In an engineering design, Bayesian estimation uses subjective judgement. The estimation is an estimated value that decreases the posterior expected value of a loss function. Also, it increases the posterior expected value of utility function.
For Bayesian estimation, for discrete cases, if the parameter takes a value of, where i=1, 2,….,n, with probability and let be the resultant outcome.
With this, the following can be obtained,
If the case be continuous, then let 8 be the random variable of the parameter of distribution denoted by the density function f’(.
If θ0 is the observed experimental outcome, then
f” () ∆θwhere i=1, 2, 3,…., n.
In the limit, f”(
Therefore, the Bayesian estimator is
This can be used to calculate P