How it Works?


A Probabilistic Expert System based on a
        Bayesian Belief Network
Bayesian Belief Networks are made of Two Distinct parts


          Structure
                Directed Acyclic Graph

    ...
Bayesian Belief Networks are Powerful Inference Engines




We exploit all the information available on a subset of variab...
The Bayesian Network used for the Application
The structure: 3 layers




                                                           The 6 matches of
                  ...
The Parameters



        Marginal probability distribution defined as Equiprobable.
        The user will define his/her ...
Probabilistic Computation: Simulation

“What are the consequences on the Qualification probability for Stage 2 when the te...
Probabilistic Computation: Diagnosis

“When a team is qualified for Stage 2, what is the probability that this team has lo...
Probabilistic Computation

“When a team is qualified for Stage 2, with a draw during its first match, what is the probabil...
Probabilistic Computation


                           “Is it possible to be qualified for Stage 2 with 2 points only?”


...
We wish you pleasant
     simulations ...
and a great World Cup
  http://worldcup.bayesialab.com
Contact



6 rue Léonard de Vinci BP0119
53001 LAVAL Cedex
FRANCE




       Dr. Lionel JOUFFE
        President / CEO
   ...
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World Cup Qualification Prediction - How it works

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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 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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World Cup Qualification Prediction - How it works

  1. 1. How it Works? A Probabilistic Expert System based on a Bayesian Belief Network
  2. 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. 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. 4. The Bayesian Network used for the Application
  5. 5. The structure: 3 layers The 6 matches of Group A The points for each team The qualification for each team
  6. 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. 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. 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. 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. 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. 11. We wish you pleasant simulations ... and a great World Cup http://worldcup.bayesialab.com
  12. 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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