Robin Evans:
 Models based on marginalised DAGs
<br><br>
Directed acyclic graphs (DAGs) form a convenient and intuitive class of
models for working with multivariate data, as they have good 
computational
properties, impose only non-parametric independence constraints, and if
chosen
suitably, can lead to parsimonious models.  In some circumstances, it may
also
be realistic in practice to believe that a system of interest
corresponds to a DAG.
<br><br>
However DAG models are not closed under marginalisation and conditioning,
which
means that even when this modelling assumptions holds, if some of the
variables are
unobservable then the distribution over the remaining variables will
not necessarily
correspond to a DAG model.
<br><br>
We will cover basic DAG theory, known constraints which arise on
marginalised
DAGs (conditional independences, Verma constraints, inequalities), as 
well
as
some new results on equivalence.