One of the first simplifying assumptions a scientist makes when studying a system is that nothing in the system interacts with anything else or that each object is independent. This seems like a fairly naïve assumption because experience tells us that everything interacts with...well, everything else. However, there are a couple of major advantages that a scientist gains by making this assumption. One is that her equations for studying the system can be simplified greatly so that a low cost solution can be attained quickly. Another important advantage is that she now has a baseline that acts as a "sanity check" and can be compared with results from the more complicated interactive model. The example most people are familiar with from science is the Ideal Gas Model where the assumption is that the particles making up the gas do not interact with one another.

In the world of Data Mining, the Naïve Bayes Model plays a similar role to the Ideal Gas Model because it provides a much faster and simpler way to calculate a model that gives us an idea of the predictive characteristics of a dataset. It also provides an easy way to check the results of the application of a much more complicated algorithm. 

Yet, what does independence mean in the context of data? 

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Billy Decker, Consultant at StatSlice Systems