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Those slides describe how the probabilistic computations are handle in the application http://worldcup.bayesialab.com. This application computes the Stage 2 qualification probability of any team of ...

Those slides describe how the probabilistic computations are handle in the application http://worldcup.bayesialab.com. This application computes the Stage 2 qualification probability of any team of any Group of the next FIFA World Cup. Based on the user input (with probability distributions on the Group matches' result: win, draw, and loss), a Bayesian Network is used to rigorously compute the qualification probabilities.

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- 1. How it Works? A Probabilistic Expert System based on a Bayesian Belief Network
- 2. Bayesian Belief Networks are made of Two Distinct parts Structure Directed Acyclic Graph Nodes represent the variables of the studied domain (e.g.: URU-FRA to model the Match Uruguay versus France) Each node has exclusive states (e.g.: FRA, Draw, URU) Arcs represent the direct probabilistic influences between the variables (possibly causal), e.g.: the results of the matches implying France have a direct impact on the final number of points of France Parameters Probability distributions are associated to each node, usually by using tables CONDITIONAL PROBABILITY DISTRIBUTION Here, for a France’s defeat MARGINAL PROBABILITY The result of the first match has an impact on the against Uruguay, we set a 45% DISTRIBUTION team’s spirit and then on the probability chance that France wins the We here consider that Uruguay has a 15% chance distribution of the second match second match vs Mexico, 40% to win the match against France, 60% that it will for a draw, and 15% for a be a draw, and 25% that France will win it defeat. On the other hand, if France wins, we set a 85% chance for a win in the second match, 10% for a draw, and 5% for a defeat
- 3. Bayesian Belief Networks are Powerful Inference Engines We exploit all the information available on a subset of variables for updating, in a rigorous way, the probability distribution of the other variables All kinds of inference are allowed: Simulation: from “causes” toward “effects” “What are the consequences on the Qualification probability for Stage 2 when the team loses its first match?” Diagnosis: from “effects” toward “causes” “When a team is qualified for Stage 2, what is the probability that this team has lost its first match?” All the combinations of those two kinds of inference: “When a team is qualified for Stage 2, with a draw during its first match, what is the probability that this team has won its second match?”
- 4. The Bayesian Network used for the Application
- 5. The structure: 3 layers The 6 matches of Group A The points for each team The qualification for each team
- 6. The Parameters Marginal probability distribution defined as Equiprobable. The user will define his/her own distribution by using the web application’s sliders, for describing his/her own knowledge/belief Deterministic relation between the 3 matches and the total number of points for Stage 1 A probabilistic equation describes the different qualification scenarios
- 7. Probabilistic Computation: Simulation “What are the consequences on the Qualification probability for Stage 2 when the team loses its first match?” Initially, without modifying the equiprobable distribution on the matches’ results, the Qualification probability is 50% If Uruguay loses the first match, the Qualification probability falls from 50% to 23.59% (without any information on the other matches’ results)
- 8. Probabilistic Computation: Diagnosis “When a team is qualified for Stage 2, what is the probability that this team has lost its first match?” Given that France is qualified for Stage 2 ..... ... there is a 15.73% chance that France has lost the first match
- 9. Probabilistic Computation “When a team is qualified for Stage 2, with a draw during its first match, what is the probability that this team has won its second match?” Given that France made a draw during the first match .... ... and France is qualified for Stage 2 ..... ... there is then a 58.49% chance that France won the second match
- 10. Probabilistic Computation “Is it possible to be qualified for Stage 2 with 2 points only?” Given that South Africa gets 2 points only .... ... there is still a 1.23% chance that South Africa is qualified
- 11. We wish you pleasant simulations ... and a great World Cup http://worldcup.bayesialab.com
- 12. Contact 6 rue Léonard de Vinci BP0119 53001 LAVAL Cedex FRANCE Dr. Lionel JOUFFE President / CEO Tel.: +33(0)243 49 75 58 Skype: +33(0)970 46 42 68 Mobile: +33(0)607 25 70 05 Fax: +33(0)243 49 75 83

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