---
title: "Bayesian Belief Networks"  
description: "Brief Description about Bayesian Belief Networks with real life examples"  
author: "Bhavesh Badani"  
published: 2024-04-09  
updated: 2024-04-09  
canonical: https://www.mindstick.com/articles/335620/bayesian-belief-networks  
category: "artificial intelligence"  
tags: ["artificial intelligence"]  
reading_time: 2 minutes  

---

# Bayesian Belief Networks

## What Are BBNs?

- A **Bayesian Belief Network** is a graphical representation of probabilistic [relationships](https://www.mindstick.com/blog/11850/how-to-build-stronger-relationships-with-your-employees) among different **random [variables](https://www.mindstick.com/forum/34626/global-variables-superglobals)**.
- These variables can represent anything: diseases, [weather conditions](https://answers.mindstick.com/qa/33649/what-country-has-the-best-climate-in-the-world-not-too-hot-not-too-cold-no-extreme-weather-conditions-etc), [financial markets](https://answers.mindstick.com/qa/42737/what-goals-did-president-roosevelt-set-for-financial-markets), or even [whether your](https://www.mindstick.com/interview/33734/how-will-you-cross-check-whether-your-seo-campaign-is-working-or-not) cat will knock over that glass of water.

**Graphical [Structure](https://www.mindstick.com/blog/302153/structured-vs-unstructured-data-key-differences):**

- Imagine nodes (circles) [connected](https://www.mindstick.com/articles/12941/link-building-and-search-engine-rankings-how-are-they-connected) by arrows (edges).
- Each node represents a random variable (e.g., “Alarm ringing,” “Burglary,” “Fire”).
- The arrows show dependencies between variables.

**Conditional [Independence](https://answers.mindstick.com/qa/62194/after-india-s-independence-the-first-state-organized-on-the-basis-of-language-age-is):**

- BBNs are conditionally independent.
- This means that each node’s probability depends only on its parents (directly connected nodes).

### Example: Alarm System

Let’s consider a simple example: an **alarm system** in a house.

## Nodes:

- **Alarm (A)**: Represents whether the alarm rings.
- **Burglary (B)**: Whether a burglary occurred.
- **Fire (F)**: Whether there’s a fire.
- **Person 1 (P1)**: Whether person 1 calls (hearing the alarm).
- **Person 2 (P2)**: Whether person 2 calls (also hearing the alarm).

## Probabilities:

We have observed probabilities for each event:

- P(B=T) = 0.001 (Burglary occurred)
- P(F=T) = 0.002 (Fire occurred)
- P(A|B,T) = 0.95 (Alarm rings given burglary and fire
- P(A|B,T) = 0.95 (Alarm rings given burglary and fire)
- P(A|B,F) = 0.94 (Alarm rings given burglary, no fire)
- P(A|~B,~F) = 0.001 (Alarm rings when no burglary or fire)

## Person Nodes:

**P1** and **P2** call based on the alarm:

- P(P1|A,T) = 0.95 (Person 1 calls if alarm rings)
- P(P2|A,T) = 0.80 (Person 2 calls if alarm rings)

## Question:

- What’s the probability that both **P1** and **P2** call when the **alarm rings**, but there’s **no burglary (B)** and **no fire (F)**?

## Solution:

- We compute: P(P1, P2, A, ~B, ~F)
- Using the observed probabilities, we find the joint probability.

#### Conclusion:

Remember, Baysian belief network's help us reason about complex systems by breaking [them down](https://answers.mindstick.com/qa/36760/do-pets-know-when-you-are-putting-them-down) into simpler parts.

---

Original Source: https://www.mindstick.com/articles/335620/bayesian-belief-networks

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