Loading…

Flash Player 9 (or above) is needed to view presentations.
We have detected that you do not have it on your computer. To install it, go here.

Like this presentation? Why not share!

Like this? Share it with your network

Share

Session 42_1 Peter Fries-Hansen

on

  • 595 views

 

Statistics

Views

Total Views
595
Views on SlideShare
595
Embed Views
0

Actions

Likes
1
Downloads
1
Comments
0

0 Embeds 0

No embeds

Accessibility

Categories

Upload Details

Uploaded via as Microsoft PowerPoint

Usage Rights

© All Rights Reserved

Report content

Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
  • Full Name Full Name Comment goes here.
    Are you sure you want to
    Your message goes here
    Processing…
Post Comment
Edit your comment
  • 31 October 2011 … since we are dealing with complex and intricate matters it is necessary to build models of the problem
  • 31 October 2011 Just before the last lap in the Giro d’Italia in 1999, the Italian Marco Pantani was excluded from the race because of a positive EPO doping test. Marco Pantani was leading the race when he was excluded. In this exercise we will try to address the burning question regarding dope in the cycling sport somewhat closer. The main question is whether the bare knowledge of a doping test may reveal if a competitor has used dope.   Let us assume that the EPO test is able to detect the use of EPO with a probability of 95% (this number is often cited in newspapers). Moreover, let us assume that Pantani just has been tested positive in the EPO test. Our question is then, what is the probability that he is using EPO – or more precisely, what is the probability that Pantani has used EPO given that he was tested positive? No, the probability is not 95%, since we need information on the probability for a false positive test, and the prior probability that Pantani did use EPO.   In the newspapers nothing has been said regarding the false positive test, i.e., the probability of a positive EPO test given Pantani did not use EPO. Let us assume that this probability is 15%. Next we need to know the probability of the Giro d’Italia participants are using EPO (we cannot just say that all participants are using EPO, because then we did not need the testing). Let us assume that 10% are using EPO.
  • 31 October 2011 1.     Why is the cost of the cargo damage dependent on whether or not the damage is repairable? Check the costs at the end of the branch 1Y-2Y-3Y-4N-5Y – 6Y/N. 2.     There is not assigned any cargo damage cost to the branch 1Y-2N-3Y-4N, which is wrong. Compare to the branch discussed above. 3.     If we check the branch 1Y-2Y-3Y-4N we see that the expected structural damage is E[L]=0.3  60,000 + 0.7  420,000 = 312,000. This branch is comparable to the branch 1Y-2N-3Y-4N (the difference is in whether or not the damage is detected) where the expected structural damage is E[L]=0.2  240,000 + 0.8  240,000 = 240,000. Why does the effect of damage detection increase the structural damage costs by 30%? 4.     In the branch 1N-2N-3Y-4N-5N it is seen that there is assigned a large cargo damage cost to this case when the cargo is not sensitive to humidity. Why? In the branches above this was not the case. 5.     Does “Is vessel on voyage?” mean at sea? If “Is vessel on voyage=No” mean that the vessel is at harbour then it is surprising to see that 1 out of 16 lost bulk carriers due to “Damage to Hatchway Watertight Integrity on Bulk Carriers” are lost in harbours. ( P[Loss at sea]= 3.44E-4+8.03E-4+3.28E-5+7.64E-5=1.26E-3 and P[Loss in harbour] = 2.34E-5+5.46E-5 = 7.80E-5). Can this be verified? The cost of cargo damage is given with a precision that does not reflect the uncertainty in the assessment of the costs.
  • 31 October 2011

