Examples¶

This page provides detailed examples of using BayesCalc2 for various probabilistic reasoning tasks.

Medical Diagnosis¶

The medical diagnosis network demonstrates Bayesian reasoning about diseases and test results.

Network Definition (`medical_test.net`)¶

variable Disease {Present, Absent}
variable TestResult {Positive, Negative}
variable Symptom {Severe, Mild, None}

Disease { P(Present) = 0.01 }

Symptom | Disease {
    P(Severe | Present) = 0.6
    P(Mild | Present) = 0.3
    P(None | Present) = 0.1
    P(Severe | Absent) = 0.01
    P(Mild | Absent) = 0.09
    P(None | Absent) = 0.9
}

TestResult | Disease {
    P(Positive | Present) = 0.95
    P(Negative | Present) = 0.05
    P(Positive | Absent) = 0.10
    P(Negative | Absent) = 0.90
}

Example Queries¶

Prior probability of disease:

BayesCalc> P(Disease=Present)
P(Disease=Present) = 0.0100

Probability with positive test:

BayesCalc> P(Disease=Present|TestResult=Positive)
P(Disease=Present | TestResult=Positive) = 0.0876

Probability with symptoms and positive test:

BayesCalc> P(Disease=Present|TestResult=Positive, Symptom=Severe)
P(Disease=Present | TestResult=Positive, Symptom=Severe) = 0.8632

Insights¶

A positive test alone only raises disease probability to ~9% (from 1% prior)
Combining positive test with severe symptoms raises probability to ~86%
This demonstrates the importance of multiple evidence sources

Weather Prediction¶

A classic Bayesian network example showing how rain and sprinklers affect grass wetness.

Network Definition (`rain_sprinkler_grass.net`)¶

variable Rain {True, False}
variable Sprinkler {On, Off}
variable GrassWet {Yes, No}

Rain { P(True) = 0.2 }

Sprinkler | Rain {
    P(On | True) = 0.01
    P(On | False) = 0.4
}

GrassWet | Rain, Sprinkler {
    P(Yes | True, On) = 0.99
    P(Yes | True, Off) = 0.90
    P(Yes | False, On) = 0.85
    P(Yes | False, Off) = 0.05
}

Example Queries¶

Explaining away phenomenon:

BayesCalc> P(Rain|GrassWet=Yes)
P(Rain=True | GrassWet=Yes) = 0.6203

BayesCalc> P(Rain|GrassWet=Yes, Sprinkler=On)
P(Rain=True | GrassWet=Yes, Sprinkler=On) = 0.2686

Learning the sprinkler was on "explains away" some of the evidence for rain.

Student Network¶

Models student exam performance based on intelligence and exam difficulty.

Network Definition (`student_network.net`)¶

variable Intelligence {High, Medium, Low}
variable Difficulty {Hard, Easy}
variable Grade {A, B, C}

Intelligence {
    P(High) = 0.3
    P(Medium) = 0.5
    P(Low) = 0.2
}

Difficulty { P(Hard) = 0.4 }

Grade | Intelligence, Difficulty {
    P(A | High, Hard) = 0.6
    P(B | High, Hard) = 0.3
    P(C | High, Hard) = 0.1

    P(A | High, Easy) = 0.9
    P(B | High, Easy) = 0.08
    P(C | High, Easy) = 0.02

    P(A | Medium, Hard) = 0.2
    P(B | Medium, Hard) = 0.5
    P(C | Medium, Hard) = 0.3

    P(A | Medium, Easy) = 0.5
    P(B | Medium, Easy) = 0.4
    P(C | Medium, Easy) = 0.1

    P(A | Low, Hard) = 0.05
    P(B | Low, Hard) = 0.25
    P(C | Low, Hard) = 0.7

    P(A | Low, Easy) = 0.2
    P(B | Low, Easy) = 0.4
    P(C | Low, Easy) = 0.4
}

Example Queries¶

Inferring intelligence from grade:

BayesCalc> P(Intelligence|Grade=A)
P(Intelligence=High | Grade=A) = 0.5368
P(Intelligence=Medium | Grade=A) = 0.3473
P(Intelligence=Low | Grade=A) = 0.1159

Effect of knowing difficulty:

BayesCalc> P(Intelligence=High|Grade=A, Difficulty=Hard)
P(Intelligence=High | Grade=A, Difficulty=Hard) = 0.7568

A grade of 'A' on a hard exam is stronger evidence of high intelligence.

Asia Chest Clinic¶

A more complex medical diagnosis network from the Bayesian network literature.

Network Structure¶

Visit to Asia: Binary variable
Tuberculosis: Influenced by Asia visit
Smoking: Binary variable
Lung Cancer: Influenced by smoking
Bronchitis: Influenced by smoking
TuberculosisOrCancer: Logical OR of tuberculosis and lung cancer
X-Ray Result: Influenced by TuberculosisOrCancer
Dyspnoea: Influenced by TuberculosisOrCancer and bronchitis

Example Queries¶

BayesCalc> load examples/asia_chest_clinic.net
Network loaded successfully.

