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 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 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 Connected nodes Common effect Common effect 2 or more causes same effect2 or more causes same effect  Independencies: Common cause Common cause 2 or more effects, same cause2 or more effects, same cause Nodes arranged in a series 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 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 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 it Works well with small dependencies Works well with small dependencies  Redo the causes and consequences Refine the consequence so that it is specific to occurring through the target event Refine the consequence so that it is specific to occurring through the target event Combine multiple causes into one generalized cause Combine multiple causes into one generalized cause  Change the odds form formula

Bayes Formula for Joining HMO 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 Accounting for dependency Ignoring it

Take Home Lesson A cause & consequence graph can tell us a great deal about model structure