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.
Therefore, by Bayes’ theorem we get,
P where i=1, 2, ….., n.
Thus, as a result, the expected value of 8 is known as Bayesian estimator of the parameter, that is,
With this, the following can be obtained,
P
If the case be continuous, then let 8 be the random variable of the parameter of distribution denoted by the density function f’(.
Therefore, P [< θ < + ∆θ] = f'() . ∆θ, where i=1, 2, …, n.
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
Links of Previous Main Topic:-
- Introduction to statistics
- Knowledge of central tendency or location
- Definition of dispersion
- Moments
- Bivariate distribution
- Theorem of total probability addition theorem
- Random variable
- Binomial distribution
- What is sampling
- Estimation
- Point estimation
- Interval estimation
Links of Next Statistics Topics:-
- Statistical hypothesis and related terms
- Analysis of variance introduction
- Definition of stochastic process
- Introduction operations research
- Introduction and mathematical formulation in transportation problems
- Introduction and mathematical formulation
- Queuing theory introduction
- Inventory control introduction
- Simulation introduction
- Time calculations in network
- Introduction of game theory
