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. P(x|ω), prior distribution, is the true population characteristics and supposes a spam probability for x.P(ω|x)., posterior distribution, describes a belief that ω is the true value of spam, having observed dataset x.
The posterior distribution is obtained...