Unbiased

To simulate noise of different levels The most unbiased noise was taken as white Gaussian distributed one. Its variance a was chosen as its main parameter, because its mean value equaled zero. The ratio of ct to the maximum level of intensity on the projections... 

Furthermore, it was possible to suppress liftoff and offset effects by using efficient digital filter algorithms. These measures provide the tester with a nearly unbiased picture of the wheel that is to be tested and he can thus conduct a reliable evaluation. 

Selecting trial moves in an unbiased way typically means (a) choose an atom randomly , with equal probability from the complete set (b) displace it by random amounts in the v, y and z directions, chosen... 

It should be pointed out that external polarization differs from the unbiased (open circuit) case in that after application of, say, an anodic voltage only the oxidation reaction takes place on the metal, whereas the cathodic reaction (H — H2) occurs at the external counter-electrode. 

So basic is the notion of a statistical estimate of a physical parameter that statisticians use Greek letters for the parameters and Latin letters for the estimates. For many purposes, one uses the variance, which for the sample is s and for the entire populations is cr. The variance s of a finite sample is an unbiased estimate of cr, whereas the standard deviation 5- is not an unbiased estimate of cr. 

Earlier we introduced the confidence interval as a way to report the most probable value for a population s mean, p, when the population s standard deviation, O, is known. Since is an unbiased estimator of O, it should be possible to construct confidence intervals for samples by replacing O in equations 4.10 and 4.11 with s. Two complications arise, however. The first is that we cannot define for a single member of a population. Consequently, equation 4.10 cannot be extended to situations in which is used as an estimator of O. In other words, when O is unknown, we cannot construct a confidence interval for p, by sampling only a single member of the population. 

The second complication is that the values of z shown in Table 4.11 are derived for a normal distribution curve that is a function of O, not s. Although is an unbiased estimator of O, the value of for any randomly selected sample may differ significantly from O. To account for the uncertainty in estimating O, the term z in equation 4.11 is replaced with the variable f, where f is defined such that f > z at all confidence levels. Thus, equation 4.11 becomes... 

Historically, physical evidence has taken on increasing importance in criminal matters. Court decisions have consistentiy looked askance at a defendant s admissions of guilt and even question eyewitness testimony. Physical evidence has traditionally been viewed as impartial and unbiased, and not subject to the problems associated with confessions made by an accused or the testimony of witnesses. 

Entities involved in long-term contracts with electric utihties, such as fuel supphers and NUGs selling power to utihties, also have concerns that some utihties or industrial customers will not be able to honor their contracts under the new, more competitive system. Einahy, some utihties are concerned that they wih not be adequately reimbursed for opening up their transmission systems to competitors. The potential competitors in turn are concerned that utihties whl not provide unbiased access to their transmission systems if the utihties themselves are also in business of marketing power. There has also been some debate regarding which transmission facihties are eligible for open access. This is because some facihties are considered local distribution systems by utihties, which feel they should not be opened to competitors. 

ROBUST AND UNBIASED ESTIMATIONS IN CHEMICAL DATA TREATMENT... 

The fractional error is logarithmically unbiased that is, an M which is k times produces the same magnitude fractional error (but of opposite sign) as an M which is l/k times E. 

When one takes a sample at the rate of 0.3 liter min from a stack discharging 2000 m min to the atmosphere, the chances for error become quite large. If the sample is truly representative, it is said to be both accurate and unbiased. If it is not representative, it may be biased because of some consistent phenomenon (some of the hydrocarbons condense in the tubing ahead of the trap) or in error because of some uncontrolled variation (only 1.23 gm of sample was collected, and the analytical technique is accurate to 0.5 gm) (1). 

If the sample is unbiased, estimate the source mean, so that... 

The source mean is assumed to be the same if the sample is unbiased, as seen by... 

The variance of the sample and the population (source) may also be assumed equal if the sample is unbiased. The variance is S, defined as... 

Tbe partial results are shown in Figure 2-6.2.1. Tbe ranges of ignitable concentrations are superimposed on a spark ignition energy curve for bexane in air calculated from data in [56]. Both data sets are assumed to be characteristic ofn-hexane, unbiased by the presence of methylcyclopentane or hexane isomers (dimethylbutanes and methylpentanes). 

Once the bidders have been selected, an Invitation to Tender (ITT) needs to be prepared to provide a fixed baseline against which unbiased competitive bids may be made. The technical, commercial, and managerial requirements should be finalized and subject to review and approval prior to release. It is important that all functions with responsibili-... 

A theoretical model ought to be unbiased. It should rely on no presuppositions about molecular structure or chemical processes which would make it inapplicable to classes of systems or phenomena where these assumptions did not apply. It should not in general invoke special procedures for specific types of molecules. 

In the first chapter, we described a model chemistry as an unbiased, uniquely defined, and uniformly applicable theoretical model for predicting the properties of chemical systems. A model chemistry generally consists of the combination of a theoretical method with a basis set. Each such unique pairing of method with basis set represents... 

Finally we need to compare the variance of our estimator with the best attainable. It can be shown that The Cramer-Rao lower bound (CRLB) is a lower bound on the variance of an unbiased estimator (Kay, 1993). The quantities estimated can be fixed parameters with unknown values, random variables or a signal and essentially we are finding the best estimate we can possibly make. 

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