سوال ۱۹ کنکور ارشد علوم کامپیوتر ۱۳۹۸

Read the following passage and answer the question by marking the best choice.

PASSAGE I

Perhaps the richest and most exciting area of application of the projection theorem is the area of statistical estimation. It appears in virtually all branches of science, engineering, and social science for the analysis of experimental data, for control of systems subject to random disturbances, or for decision making based on incomplete information.

All estimation problems discussed in this chapter are ultimately formulated as equivalent minimum norm problems in Hilbert space and are resolved by an appropriate application of the projection theorem. This approach has several practical advantages but limits our estimation criteria to various forms of least squares. The differences lie primarily in the choice of optimality criterion and in the statistical assumptions required.

Least squares is, of course, only one of several established approaches to estimation theory, the main alternatives being maximum likelihood and Bayesian techniques. These other techniques usually require a complete statistical description of the problem variables in terms of joint probability distribution functions, whereas least squares requires only means, variances, and covariances. In complicated, multivariable problems the equations resulting from the other approaches are often nonlinear, difficult to solve, and impractical to implement. It is only when all variables have Gaussian statistics that these techniques produce linear equations, in which case the estimate is identical with that obtained by least squares. In many practical situations then, the analyst is forced by the complexity of the problem to either assume Gaussian statistics or to employ a least-squares approach. Since the resulting estimates are identical, which is used is primarily a matter of taste.

The estimate by various approaches is identical if ______.