Bayesian Models Homework (Individual Work)

Bayesian Models Homework (Individual work) · Please provide your answers as a pdf file (first file)

Bayesian Models Homework (Individual work) · Please provide your answers as a pdf file (first file) · Please upload your model file (second file) · Late uploads will receive a 10 point deduction for each day the upload is late Use a Bayesian Belief Network software to create a model and provide answers to the following problem (excel solutions or manual calculations are not accepted) Problem 1 A. Build a Bayesian Network based on the diagram provided above (Diagram A). Use the probability tables to define the probability distributions for each node. a. What is the probability of “Slippery” given that the season is “fall” and “watering” is false? b. What is the season if “slippery” is true and “Sprinkler” is false?

Paper For Above instruction

Bayesian networks are probabilistic graphical models that represent a set of variables and their conditional dependencies via a directed acyclic graph (DAG). They are valuable for modeling complex stochastic systems and reasoning under uncertainty. The task involves constructing a Bayesian network based on a diagram (Diagram A) and probability tables, then answering specific probabilistic queries using Bayesian Belief Network software. This paper discusses the process of constructing the model, defining the probability distributions, and computing the required probabilities.

Building the Bayesian Network

The first step in addressing the problem is to create a Bayesian network that accurately reflects the relationships among the variables depicted in Diagram A. Although the diagram itself is not provided here, typical relationships in such models often include nodes such as “Season,” “Watering,” “Slippery,” and possibly other factors like “Sprinkler.” The nodes are arranged to reflect causal or conditional dependencies. For example, “Slippery” might depend on “Season” and “Watering,” while “Watering” could depend on “Season” or other environmental factors.

Using Bayesian network software such as Netica, Hugin, or GeNIe, the nodes are created, and directed edges are designed based on the dependencies suggested by Diagram A. Once the structure is established, the conditional probability tables (CPTs) for each node are input based on the provided data or estimates. These CPTs quantify the probability of a node given its parent nodes.

Defining Probability Distributions

For each node, the probability distribution must be specified. For instance, if “Slippery” depends on “Season” (with states like fall, winter, spring, summer) and “Watering” (true/false), the CPT for “Slippery” would list probabilities for each combination of parent states. Similarly, the prior probabilities for “Season” or “Watering” are input based on the data.

Accurate data entry ensures the Bayesian network adequately models the real-world system, allowing for meaningful inference. Once the model is configured, the software can be used to perform probabilistic queries as needed.

Answering the Queries

a. Probability of “Slippery” given “Season” is “fall” and “Watering” is false

Using the Bayesian network software, this probability is computed by setting “Season” to “fall” and “Watering” to false, then querying the network for the probability of “Slippery” = true and “Slippery” = false. The software propagates the evidence through the network, considering all factors, to yield the posterior probability of “Slippery.”

b. Determining “Season” given “Slippery” is true and “Sprinkler” is false

This involves performing a backward inference: setting “Slippery” to true and “Sprinkler” to false as observed evidence, then calculating the posterior distribution over “Season.” The software computes the likelihood of each season being the true state given these observed variables, allowing identification of the most probable season or the full probability distribution.

Conclusion

Constructing a Bayesian network based on a diagram and probability tables involves defining nodes, dependencies, and CPTs, then performing probabilistic inference using specialized software. This process enables answering complex conditional questions, enhancing understanding of the modeled domain. Proper application of Bayesian reasoning supports decision-making under uncertainty, highlighting the value of such models in real-world scenarios.

References

• Buntine, W. (1994). Operations for learning with graphical models. Journal of Artificial Intelligence Research, 2, 159-225.