By Adriaan van den Bos
ISBN-10: 0470147814
ISBN-13: 9780470147818
ISBN-10: 0470173858
ISBN-13: 9780470173855
The topic of this publication is estimating parameters of expectation types of statistical observations. The ebook describes an important facets of the topic for utilized scientists and engineers. This team of clients is usually no longer acutely aware of estimators except least squares. consequently one goal of this ebook is to teach that statistical parameter estimation has even more to supply than least squares estimation on my own. within the method of this booklet, wisdom of the distribution of the observations is taken with the alternative of estimators. an additional good thing about the selected technique is that it unifies the underlying concept and decreases it to a comparatively small selection of coherent, more often than not appropriate rules and notions.
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Extra resources for Parameter Estimation for Scientists and Engineers
Sample text
5. Generally, carefully modeling the expectations of the observations is essential. The model chosen should be complete in the sense that it must be capable of representing the true expectations of the observations but with the smallest number of parameters. A further important statistical property of the observations modeled as stochastic variables is their covariance. 22) C O V ( W ~ w,) , = E[(wm- Ew,)(w, - Ew,)]. Therefore, if m = n, cov(w,, w,) is equal to the variance uk where urnis the standard deviation of w,.
W N ) T correspond to those of the vector of stochastic variables w = (w1. . 22) is N ( P C). 23) C = diag (a:.. 25) This is the product of all marginal probability density functions of the 20,. Therefore, if normally distributed stochastic variables are uncorrelated, they are also independent. 26) If, in addition, all pn are identical, the stochastic variables 20, are called independent and identically normally distributed (iind). 22), the general expression for q(w) = lnp(w) for normally distributed w is N 2 1 2 1 2 q(w) = -- ln27r - - lndet C - -(w - P ) ~ C - ~ -( p )W .
W N ) be ~ modeled as a vector of stochastic variables. Then, the N x 1 (vector) expectation p of w is defined as .. p = EW = ( E w ~ E w , ) ~ . 1) 21 22 DISTRIBUTIONSOF OBSERVATIONS Thus, the nth element of p is described by p n = Ew,. 4) and p ( w ) is the joint probability densityfunction of the elements of w. Thus, w, is a stochastic variable while w, is the independent variable corresponding to it. Furthermore, dw = dw1 d w 2 . . 5) where the integrations are performed over all possible values the elements of w may assume.
Parameter Estimation for Scientists and Engineers by Adriaan van den Bos
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