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:
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: