The Bayesian Theorem
Bayesian Theorem
The Bayesian theorem states the following equation:
where
is a conditional probability, also called posterior. is also a conditional probability, also called the likelihood. and are probabilities of observing and respectively without any given conditions, are known as the prior probability and marginal probability.
Bayesian Inference
Estimator
Suppose a fixed parameter
needs to be estimated. An estimator of , written as is a function that maps the observation space to the parameter space, which is naturally a random variable.
Bias
The bias of an estimator
is defined as If , then we call the estimator unbiased, otherwise it is biased.