1 / 16

On the Revision of Probabilistic Beliefs using Uncertain Evidence

On the Revision of Probabilistic Beliefs using Uncertain Evidence. Hei Chan and Adnan Darwiche UCLA Presented by: Valerie Sessions October 6, 2004. Overview. Jeffrey’s Rule / Probability Kinematics Virtual Evidence Method Switching between methods Interpreting evidential statements

addison
Download Presentation

On the Revision of Probabilistic Beliefs using Uncertain Evidence

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. On the Revision of Probabilistic Beliefs using Uncertain Evidence Hei Chan and Adnan Darwiche UCLA Presented by: Valerie Sessions October 6, 2004

  2. Overview • Jeffrey’s Rule / Probability Kinematics • Virtual Evidence Method • Switching between methods • Interpreting evidential statements • Commutativity of Revisions • Bounding Belief Change

  3. Questions to Keep in Mind • How should one specify uncertain evidence? • How should one revise a probability distribution? • How should one interpret informal evidential statements? • Should, and do, iterated belief revisions commute? • What guarantees can be offered on the amount of belief change induced by a particular revision?

  4. Probability Kinematics • Two probability distributions disagree on probabilities for a set of events, but agree on how that event affects another event.

  5. Jeffrey’s Rule • Uses Probability Kinetics • Given a probability distribution and some uncertain evidence bearing on this we have…

  6. Example 1 = 0.28

  7. Virtual Evidence Method • Given PR and new evidence n we have

  8. Example 2

  9. Virtual Evidence -> Jeffrey’s Rule Virtual Evidence To Jeffrey’s:

  10. Jeffrey’s Rule -> Virtual Evidence • Divide new Prob. by old Prob. for ratio

  11. Virtual Evidence and Jeffrey’s Rule in Belief Networks • Virtual Evidence was built for this P(A) P(B) P(n|A) For Jeffrey’s Rule -> Convert to Virtual Evidence and then put in belief network (cheat)

  12. Interpreting Evidential Statements • Looking at the evidence, I am willing to bet 2:1 that David is not the killer. • Jeffrey’s Rule – “All things considered” • Pr'(killer) = 2/3 • Pr'(not killer) = 1/3 • Virtual Evidence – “Nothing else considered” • Pr(evidence|killer):Pr(evidence|not killer) = 2 : 1

  13. Process for Mapping Evidence • One must adopt a formal method for specifying evidence (Jeffrey’s Rule or Virtual Evidence) • One must interpret the informal evidence statement as a formal piece of evidence using the method chosen • One must apply a revision, by mapping the original probability distribution and formal piece of evidence into a new distribution, according to a belief revision principle

  14. Commutativity of Iterated Revisions • Jeffrey’s Rule is not commutative • Wagner suggests Bayes Factors Odd of a given b are defined by: Bayes factor given by:

  15. Bounding Belief Change • Chan and Darwiche present a distance measure to bind belief revisions

  16. Bounding Belief Change • Using these theorems with Jeffrey’s Rule and the Virtual Evidence Method Jeffrey’s Rule Virtual Evidence Method

More Related