Bayesian uses the manipulation of conditional probabilities approach to interpret data. In this section, we build a decision system using the Bayesian method.

Consider *D*, called the decision space, which denotes the space of all possible decisions *d* that could be chosen by the **decision maker** (**DM). **
**Θ** is the space of all possible outcomes or state of nature ω, ω∈Θ.

Decision system-based Bayesian is built by Bayesian theory. For illustration, I show a simple spam filter using Bayesian. Imagine the sample space *X* is the set of all possible datasets of words, from which a single dataset word *x* will result. For each ω∈Θ and x∈X, the sampling model P(ω) describes a belief that *x* would be the outcome of spam probability. ...

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