Bayesian estimation uses subjective judgment in an engineering design.

For discrete case, let the parameter θ takes the values θi; *i *= 1, 2, ... , *n *with the probabilities *Pi *= P [θ = θi]. Let θ_{0} be the observed outcome of the experiment. Then by Bayes' theorem

Then the expected value of 8 is called Bayesian estimator of the parameter, *i.e.,*

For continuous case, let 8 be a random variable of the parameter of the distribution given by the density function f '(θ). Then

P[θi < θ < θi + ∆θ] = f'(θi) . ∆θ, *i *= 1, 2, ... , *n*

If θ_{0} is an observed experimental outcome, then

i = 1, 2, ... , *n*

In the limit we obtain, *f" *(θ) =