Session 42_1 Peter Fries-Hansen Presentation Transcript

  • 1. Bayesian Network and its use in risk analysis Transportforum, 13-14 januari, 2010, Linköbing, Sweden
  • 2.
    • Structure and materials
    • Propulsion
    • Compartmentation
    • Manoeuvring characteristics
    • Bridge layout
    • Quality of crew
    • +++
    Frequency Consequence Risk based procedures requires insight deeply into very complex matters Accidents: ?
  • 3. Structuring complex systems
    • REQUIREMENTS
    • Transparency
    • Uniformity in modelling complexity
    • Verifiability of probabilistic modelling
    • Bayesian Networks bridges the gab between model formulation and analysis
  • 4. Content
    • Why Bayesian Networks?
    • Elements of Bayesian Network
    • Building Bayesian Networks
    • Modelling decisions
  • 5. Introducing Bayesian Networks
    • A Bayesian Network
      • is a graphical representation of uncertain quantities
      • reveals explicitly the probabilistic dependence between the set variables
      • is designed as a knowledge representation of the considered problem
    • A BN is a network with directed arcs and no cycles
    • The nodes represents random variables and/or decisions
    • Arcs into random variables indicate probabilistic dependence
    • Causal modelling most effectively does the model building
  • 6. What do Bayesian methods offer ?
    • Allows one to learn about causal relationships
      • this knowledge allow to make predictions in the presence of interventions / observations
    • BN in conjunction with Bayesian statistical techniques facilitate the combination of domain knowledge and data
      • prior or domain knowledge
    • BN can readily handle incomplete data
      • missing data
    • Bayesian methods in conjunction with BN and other methods offers efficient methods to avoid over fitting of data
  • 7. BN for a set of variables Battery Gauge Fuel Turnover Start p(B) p(T|B) p(G|B, F) p(F) p(S| F, T) Directed Acyclic Graph low, normal, high none, click, normal low, normal, high empty, medium, full yes, no
  • 8. BN - elements
    • BN for a set of variables consists of:
    • 1. A network structure S that encodes a set of conditional independence assertions about the variables in X
    • 2. A set P of local, conditional probability distributions associated with each variable in X
    • 1. & 2. defines the joint probability distribution for X .
    • S is a Directed Acyclic Graph (DAG)
    • Nodes are in one-to-one correspondence with the variables in X
    • denotes both the stochastic variable and the associated node
    • denotes the parents to in S
    • Lack of possible arcs in S encode conditional independence
  • 9. Description (nodes) Probability node (discrete) Decision node Utility node Link / arc Local probability distribution (conditional)
  • 10. Bayesian Network
    • T
    Turnover - none - click - normal S Start - yes - no
  • 11. Missing arcs encode conditional independence Turnover T Gauge G
  • 12. Bayesian Network Structure: Definition
    • 1. Find the variables of the model
    • 2. Build a DAG that encodes assertions of conditional independence
      • Given an ordering of the variables
  • 13. Example Fuel Battery Turnover Gauge Start
  • 14. Example Fuel Battery Turnover Gauge Start
  • 15. Example Fuel Battery Turnover Gauge Start
  • 16. Variable order is important! Start Gauge Turnover Battery Fuel
  • 17. Causal knowledge simplifies the construction Battery Gauge Fuel Turnover Start
  • 18. Conditional independence simplifies Probabilistic Inference Battery Gauge Fuel Turnover Start g s f
  • 19. “ Explaining Away” Turnover Start Fuel If the car does not start, hearing the engine turn over makes no fuel more likely.
  • 20. Did Marco Pantani use EPO?
    • Just before the last lap in the Giro d’Italia in 1999, the Italian Marco Pantani was excluded from the race because of a positive EPO doping test. Marco Pantani was leading the race when he was excluded.
    • Question: does the bare fact of a positive EPO test reveal his quilt?
    • Assumptions:
    • The EPO test is able to detect the use of EPO with a probability of 95%
    • False positive test: Let us assume that this probability is 15%.
    • Probability of riders are using EPO: say, 10% are using EPO.
    HUGIN
  • 21. Max propagation – what is it ?
    • That configuration in the joint probability distribution that has the largest value
    • Identical to the ” FORM design point” in x -space
    • Identical to finding the dominant cut set for fault trees
  • 22. Hidden variables
    • Factors influencing high school students college plans. 10318 observations of SEX , SES ( S ocial E conomical S tatus), PE ( P arental E ducation), IQ , and CP ( C ollege P lans).
