# 本次加拿大留学生统计作业代写主要是完成贝叶斯网络的推理

CMPT 310 Artificial Intelligence Survey

Simon Fraser University Spring 2021

Assignment 4: Probabilistic Reasoning and Learning

P（所有节点均为假）=
P（喉咙痛=假|所有其他节点均为假）×P（所有​​其他节点均为假）。您可以通过使用该工具执行查询来获得第一个条件概率。

P（所有节点为假）
P（喉咙痛=真，所有其他节点均为假）
P（喉咙痛以外的所有其他节点为false）
P（所有节点均为假）= P（喉咙痛=假|其他所有节点均为假）x P（所有其他节点均为假）。
P（喉咙痛=真，发烧=真）

“如果没有观察到证据，流感和吸烟是概率独立的。”

（10分）从数字语义上证明这一说法，即表明流感和烟的值在所有可能性上都是独立的。您可以在工具中使用查询来执行此操作。

（10分）从拓扑语义学上证明这一点，即使用马尔可夫条件，即给定其父代的值，该变量在概率上独立于其所有后代。

Probabilistic Reasoning With Bayesian Networks 75 points total.

Go to www.aispace.org and start the “belief and decision network” tool. Load the sample file “File/Load Sample Problem/Simple Diagnostic Example”. We will use this to test some of the basic probability laws. The AIspace tool can do many of these calculations for you, but the purpose of the exercise is to learn the principles behind the calculations. You can use the tool to check your answers, but you should compute them yourself using the probability calculus together with the conditional probabilities from the Bayesian network. If you have difficult running the tool in the browser, try downloading the jar file.

Joint Probabilities. 25 points
Compute the following joint probabilities up to 6 significant digits.

1. Use the product formula of Bayes nets and the conditional probability parameters specified by AIspace to compute the probability that: all nodes are false.
2. Use the product formula of Bayes nets and the conditional probability parameters specified by Aispace to compute the probability that: all nodes are false except for Sore Throat, and that Sore Throat is true.
3. Show how can you use these two joint probabilities to compute the probability that: all nodes other than Sore Throat are false. (Where the value of Sore Throat is unspecified.)
4. Verify the product rule:
P(all nodes are false) =
P(Sore Throat = false| all other nodes are false) x P(all other nodes are false). You may get the first conditional probability by executing a query with the tool.
5. Compute the probability that Sore Throat is true and that Fever is true. (Hint: If you use the right formula, you only need 4 conditional probabilities.)

You can enter the computed probabilities in the table below.

Probability to be Computed
P(all nodes false)
P(Sore Throat = True, all other nodes false)
P(all nodes other than Sore Throat false)
P(all nodes are false) = P(Sore Throat = false| all other nodes are false) x P(all other nodes are false).
P(Sore Throat = true, Fever = True)

Independence. 20 points

“If no evidence is observed, Influenza and Smoking are probabilistically independent.”

1. (10 points) Prove this statement from the numerical semantics, i.e. show that the values of Influenza and Smokes are independent for all possibilities. You may use queries in the tool to do this.
2. (10 points) Prove this from the topological semantics, i.e. using the Markov condition that given values for its parents, a variable is probabilistically independent of all its nondescendants.

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