LLM-BN Decision Support Application

Summary

The LLM-generated Bayesian network is applied as a decision support tool for the Sleep Health and Lifestyle dataset. Conditional probability tables (CPTs) are populated from data; Bayesian inference enables probabilistic queries about stress, sleep quality, and health conditions given observed evidence. Two worked examples demonstrate clinical reasoning about nurses and doctors.

Overview

Once the BN structure is established (via LLM expert elicitation), it is operationalized as a decision support system by:

1. Populating Conditional Probability Tables (CPTs) for each node from the dataset
2. Performing probabilistic inference (using Bayes’ formula)
3. Querying the network with observed evidence to compute posterior probabilities over target variables

Implementation: PyAgrum library (Python) for BN creation and inference.

Bayesian Inference Framework

The BN propagates evidence using Bayes’ formula:

$$P(A\mid B)=\frac{P(B\mid A)\cdot P(A)}{P(B)}$$

where $P(A\mid B)$ is the posterior probability, $P(B\mid A)$ is the likelihood, $P(A)$ is the prior, and $P(B)$ is the marginal probability of the evidence.

Inference in the BN updates marginal distributions of all nodes when evidence is provided at any node — enabling both predictive (cause → effect) and diagnostic (effect → cause) reasoning.

CPT Structure

The BN consists of 10 nodes. Key CPTs (from Fig. 5 in paper):

• Sleep Duration: Low (<7 hrs) / Normal (≥7 hrs)
• Stress Level: Low / Moderate / High
• Quality of Sleep: Bad / Normal / Good

Worked Examples

Example 1: Impact of Sleep Quality on Nurses' Stress

Setup: A nurse with poor sleep quality (Sleep Duration = Low) and low physical activity.

Query: What is the probability of High stress?

Result:

• Poor sleep quality → P(High stress) = 41.56% (vs. 18.40% for normal or 4.32% for good sleep quality)
• Good sleep quality → P(Low stress) = 92.41%

Interpretation: Strong connection between sleep quality and stress levels. Nurses without adequate rest face a significantly higher probability of high stress.

Example 2: Impact of Health Conditions on Stress and Sleep Duration

Setup: A male doctor with a sleep disorder (insomnia) engaging in moderate physical activity.

Query: How do health conditions influence stress levels and sleep duration?

Method: Query the CPT values for stress and sleep duration given Sleep_Disorder = insomnia and Gender = male, Occupation = doctor.

Result: (Specific numerical output from Table 6 in paper) The BN accounts for occupation-specific factors — doctors and nurses have different work stressors and shift patterns captured through the Occupation node.

Two Types of BN Inference

Type	Direction	Example
Predictive inference	Cause → Effect	”Given low sleep duration, what is the probability of high stress?”
Diagnostic inference	Effect → Cause	”Given high stress, what is the most probable cause among observed variables?”

Connections

• Built on LLM Expert Elicitation for Bayesian Networks for the BN structure
• Demonstrates practical value of Entropy-Based BN Evaluation — a structured BN produces more useful conditional probabilities
• Related to Bayesian Outcome Models — different context (Bayesian networks vs Bayesian regression), but same core idea of probabilistic inference over causal structures

See Also

• Shaposhnyk 2025 - Overview — paper context
• LLM Expert Elicitation for Bayesian Networks — how the BN was built
• Directed Acyclic Graphs — BNs are DAGs; d-separation and causal identification concepts transfer directly
• Model Checking — validating BN conditional probability tables via posterior-predictive-style checks