# Naïve Bayesian Models (Evidence Models)

Naïve Bayesian models extend the idea of lookup models for probabilities to the extreme. It is possible to have any number of dimensions and still use the information along each dimension to get sensible results, even when the corresponding lookup model would have an empty cell for that combination of values—or even for *all* combinations of values. Instead of creating ever smaller cells, naïve Bayesian models combine the information from each dimension, making a simple assumption.

The “naïve” part of the name is this assumption: The dimensions are independent of each other, statistically speaking. This makes it possible to combine information along the dimensions into a single score. The Bayesian part of the name refers to a simple idea from probability. Understanding this idea is a good place to start.

## Some Ideas in Probability

The chi-square calculation uses expected values, and the calculation works for...