Calculation
The posterior probability distribution of one random variable given the value of another can be calculated with Bayes' theorem by multiplying the prior probability distribution by the likelihood function, and then dividing by the normalizing constant, as follows:
gives the posterior probability density function for a random variable X given the data Y = y, where
- is the prior density of X,
- is the likelihood function as a function of x,
- is the normalizing constant, and
- is the posterior density of X given the data Y = y.
Read more about this topic: Posterior Probability
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