BayesCalc> P(LungCancer|Dyspnoea=Yes, XRayResult=Abnormal)
P(LungCancer=Yes | Dyspnoea=Yes, XRayResult=Abnormal) = 0.1025

BayesCalc> P(LungCancer|Dyspnoea=Yes, XRayResult=Abnormal, Smoking=Yes)
P(LungCancer=Yes | Dyspnoea=Yes, XRayResult=Abnormal, Smoking=Yes) = 0.1217

Boolean Shorthand¶

BayesCalc2 supports convenient shorthand for Boolean variables:

variable Rain {True, False}

Rain { P(True) = 0.2 }

Query with shorthand:

BayesCalc> P(Rain)        # Same as P(Rain=True)
P(Rain=True) = 0.2000

BayesCalc> P(!Rain)       # Same as P(Rain=False)
P(Rain=False) = 0.8000

Conditional queries:

BayesCalc> P(Rain|GrassWet)  # Same as P(Rain=True|GrassWet=True)
P(Rain=True | GrassWet=True) = 0.6203

Expression Evaluation¶

Combine multiple probabilities in arithmetic expressions:

BayesCalc> P(Rain) * P(Sprinkler)
0.0200

BayesCalc> P(Rain|GrassWet) / P(Rain)
3.1015

BayesCalc> 1 - P(Rain)
0.8000

Network Visualization¶

Generate PDF diagrams of your networks:

BayesCalc> visualize network.pdf
Visualization saved to network.pdf

BayesCalc> visualize network.pdf --page-size=letter --scale=1.2
Visualization saved to network.pdf (letter size, 120% scale)

Supported page sizes: a4, letter, legal, a3, tabloid

Batch Processing¶

Create a command file analysis.txt:

# Load network
load examples/medical_test.net

# Basic queries
P(Disease=Present)
P(TestResult=Positive)

# Conditional probabilities
P(Disease=Present|TestResult=Positive)
P(Disease=Present|TestResult=Positive, Symptom=Severe)

# Visualize
visualize medical_diagnosis.pdf

# Save results
# (Would need to redirect stdout in shell)

Run in batch mode:

bayescalc -b analysis.txt

Advanced Analysis¶

Information Theory¶

Calculate entropy and mutual information:

BayesCalc> entropy(Disease)
H(Disease) = 0.0808 bits

BayesCalc> mutualInformation(Disease, TestResult)
I(Disease; TestResult) = 0.0352 bits

Network Inspection¶

BayesCalc> ls
Variables:
  - Disease: {Present, Absent}
  - TestResult: {Positive, Negative}
  - Symptom: {Severe, Mild, None}

BayesCalc> printCPT Disease
CPT for Disease:
P(Disease=Present) = 0.0100
P(Disease=Absent) = 0.9900

BayesCalc> printCPT TestResult
CPT for TestResult | Disease:
P(TestResult=Positive | Disease=Present) = 0.9500
P(TestResult=Negative | Disease=Present) = 0.0500
P(TestResult=Positive | Disease=Absent) = 0.1000
P(TestResult=Negative | Disease=Absent) = 0.9000

Tips and Tricks¶

1. Use Tab Completion¶

In interactive mode, press Tab to complete: - Variable names - Command names - Domain values

2. Auto-normalization¶

You don't need to specify all probabilities:

variable Coin {Heads, Tails}
Coin { P(Heads) = 0.5 }  # Tails automatically gets 0.5

3. Missing Probabilities¶

If you don't specify probabilities for some combinations, they're auto-normalized:

GrassWet | Rain, Sprinkler {
    P(Yes | True, On) = 0.99
    P(Yes | True, Off) = 0.90
    # Other combinations auto-normalized
}

4. Error Checking¶

BayesCalc2 validates your network definition: - Probabilities must sum to 1.0 - All parent configurations must be covered - Variable names must be unique - Domain values must be unique within a variable

5. Performance¶

For large networks: - Variable elimination is efficient (much better than joint tables) - Order queries from most to least specific evidence - Consider breaking very large networks into subnetworks

More Examples¶

Explore the examples/ directory for more networks:

alarm_network.net - Home alarm system
car_starting.net - Car troubleshooting
credit_approval.net - Credit risk assessment
genetic_inheritance.net - Genetic traits
heart_disease.net - Cardiovascular diagnosis
marketing_funnel.net - Customer conversion
monty_hall.net - The famous probability puzzle
text_classification.net - Document categorization

Each demonstrates different aspects of Bayesian reasoning!

Examples¶

Medical Diagnosis¶

Network Definition (medical_test.net)¶

Example Queries¶

Insights¶

Weather Prediction¶

Network Definition (rain_sprinkler_grass.net)¶

Example Queries¶

Student Network¶

Network Definition (student_network.net)¶

Example Queries¶

Asia Chest Clinic¶

Network Structure¶

Example Queries¶

Boolean Shorthand¶

Expression Evaluation¶

Network Visualization¶

Batch Processing¶

Advanced Analysis¶

Information Theory¶

Network Inspection¶

Tips and Tricks¶

1. Use Tab Completion¶

2. Auto-normalization¶

3. Missing Probabilities¶

4. Error Checking¶

5. Performance¶

More Examples¶

Network Definition (`medical_test.net`)¶

Network Definition (`rain_sprinkler_grass.net`)¶

Network Definition (`student_network.net`)¶