Overview
Conditional Probability Models use Bayes Rule to represent a distribution as the result of multiplying various conditional probabilty factors. In the most general form, the probability can be written as
{% p(x_1, ... , x_n) = \Pi_{n=1}^N p(x_n|x_1, ..., x_{n-1}) %}
Various models will simplify the above equation by layering additional assumptions onto it.
Independence
In the case of independence, each variable is assumed to be independent of the others. This results in
{% p(x_1, ... , x_n) = \Pi_{n=1}^N p(x_n) %}
Markov
{% p(x_1, ... , x_n) = p(x_1) \Pi_{n=2}^N p(x_n|x_{n-1}) %}