Network From Data
  Shenoy and Shafer {Shenoy:90} demonstrated that both for Dempster-Shafer
Theory and probability theory there exists a possibility to calculate
efficiently marginals of joint belief distributions (by so-called local
computations) provided that the joint distribution can be decomposed
(factorized) into a belief network. A number of algorithms exists for
decomposition of probabilistic joint belief distribution into a bayesian
(belief) network from data. For example
  Spirtes, Glymour and Schein{Spirtes:90b} formulated a Conjecture that a
direct dependence test and a head-to-head meeting test would suffice to
construe bayesian network from data in such a way that Pearl's concept of
d-separation {Geiger:90} applies.
  This paper is intended to transfer Spirtes, Glymour and Scheines
{Spirtes:90b} approach onto the ground of the Dempster-Shafer Theory (DST). For
this purpose, a frequentionistic interpretation of the DST developed in
{Klopotek:93b} is exploited. A special notion of conditionality for DST is
introduced and demonstrated to behave with respect to Pearl's d-separation
{Geiger:90} much the same way as conditional probability (though some
differences like non-uniqueness are evident). Based on this, an algorithm
analogous to that from {Spirtes:90b} is developed.
  The notion of a partially oriented graph (pog) is introduced and within this
graph the notion of p-d-separation is defined. If direct dependence test and
head-to-head meeting test are used to orient the pog then its p-d-separation is
shown to be equivalent to the Pearl's d-separation for any compatible dag.
