<s>
Causal	B-General_Concept
analysis	I-General_Concept
is	O
the	O
field	O
of	O
experimental	O
design	O
and	O
statistics	O
pertaining	O
to	O
establishing	O
cause	O
and	O
effect	O
.	O
</s>
<s>
Exploratory	B-General_Concept
causal	I-General_Concept
analysis	I-General_Concept
(	O
ECA	O
)	O
,	O
also	O
known	O
as	O
data	B-General_Concept
causality	I-General_Concept
or	O
causal	B-General_Concept
discovery	I-General_Concept
is	O
the	O
use	O
of	O
statistical	O
algorithms	O
to	O
infer	O
associations	O
in	O
observed	O
data	O
sets	O
that	O
are	O
potentially	O
causal	O
under	O
strict	O
assumptions	O
.	O
</s>
<s>
Data	B-General_Concept
analysis	I-General_Concept
is	O
primarily	O
concerned	O
with	O
causal	O
questions	O
.	O
</s>
<s>
ECA	O
postulates	O
that	O
there	O
exist	O
data	B-General_Concept
analysis	I-General_Concept
procedures	I-General_Concept
performed	O
on	O
specific	O
subsets	O
of	O
variables	O
within	O
a	O
larger	O
set	O
whose	O
outputs	O
might	O
be	O
indicative	O
of	O
causality	B-Application
between	O
those	O
variables	O
.	O
</s>
<s>
Granger	B-General_Concept
causality	I-General_Concept
can	O
also	O
be	O
used	O
to	O
find	O
the	O
causality	B-Application
between	O
two	O
observational	O
variables	O
under	O
different	O
,	O
but	O
similarly	O
strict	O
,	O
assumptions	O
.	O
</s>
<s>
The	O
two	O
broad	O
approaches	O
to	O
developing	O
such	O
procedures	O
are	O
using	O
operational	O
definitions	O
of	O
causality	B-Application
or	O
verification	O
by	O
"	O
truth	O
"	O
(	O
i.e.	O
,	O
explicitly	O
ignoring	O
the	O
problem	O
of	O
defining	O
causality	B-Application
and	O
showing	O
that	O
a	O
given	O
algorithm	O
implies	O
a	O
causal	O
relationship	O
in	O
scenarios	O
when	O
causal	O
relationships	O
are	O
known	O
to	O
exist	O
,	O
e.g.	O
,	O
using	O
synthetic	B-General_Concept
data	I-General_Concept
)	O
.	O
</s>
<s>
Clive	O
Granger	O
created	O
the	O
first	O
operational	O
definition	O
of	O
causality	B-Application
in	O
1969	O
.	O
</s>
<s>
Granger	O
made	O
the	O
definition	O
of	O
probabilistic	O
causality	B-Application
proposed	O
by	O
Norbert	O
Wiener	O
operational	O
as	O
a	O
comparison	O
of	O
variances	O
.	O
</s>
<s>
Some	O
authors	O
prefer	O
using	O
ECA	O
techniques	O
developed	O
using	O
operational	O
definitions	O
of	O
causality	B-Application
because	O
they	O
believe	O
it	O
may	O
help	O
in	O
the	O
search	O
for	O
causal	O
mechanisms	O
.	O
</s>
<s>
Peter	O
Spirtes	O
,	O
Clark	O
Glymour	O
,	O
and	O
Richard	O
Scheines	O
introduced	O
the	O
idea	O
of	O
explicitly	O
not	O
providing	O
a	O
definition	O
of	O
causality	B-Application
.	O
</s>
<s>
Spirtes	O
and	O
Glymour	O
introduced	O
the	O
PC	O
algorithm	O
for	O
causal	B-General_Concept
discovery	I-General_Concept
in	O
1990	O
.	O
</s>
<s>
Many	O
recent	O
causal	B-General_Concept
discovery	I-General_Concept
algorithms	O
follow	O
the	O
Spirtes-Glymour	O
approach	O
to	O
verification	O
.	O
</s>
<s>
There	O
are	O
many	O
surveys	O
of	O
causal	B-General_Concept
discovery	I-General_Concept
techniques	O
.	O
</s>
<s>
Many	O
of	O
these	O
techniques	O
are	O
discussed	O
in	O
the	O
tutorials	O
provided	O
by	O
the	O
Center	O
for	O
Causal	B-General_Concept
Discovery	I-General_Concept
(	O
CCD	O
)	O
.	O
</s>
<s>
Granger	B-General_Concept
causality	I-General_Concept
has	O
been	O
applied	O
to	O
fMRI	B-Algorithm
data	O
.	O
</s>
<s>
ECA	O
is	O
used	O
in	O
physics	O
to	O
understand	O
the	O
physical	O
causal	O
mechanisms	O
of	O
the	O
system	O
,	O
e.g.	O
,	O
in	O
geophysics	O
using	O
the	O
PC-stable	O
algorithm	O
(	O
a	O
variant	O
of	O
the	O
original	O
PC	O
algorithm	O
)	O
and	O
in	O
dynamical	O
systems	O
using	O
pairwise	O
asymmetric	O
inference	O
(	O
a	O
variant	O
of	O
convergent	B-General_Concept
cross	I-General_Concept
mapping	I-General_Concept
)	O
.	O
</s>
<s>
There	O
is	O
debate	O
over	O
whether	O
or	O
not	O
the	O
relationships	O
between	O
data	O
found	O
using	O
causal	B-General_Concept
discovery	I-General_Concept
are	O
actually	O
causal	O
.	O
</s>
<s>
is	O
an	O
open	O
source	O
GUI-based	O
Java	O
program	O
that	O
provides	O
a	O
collection	O
of	O
causal	B-General_Concept
discovery	I-General_Concept
algorithms	O
.	O
</s>
<s>
The	O
algorithm	O
library	O
used	O
by	O
Tetrad	O
is	O
also	O
available	O
as	O
a	O
command-line	B-Application
tool	I-Application
,	O
Python	B-Language
API	B-Application
,	O
and	O
R	B-Language
wrapper	O
.	O
</s>
<s>
is	O
an	O
open	O
source	O
Java	O
library	O
for	O
performing	O
information-theoretic	O
causal	B-General_Concept
discovery	I-General_Concept
(	O
i.e.	O
,	O
transfer	O
entropy	O
,	O
conditional	O
transfer	O
entropy	O
,	O
etc	O
.	O
)	O
.	O
</s>
<s>
Examples	O
of	O
using	O
the	O
library	O
in	O
MATLAB	B-Language
,	O
GNU	B-Language
Octave	I-Language
,	O
Python	B-Language
,	O
R	B-Language
,	O
Julia	B-Application
and	O
Clojure	B-Language
are	O
provided	O
in	O
the	O
documentation	O
.	O
</s>
<s>
is	O
an	O
R	B-Language
package	O
that	O
provides	O
some	O
of	O
the	O
same	O
causal	B-General_Concept
discovery	I-General_Concept
algorithms	O
provided	O
in	O
Tetrad	O
.	O
</s>
<s>
There	O
is	O
also	O
a	O
collection	O
of	O
tools	O
and	O
data	O
maintained	O
by	O
the	O
Causality	B-Application
Workbench	O
team	O
and	O
the	O
CCD	O
team	O
.	O
</s>
