- Backpropagation
- Backpropagation Decorrelation
- Backpropagation Through Structure
- Backpropagation Through Time
- Bag of Words
- Bagging
- Batch Normalization
- Bayesian Deep Learning
- Bayesian Deep Reinforcement Learning
- Bayesian Inference
- Bayesian Information Criterion
- Bayesian Network
- Bayesian Networks
- Bayesian Optimization
- Bayesian Reasoning
- Behavior Cloning
- Behavior Trees
- Bias-variance tradeoff
- Bidirectional Encoder Representations from Transformers
- Bidirectional Long Short-Term Memory
- Big Data
- Bio-inspired Computing
- Bio-inspired Computing Models
- Boltzmann Machine
- Boosting
- Boosting Algorithms
- Boosting Techniques
- Brain-Computer Interface
- Brain-inspired Computing
- Broad Learning System

# Bayesian Network with example

**Introduction:**

Bayesian Network is a probabilistic graphical model used to represent probabilistic relationships among variables. It is broadly used to support decision-making under uncertainty. It is a graphical model that represents a set of random variables and their conditional dependencies via directed acyclic graphs (DAG). This article aims to provide a detailed understanding of Bayesian Networks, their applications and an example depicting how Bayesian Networks work.
**What are Bayesian Networks:**

**How do Bayesian Networks work:**

**Example: Counterfeit Money Detection**
Consider a scenario where some counterfeit money has been discovered in a bank, and the bank wants to know how the counterfeit money got inside the bank. The bank suspects that the counterfeit money was either deposited by an employee or a customer. The bank has collected the following data:

- There are 100 employees and 1000 customers
- 5% of the employees and 10% of the customers have a motive to deposit counterfeit money
- 30% of the counterfeit money deposited by employees was detected, and 20% of the counterfeit money deposited by customers was detected.

Now, we will add the probabilities to the nodes and edges. We will use the data provided in the problem statement to determine the probabilities.

- P (Employee) = 0.01 and P (Customer) = 0.99 (The sum of these probabilities is 1).
- P (Counterfeit | Employee) = 0.05 and P (Counterfeit | Customer) = 0.10 (The probability of Employees or Customers depositing counterfeit money)
- P (Detection | Employee) = 0.3 and P (Detection | Customer) = 0.2

Using Bayes' theorem, we can calculate the probability of the counterfeit money deposited by employees given that it was detected by the bank. We can compute this probability using the following formula:
**P (Employee | Detection) = P (Detection | Employee) * P (Employee) / P (Detection)**
Now, we will use the probabilities in the Bayesian network we have created to calculate the probabilities and answer the question. Suppose we want to calculate the probability of counterfeit money deposited by customers given that it was not detected by the bank. We can compute this probability using the following formula:
**P (Customer | Not Detection) = P (Not Detection | Customer) * P (Customer) / P (Not Detection)**
After the calculation, we can determine that the probability of counterfeit money deposited by customers given that it was not detected by the bank is 0.176.
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