To implement the inference Burglary P(B| j,⥗m) in alarm problem by using Variable Elimination method in Python.
Step 1: Define the Bayesian Network structure for alarm problem with 5 random variables, Burglary,Earthquake,John Call,Mary Call and Alarm.
Step 2: Define the Conditional Probability Distributions (CPDs) for each variable using the TabularCPD class from the pgmpy library.
Step 3: Add the CPDs to the network.
Step 4: Initialize the inference engine using the VariableElimination class from the pgmpy library.
Step 5: Define the evidence (observed variables) and query variables.
Step 6: Perform exact inference using the defined evidence and query variables.
Step 7: Print the results.
#import required libraries
from pgmpy.models import BayesianNetwork
from pgmpy.factors.discrete import TabularCPD
from pgmpy.inference import VariableElimination
#define bayesian network structure
network=BayesianNetwork([
('Burglary','Alarm'),
('Earthquake','Alarm'),
('Alarm','JohnCalls'),
('Alarm','MaryCalls')
])
#define the conditional probability distributions
cpd_burglary = TabularCPD(variable='Burglary',variable_card=2,values=[[0.999],[0.001]])
cpd_earthquake = TabularCPD(variable='Earthquake',variable_card=2,values=[[0.998],[0.002]])
cpd_alarm = TabularCPD(variable ='Alarm',variable_card=2, values=[[0.999, 0.71, 0.06, 0.05],[0.001, 0.29, 0.94, 0.95]],evidence=['Burglary','Earthquake'],evidence_card=[2,2])
cpd_john_calls = TabularCPD(variable='JohnCalls',variable_card=2,values=[[0.95,0.1],[0.05,0.9]],evidence=['Alarm'],evidence_card=[2])
cpd_mary_calls = TabularCPD(variable='MaryCalls',variable_card=2,values=[[0.99,0.3],[0.01,0.7]],evidence=['Alarm'],evidence_card=[2])
#Add CPDs to the network
network.add_cpds(cpd_burglary,cpd_earthquake,cpd_alarm,cpd_john_calls,cpd_mary_calls)
#Initialize the inference engine
inference = VariableElimination(network)
#perform exact inference-------1
evidence ={'JohnCalls':1,'MaryCalls':0} #john called(1) and mary didn't call (0) as evidence
query_variable ='Burglary'
result = inference.query(variables=[query_variable],evidence=evidence)
print(result)
#perform exact inference--------2
evidence1 ={'JohnCalls':1,'MaryCalls':1} #john called(1) and mary called (1) as evidence
query_variable ='Burglary'
result2 = inference.query(variables=[query_variable],evidence=evidence)
print(result2)
Thus, Bayesian Inference was successfully determined using Variable Elimination Method
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