Verifying Conditional Verifying Conditional IndependenceIndependence Clues for Clues for

Odds Form of Bayes Odds Form of Bayes through Graphsthrough Graphs

Farrokh Alemi, Ph.D.Farrokh Alemi, Ph.D.

Draw the consequences (signs & Draw the consequences (signs & symptoms) & causes of target eventsymptoms) & causes of target event

Set a node for target eventSet a node for target event Set nodes containing the causes Set nodes containing the causes

Connect by an arrow pointing to target eventConnect by an arrow pointing to target event Set nodes containing the consequences Set nodes containing the consequences

(signs, symptoms or characteristics (signs, symptoms or characteristics commonly found)commonly found) Connect by an arrow pointing to Connect by an arrow pointing to

consequencesconsequences

Possible ModelPossible Model Include only directcauses &

consequences

Possible ModelPossible Model

Question & AnswerQuestion & Answer

Why look at consequences, isn’t Why look at consequences, isn’t it enough to look at causes?it enough to look at causes?

In a prediction task, both are In a prediction task, both are clues. For example, you can use clues. For example, you can use both a runny nose ( a sign) and both a runny nose ( a sign) and exposure to an infected person (a exposure to an infected person (a cause) as clues in predicting if cause) as clues in predicting if the person has upper respiratory the person has upper respiratory infection.infection.

Question & AnswerQuestion & Answer

In breast cancer, is the In breast cancer, is the cancer the cause of lump or cancer the cause of lump or the lump the cause of breast the lump the cause of breast cancer?cancer?

Causes always precede the Causes always precede the event. Most people would event. Most people would say that cancer precedes the say that cancer precedes the appearance of a lump. appearance of a lump.

Example in Joining HMOExample in Joining HMO

What does a graph tell us?What does a graph tell us?

Dependencies:Dependencies: Connected nodesConnected nodes Common effectCommon effect

• 2 or more causes same effect2 or more causes same effect

Independencies:Independencies: Common cause Common cause

• 2 or more effects, same cause2 or more effects, same cause Nodes arranged in a seriesNodes arranged in a series

Check for Connected NodesCheck for Connected Nodes

Joining HMO depends Joining HMO depends on:on:

time pressurestime pressures frequency of travelfrequency of travel age of employeesage of employees gender of employeesgender of employees employees computer employees computer

usage. usage.

Check for Common EffectCheck for Common Effect

For employees who For employees who have joined the HMO, have joined the HMO, time pressures time pressures depends on depends on frequency of travelfrequency of travel

Check for Common CauseCheck for Common Cause

For employees who For employees who have joined the HMO, have joined the HMO, age, gender & age, gender & computer use are computer use are independentindependent

Check for Common CauseCheck for Common Cause

For employees who For employees who have joined the HMO, have joined the HMO, age, gender & age, gender & computer use are computer use are independentindependent Violated if an arrow Violated if an arrow

connects any of the connects any of the consequences directly consequences directly to each otherto each other

Check for SeriesCheck for Series

For employees who For employees who have joined the HMO, have joined the HMO, age, gender & age, gender & computer use are computer use are independent of time independent of time pressure and pressure and frequency of travelfrequency of travel

Check Graph for SeriesCheck Graph for Series

For employees who For employees who have joined the HMO, have joined the HMO, age, gender & age, gender & computer use are computer use are independent of time independent of time pressure and pressure and frequency of travelfrequency of travel Violated if an arrow Violated if an arrow

connects causes to connects causes to the consequences the consequences directlydirectly

Question & AnswerQuestion & Answer

Can you give an example of Can you give an example of causes linking directly to effects?causes linking directly to effects?

Aging leads to weight gain which Aging leads to weight gain which in turn leads to high blood in turn leads to high blood pressure. In addition, aging can pressure. In addition, aging can also lead to high blood pressure also lead to high blood pressure without the person gaining without the person gaining weight. There maybe other weight. There maybe other mechanism besides weight gain, mechanism besides weight gain, for example high cholesterol for example high cholesterol levelslevels

What to Do with Dependence?What to Do with Dependence?

Ignore itIgnore it Works well with small dependenciesWorks well with small dependencies

Redo the causes and consequencesRedo the causes and consequences Refine the consequence so that it is specific Refine the consequence so that it is specific

to occurring through the target event to occurring through the target event Combine multiple causes into one generalized Combine multiple causes into one generalized

causecause Change the odds form formula Change the odds form formula

Bayes Formula for Joining Bayes Formula for Joining HMOHMO

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

Accountingfor dependency

Ignoring it

Take Home LessonTake Home Lesson

A cause & consequence graph A cause & consequence graph can tell us a great deal about can tell us a great deal about

model structuremodel structure