Filtration (probability theory)

Okay, let me explain filtration like you are 5 years old.

Imagine you have a big water tank filled with dirty water with some small rocks, sand and other impurities. Now, you want to clean it and make it pure to drink.

So, what do you do? You take a filter and slowly pour the water into it. The filter has small holes that only allow clean water to pass through and trap all the dirt and impurities.

In probability theory, filtration is a similar concept. It's like filtering information from a big pool of data or events. You have a set of events happening over time, and you want to understand what's happening over time, just like pouring water through a filter to get clean water.

Each time an event happens, some information is revealed, and more events happen, more information is revealed. We can think of this information flow as a filter with small holes.

This filtering process helps us understand the probability of future events based on the information we have so far. It's like predicting what will happen tomorrow based on what happened yesterday and today.

So, filtration is just like using a filter to extract only the important information from a pool of events to make better predictions.