Evaluating a posterior density can sometimes be a daunting prospect and is a complicated solution to the multidimensional inference problem. Consider a point estimate which is an educated guess of the parameter value given the observations at hand. An analytical method to generate a point estimate based on all available observations can be designated as an estimator of x. The actual value obtained for will vary based on the estimator used. In addition, it will vary from experiment to experiment using the same estimator. Thus, the point estimate should itself be viewed as a stochastic variable.

To find a suitable estimator we define a cost function, , which defines a penalty for an erroneous estimate . In general, we would prefer cost functions where the penalty increases based on the magnitude of the difference error . Without loss of generality, we assume that the ...

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