Verifying Conditional
Independence Clues for
Odds Form of Bayes
through Graphs
Farrokh Alemi, Ph.D.
Draw the consequences (signs &
symptoms) & causes of target event
 Set
a node for target event
 Set nodes containing the causes

Connect by an arrow pointing to target event
 Set
nodes containing the consequences
(signs, symptoms or characteristics
commonly found)

Connect by an arrow pointing to
consequences
Possible Model
Include
only direct
causes &
consequence
s
Possible Model
Question & Answer
Why look at consequences, isn’t
it enough to look at causes?
 In a prediction task, both are
clues. For example, you can use
both a runny nose ( a sign) and
exposure to an infected person (a
cause) as clues in predicting if
the person has upper respiratory
infection.

Question & Answer
 In
breast cancer, is the
cancer the cause of lump or
the lump the cause of breast
cancer?
 Causes always precede the
event. Most people would
say that cancer precedes the
appearance of a lump.
Example in Joining HMO
What does a graph tell us?
Dependencies:



Connected nodes
Common effect
•
2 or more causes same effect
Independencies:


Common cause
•

2 or more effects, same cause
Nodes arranged in a series
Check for Connected Nodes
Joining HMO depends
on:
 time pressures
 frequency of travel
 age of employees
 gender of employees
 employees computer
usage.
Check for Common Effect

For employees who
have joined the HMO,
time pressures
depends on
frequency of travel
Check for Common Cause

For employees who
have joined the HMO,
age, gender &
computer use are
independent
Check for Common Cause

For employees who
have joined the HMO,
age, gender &
computer use are
independent

Violated if an arrow
connects any of the
consequences directly
to each other
Check for Series

For employees who
have joined the HMO,
age, gender &
computer use are
independent of time
pressure and
frequency of travel
Check Graph for Series

For employees who
have joined the HMO,
age, gender &
computer use are
independent of time
pressure and
frequency of travel

Violated if an arrow
connects causes to
the consequences
directly
Question & Answer

Can you give an example of
causes linking directly to effects?
 Aging leads to weight gain which
in turn leads to high blood
pressure. In addition, aging can
also lead to high blood pressure
without the person gaining
weight. There maybe other
mechanism besides weight gain,
for example high cholesterol
levels
What to Do with Dependence?
 Ignore

Works well with small dependencies
 Redo


it
the causes and consequences
Refine the consequence so that it is specific
to occurring through the target event
Combine multiple causes into one generalized
cause
 Change
the odds form formula
Bayes Formula for Joining
HMO
Accounting
for dependency
Posterior odds of joining =
Likelihood ratio time pressure & travel frequency *
Likelihood ratio age *
Likelihood ratio gender *
Likelihood ratio computer use *
Prior odds of joining
Posterior odds of joining =
Likelihood ratio time pressure *
Likelihood ratio travel frequency *
Likelihood ratio age *
Likelihood ratio gender *
Likelihood ratio computer use *
Prior odds of joining
Ignoring it
Take Home Lesson
A cause & consequence graph
can tell us a great deal about
model structure