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Bayesian Estimation is a methodology named after Thomas Bayer to make probability statements for different parameters. This estimation is different from maximum likelihood principle, basically because it uses the prior distribution of the parameter to provide its probability statement. The application of this method minimizes the posterior expectation of a loss function. On the contrary the use of this method shall maximize the posterior expectation of a utility function. The concepts under Bayesian estimation can be difficult to understand. Thus, Bayesian Estimation Assignment Help shall be instrumental in easy grasping of key points and the algorithm behind the method.
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Procedure and Important Factors
Following algorithm has been provided by Bayesian Estimation Assignment Help.
1. The formulation of prior distribution: Suppose that the parameter for which we seek the estimation is “X”. We need to find out its prior distribution i.e. pi of X. The prior distribution is indicative of the uncertainty attached to the parameter. As often the information regarding the parameter might be less, the prior distribution should preferably have a wide range. For instance, we have data that the average weight of a population is 50 – 100kg. So the preferential distribution should be (50-100) indicating that the average shall lie in this range itself. The Distribution charts are developed using proper skilled and statistical techniques.
2. The formulation of posterior distribution: This posterior distribution shall ultimately lead to the estimation of X. Firstly the conditional density of X has to be computed using Bayes theorem. This posterior distribution has the characteristic properties of any distribution. It shall integrate to 1. This distribution has a mean and variance like all the distributions. The mean of the posterior distribution shall be roughly close to the value of X. For step by step analysis, students are advised to refer Bayesian Estimation Assignment Help.
3. Conjugate priors: In case of sequential estimations, the conjugate parameters are extremely helpful as the posterior distribution of the present estimate shall be the prior distribution for the next measurement. If the conjugate priors are not used, the Bayesian estimation becomes complex and the use of numerical methods becomes unavoidable. Conjugate prior by definition is such a prior distribution which belongs to a particular parametric family. Interestingly, the posterior distribution that results from it shall also belong to the same parametric family. The use of conjugate priors simplifies a given estimation.
4. Risk functions: this depends on the type of measurement applied to find the distance between the parameter and estimation. The most frequently used risk function is the Mean Square Error method. However certain alternate risk functions are also available.
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