Models for Inexact Reasoning The Dempster-Shafer Theory of Evidence (A Sample Scenario) Miguel García Remesal Department of Artificial Intelligence mgremesal@fi.upm.es
Fed up with TV Series? • A patient is admitted to the hospital with the following symptoms: • Dr. Houses’ team is taking the case Dr. Gregory House Dr. Eric Foreman Dr. Alison Cameron
After the Initial Physical Exploration Gentlemen, { } { } Θ = = viral_diseases cold, flu, ... place your ( ) { } ( ) bets! = Θ = m cold, flu 0.8, m 0.2 F F ( ) { } ( ) = Θ = m flu 0.9, m 0.1 C C Yeah, I agree with It’s viral.Most Foreman. I’m probably flu or almost certain that just a regular it’s flu. cold.
Doctor, how long will it A Bit Later… take to fully recover? Don’t worry. It’s just Good. I gotta get back flu. You’ll be fine in a to work ASAP. I’ve week. been on holidays in Canada last month. I cannot afford staying in bed for longer! I have to pay my bills! What do you do for a living? I’m a vet. I visit different farms to diagnose and treat the animals. cough, cough, cough…
Just wait a minute… Ummm… I don’t really like that dry cough… Besides, he’s been in rural zones, and has recently traveled to Canada… This makes Avian Influenza and SARS a moderately relevant hypothesis. However, I cannot discard either flu or a regular cold. To be sure, I will order a chest X-Ray. { } { } Θ = = viral_diseases cold, flu, SARS, avian_influenza, ... ( ) ( ) { } { } ( ) = = Θ = m cold, flu 0.3, m SARS, avian_influenza 0.6, m 0.1 H H H
New Symptoms I find it difficult breathing!!! This makes SARS more probable. However, we will wait for the X-Rays. { } { } Θ = = viral_diseases cold, flu, SARS, avian_influenza, ... ( ) ( ) { } { } = = m SARS 0.7, m cold, flu 0.3 2 2 H H
New evidence: the X-Rays The results of the X-Rays: They show increased opacity in both lungs. This is a clear sign of pneumonia and respiratory distress syndrome. This hugely favours the SARS hypothesis. { } { } Θ = = viral_diseases cold, flu, SARS, avian_influenza, ... ( ) ( ) { } { } = = m SARS 0.99, m cold, flu 0.01 C 2 C 2
Diagnosis and Treatment It’s obviously SARS. Give him antipyretics, supplemental oxygen and ventilatory support. Hopefully he will recover quickly. Yes, Sir
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