    SEX IQ PE SES CP Hidden Posterior structure without hidden variables SEX IQ PE SES CP
  • 23. Maximise expected utility Party Location - outdoor - indoor Utility Weather indoors outdoors .7 .3 .7 .3 dry rain dry rain 50 60 100 0 EU[indoors] = 0.7 (50) + 0.3 (60) = 53 EU[outdoors] = 0.7 (100) + 0.3 (0) = 70 select “outdoor”
  • 24. Time critical decisions System State H, to E1 E2 En Action A, t Duration of Process Utility probability of hypothesises for the different system states given observations E and background information  time dependent utility as a function of action A and system state H
  • 25. Basic network for navigator reacting in time Navigational route Vessel Object Visual distance Time for detection Minimum distance to avoid critical situation v 1 v 2
  • 26. Including the time aspect - DBN a1(5) a1(4) a1(3) a1(2) a1(1) SIF1(5) SIF1(4) SIF1 (3) SIF1 (2) SIF1(1) Seastate5 Seastate4 Seastate3 Seastate2 Seastate1 Initial a_1 Model unc. Fatigue modelling
  • 27. Fatigue inspection planning
  • 28. Where to get more information ?
    • HUGIN expert AS www.hugin. com
    • Association for Uncertainty in Artificial Intelligence www.auai.org
    • Microsoft Decision Group www.research.Microsoft.com/research/dtg
    • Bibliography
    • www-users.cs.york.ac.uk/~sara/reference/biblios/
  • 29. Two line Transformer station subjected to earth quake
  • 30. Modelling the disconnect switch
  • 31. Bulk carrier safety: MSC74/INF.15, 2001 ?
  • 32. Safeguarding life, property and the environment www.dnv.com
  • 33. What is a complex system ?
    • Complex: A whole made up of dissimilar parts or parts of intricate relationship
    • Consisting of interconnected or interwoven parts; composite
    • Intricate: having a complicated organisation, with many parts or aspects difficult to follow or grasp
  • 34. A complex system: Made up of parts of intricate relationship Many aspects or parts difficult to follow or grasp
    • Organisation
    • management systems
    • Technical disciplines
    • Ship / plant / …
    • Personnel
    • Competence
    • Human errors
    • Habitability
    • Occupational health
  • 35. Bayes rule Where: Reverend Thomas Bayes 1702-1761 Joint events:
  • 36. Propagation in Bayesian Network
    • U grows exponentially with number of variables and states – for binary O(2 N )
    • Calls for efficient algorithm
    • JUNCTION TREE
      • The nodes of the junction tree are sets of variables called cliques
      • Links are separators , which is the intersection of the adjacent cliques
  • 37. Triangulated graph and junction tree 1 2 3 4 5 6 145 456 345 235 45 45 35 1 2 3 4 5 6
  • 38. Learning
    • Learning probability distributions
      • Uses EM algorithm
        • Log likelihood optimisation reformulated to nested optimisation
        • Assures better and faster convergence
      • Beta distribution
      • Dirichlet distribution
    • Learning the structure – more ambitious
      • Priors for all structures
  • 39. System knowledge and data X1 X2 X4 X3 Prior Network  Sample size Data X1 X2 X3 X4 x1 : T F T T x2 : F T T F …… xn : T T F F X1 X2 X4 X3 Priors for all structures Learned structure http://b-course.cs.helsinki.fi/
  • 40. Interpretation of critical situation Navigational route Vessel Object Visual distance Time for detection Minimum distance to avoid critical situation Legend: v 1 v 2
    • Considerations:
    • Visual detection
    • Radar detection
    • Dependency of weather
    • Correlation among variables
    • Perception and assessment of situation
  • 41. Description of the critical situation
      • “ During the watch the considered vessel is on collision course with an object. Moreover, machinery and steering gear are functioning. ”
      • “ Does the Officer On the Watch react in time so that the collision is avoided? ”
  • 42. Basic network
  • 43. Concept of the conventional bridge
    • Conventional bridge is a modern bridge
    • A rating lookout will (in principle) be present on the bridge from sunset to sunrise
    • Calling of a rating lookout during daytime if conditions causes solo watch keeping being unsafe
      • conditions of weather,
      • visibility,
      • proximity of dangers to navigation,
      • traffic situation
  • 44. Conventional bridge
  • 45. Results - conventional bridge
  • 46. Comparison with observations Japanese observations in the period from 1966 to 1971 reveals a proportionality between risk for collision and visibility r :
    • Causes ?
    • Improved radar technology
    • Difference in causes for low visibility in DK and Japan
    Obtained factor is -1.1