Identifiability analysis helps us understand how we can figure out which parts of something we are interested in can be measured or observed. Imagine you're playing a game of hide-and-seek with some of your friends. Before you start playing, you need to decide on a few rules so that you can all play fairly. One of the rules might be that you will all hide in a certain area, like a backyard, and whoever is "it" will go find the others.
Now, imagine that you are "it," and your friends have scattered all over the yard. You need to find them, but you don't know where they are. You might look around and see some clues, like footprints or giggling noises coming from behind a tree. These clues help you figure out where your friends might be hiding, and you use them to guide your search.
In the same way, identifiability analysis helps us figure out which clues we can use to learn more about a complex system or process. For example, imagine that you are a scientist studying the human brain. The brain is a very complicated system with many different parts and functions. To understand how the brain works, you might want to measure certain things, like the activity of neurons or the amount of oxygen in different parts of the brain.
However, not all of these things are easy to measure directly. For example, you can't just stick a probe into someone's brain and start measuring the activity of neurons or blood flow. Instead, you need to use indirect clues, like brain scans or behavioral studies, to get insights into what is happening in the brain.
Identifiability analysis helps you understand which clues are most useful for studying a particular aspect of the brain. For example, you might use a brain scan to measure the activity of different parts of the brain while someone is performing a certain task. By comparing these scans to scans taken while the person is resting, you can start to get an idea of which parts of the brain are most important for that task. This is called identifiability analysis, and it helps you figure out how to study complex systems like the brain in a more effective way.