UT Arlington CSE 4308 - Artificial Intelligence I Homework 5

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CSE 4308 / CSE 5360 - Artificial Intelligence I Homework 5: Probabilistic ReasoningCSE 4308 / CSE 5360 - Artificial Intelligence IHomework 5- Fall 2013Due Date: Nov. 21 2013, 12:30 pmProblems marked with a∗are required only for students in the graduate section (CSE 5360). They will begraded for extra credit for students of CSE 4308.Bayes Rule1. Disease D affects 1% of the population (P (D) = 0.01) and shows symptom S in 40% of all cases(P (S | D) = 0.4) while the same symptom can be observed only in 2% of people who do not have thedisease. There also is a test T for the disease that gives the correct diagnosis ( A or ¬A ) in 95% ofall cases. Given that you do experience symptoms and your test comes back positive, how high is theprobability that you have the disease ?Bayesian Networks2. Below is a probabilistic network to assess the probability of forest fires in a state park. The goal is to usethe available information about the presence of visitors in the park and about thunderstorms to predictthe probability of a forest fire. According to this model, the probability of a forest fire (F F ) depends oncamp fires (CF ) and on lightning (LT ). The probability of camp fires, in turn, depends on the presenceof park visitors (P V ) and thunderstorms (T S). Similarly, lightning is influenced by the presence ofthunderstorms.Park Visitors (PV)Thunderstorms (TS)Camp Fires (CF)Lightning (LT)Forest Fire (FF)a) Use the following conditional probabilities to determine the conditional probabilities of a forest firefor all possible, observable scenarios (i.e. P V ∧ T S, P V ∧ ¬T S, ¬P V ∧ T S, and ¬P V ∧ ¬T S).Make sure to show your calculations.2013 Manfred Huber Page 1CSE 4308 / CSE 5360 - Artificial Intelligence I Homework 5: Probabilistic ReasoningCF : P (CF | P V ∧ T S) = 0.3P (CF | ¬P V ∧ T S) = 0.01P (CF | P V ∧ ¬T S) = 0.7P (CF | ¬P V ∧ ¬T S) = 0.01LT : P (LT | T S) = 0.25P (LT | ¬T S) = 0.02F F : P (F F | CF ∧ LT ) = 0.3P (F F | ¬CF ∧ LT ) = 0.2P (F F | CF ∧ ¬LT ) = 0.2P (F F | ¬CF ∧ ¬LT ) = 0.01b) The same model is used in a different park with different weather patterns. Over time, the parkservice has determined that the conditional probabilities for forest fire, and campfire in this modelare the same as above. Through observations, it has also been determined that forest fires occurwith the following conditional probabilities:P (F F | ¬P V ∧ T S) = 0.05 P (F F | ¬P V ∧ ¬T S) = 0.015Calculate the conditional probabilities for lightning in the probabilistic model (i.e. P (LT | T S)and P (LT | ¬T S) ). Show your calculations.3.∗Use the AIspace Belief and Decision network solver (you can download it fromhttp://www.aispace.org/downloads.shtml or run it over the web from there) to implement the Bayesiannetwork from Problem 2 a) - with the addition of the prior probabilities for the two root nodes P (P V ) =0.75, P (T S) = 0.1 - and perform inference on the network. Submit your network in .bif format andshow the inference results for the following probabilities: P (P V | F F ∧ ¬T S), P (T S | CF ∧ ¬F F ),P (P V | ¬F F ∧ T S).2013 Manfred Huber Page


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UT Arlington CSE 4308 - Artificial Intelligence I Homework 5

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