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### Bayesian Network Analysis Consider the Bayesian network below with 4 random variables: - **Storm (S):** There is a storm. - **Flood (F):** There is a flood. - **Holiday (H):** Today is a holiday. - **Closed (C):** Schools are closed. #### Network Details The Bayesian network is composed of nodes and directed edges: - **Nodes:** Represent the random variables (Storm, Flood, Holiday, Closed). - **Directed Edges:** Show dependencies between these variables. #### Probabilities - **Probability of Storm:** - \( P(S=\text{true}) = 0.20 \) - **Conditional Probability for Flood given Storm:** - \( P(F=\text{true} \mid S) \) - When Storm is true: 0.70 - When Storm is false: 0.05 - **Probability of Holiday:** - \( P(H=\text{true}) = 0.05 \) - **Conditional Probability for Closed given Storm and Holiday:** - \( P(C=\text{true} \mid S, H) \) - \( S = \text{true}, H = \text{true} \): 0.90 - \( S = \text{true}, H = \text{false} \): 0.70 - \( S = \text{false}, H = \text{true} \): 0.90 - \( S = \text{false}, H = \text{false} \): 0.01 #### Questions 1. **Probability of Event:** - "Today is not a holiday, there is a storm, but no flood, and schools are open." 2. **Markov Blanket of Holiday:** - Identify the set of nodes that shield Holiday from the rest of the network. 3. **Independence of Storm and Holiday:** - Determine if the variables Storm and Holiday are independent. 4. **Conditional Probability:** - Given no flood but schools are closed, find the probability of a storm. This network provides a framework to understand the interplay and conditional dependencies among the four variables and aids in probabilistic reasoning based on the given data.

### Bayesian Network Analysis Consider the Bayesian network below with 4 random variables: - **Storm (S):** There is a storm. - **Flood (F):** There is a flood. - **Holiday (H):** Today is a holiday. - **Closed (C):** Schools are closed. #### Network Details The Bayesian network is composed of nodes and directed edges: - **Nodes:** Represent the random variables (Storm, Flood, Holiday, Closed). - **Directed Edges:** Show dependencies between these variables. #### Probabilities - **Probability of Storm:** - \( P(S=\text{true}) = 0.20 \) - **Conditional Probability for Flood given Storm:** - \( P(F=\text{true} \mid S) \) - When Storm is true: 0.70 - When Storm is false: 0.05 - **Probability of Holiday:** - \( P(H=\text{true}) = 0.05 \) - **Conditional Probability for Closed given Storm and Holiday:** - \( P(C=\text{true} \mid S, H) \) - \( S = \text{true}, H = \text{true} \): 0.90 - \( S = \text{true}, H = \text{false} \): 0.70 - \( S = \text{false}, H = \text{true} \): 0.90 - \( S = \text{false}, H = \text{false} \): 0.01 #### Questions 1. **Probability of Event:** - "Today is not a holiday, there is a storm, but no flood, and schools are open." 2. **Markov Blanket of Holiday:** - Identify the set of nodes that shield Holiday from the rest of the network. 3. **Independence of Storm and Holiday:** - Determine if the variables Storm and Holiday are independent. 4. **Conditional Probability:** - Given no flood but schools are closed, find the probability of a storm. This network provides a framework to understand the interplay and conditional dependencies among the four variables and aids in probabilistic reasoning based on the given data.

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### Bayesian Network Analysis Consider the Bayesian network below with 4 random variables: - **Storm (S):** There is a storm. - **Flood (F):** There is a flood. - **Holiday (H):** Today is a holiday. - **Closed (C):** Schools are closed. #### Network Details The Bayesian network is composed of nodes and directed edges: - **Nodes:** Represent the random variables (Storm, Flood, Holiday, Closed). - **Directed Edges:** Show dependencies between these variables. #### Probabilities - **Probability of Storm:** - \( P(S=\text{true}) = 0.20 \) - **Conditional Probability for Flood given Storm:** - \( P(F=\text{true} \mid S) \) - When Storm is true: 0.70 - When Storm is false: 0.05 - **Probability of Holiday:** - \( P(H=\text{true}) = 0.05 \) - **Conditional Probability for Closed given Storm and Holiday:** - \( P(C=\text{true} \mid S, H) \) - \( S = \text{true}, H = \text{true} \): 0.90 - \( S = \text{true}, H = \text{false} \): 0.70 - \( S = \text{false}, H = \text{true} \): 0.90 - \( S = \text{false}, H = \text{false} \): 0.01 #### Questions 1. **Probability of Event:** - "Today is not a holiday, there is a storm, but no flood, and schools are open." 2. **Markov Blanket of Holiday:** - Identify the set of nodes that shield Holiday from the rest of the network. 3. **Independence of Storm and Holiday:** - Determine if the variables Storm and Holiday are independent. 4. **Conditional Probability:** - Given no flood but schools are closed, find the probability of a storm. This network provides a framework to understand the interplay and conditional dependencies among the four variables and aids in probabilistic reasoning based on the given data.
Transcribed Image Text:### Bayesian Network Analysis Consider the Bayesian network below with 4 random variables: - **Storm (S):** There is a storm. - **Flood (F):** There is a flood. - **Holiday (H):** Today is a holiday. - **Closed (C):** Schools are closed. #### Network Details The Bayesian network is composed of nodes and directed edges: - **Nodes:** Represent the random variables (Storm, Flood, Holiday, Closed). - **Directed Edges:** Show dependencies between these variables. #### Probabilities - **Probability of Storm:** - \( P(S=\text{true}) = 0.20 \) - **Conditional Probability for Flood given Storm:** - \( P(F=\text{true} \mid S) \) - When Storm is true: 0.70 - When Storm is false: 0.05 - **Probability of Holiday:** - \( P(H=\text{true}) = 0.05 \) - **Conditional Probability for Closed given Storm and Holiday:** - \( P(C=\text{true} \mid S, H) \) - \( S = \text{true}, H = \text{true} \): 0.90 - \( S = \text{true}, H = \text{false} \): 0.70 - \( S = \text{false}, H = \text{true} \): 0.90 - \( S = \text{false}, H = \text{false} \): 0.01 #### Questions 1. **Probability of Event:** - "Today is not a holiday, there is a storm, but no flood, and schools are open." 2. **Markov Blanket of Holiday:** - Identify the set of nodes that shield Holiday from the rest of the network. 3. **Independence of Storm and Holiday:** - Determine if the variables Storm and Holiday are independent. 4. **Conditional Probability:** - Given no flood but schools are closed, find the probability of a storm. This network provides a framework to understand the interplay and conditional dependencies among the four variables and aids in probabilistic reasoning based on the given data.
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