In this section, we build a simple decision system using Bayesian theory. A smart water system is a smart system that controls water. In general, you can see the system architecture in the following figure:
After using a sensing process on water to obtain the water quality, you can make a decision. If the water quality is good, we can transfer the water to customers. Otherwise, we purify the water.
To implement a decision system-based Bayesian theory, firstly we define the state of nature. In this case, we define two states of nature:
ω1: Water is ready for drinking
ω2: Water should be cleaned (kotor)
For inputs, we can declare x1 and x2 as negative and positive as the observation results. We define prior values and class conditional probabilities as follows:
To build a decision, we should make a loss function. The following is a loss function for our program:
