Analytical System Administration in Java

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Analytical System Administration
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Measured value Figure 11.13 Most distributions peak at some value, indicating that there is an expected value (expectation value) which is more probable than all the others
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completely uncertain, as in Figure 11.12. To summarize, a flat distribution is unbiased, or completely random. A non-flat distribution is biased, or has an expectation value, or probable outcome. In the limit of complete certainty, the distribution becomes a spike, called the delta distribution. We are interested in determining the shape of the distribution of values on repeated measurement for the following reason. If the variation of the values is symmetrical about some preferred value, (i.e. if the distribution peaks close to its mean value), then we can probably infer that the value of the peak or of the mean is the true value of the measurement and that the variation we measured was due to random external influences. If, on the other hand, we find that the distribution is very asymmetrical, some other explanation is required and we are most likely observing some actual physical phenomenon which requires explanation.
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Observational Errors
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All measurements involve certain errors. One might be tempted to believe that, where computers are involved, there would be no error in collecting data, but this is false. Errors are not only a human failing; they occur because of unpredictability in the measurement process, and we have already established throughout this book that computer systems are nothing if not unpredictable. We are thus forced to make estimates of the extent to which our measurements can be in error. This is a difficult matter, but approximate statistical methods are well known in the natural sciences, methods which become increasingly accurate with the amount of data in an experimental sample. The ability to estimate and treat errors should not be viewed as an excuse for constructing a poor experiment. Errors can only be minimized by design.
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Observational Errors
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11.8.1 Random, Personal and Systematic Errors There are three distinct types of error in the process of observation. The simplest type of error is called random error. Random errors are usually small deviations from the 'true value' of a measurement which occur by accident, by unforeseen jitter in the system, or some other influence. By their nature, we are usually ignorant of the cause of random errors, otherwise it might be possible to eliminate them. The important point about random errors is that they are distributed evenly about the mean value of the observation. Indeed, it is usually assumed that they are distributed with an approximately normal or Gaussian profile about the mean. This means that there are as many positive as negative deviations, and thus random errors can be averaged out by taking the mean of the observations. It is tempting to believe that computers would not be susceptible to random errors. After all, computers do not make mistakes. However, this is an erroneous belief. The measurer is not the only source of random errors. A better way of expressing this is to say that random errors are a measure of the unpredictability of the measuring process. Computer systems are also unpredictable, since they are constantly influenced by outside agents such as users and network requests. The second type of error is a personal error. This is an error which a particular experimenter adds to the data unwittingly. There are many instances of this kind of error in the history of science. In a computer controlled measurement process, this corresponds to any particular bias introduced through the use of specific software, or through the interpretation of the measurements. The final and most insidious type of error is the systematic error. This is an error which runs throughout all of the data. It is a systematic shift in the true value of the data, in one direction, and thus it cannot be eliminated by averaging. A systematic error also leads to an error in the mean value of the measurement. The sources of systematic error are often difficult to find, since they are often a result of misunderstandings, or of the specific behaviour of the measuring apparatus. In a system with finite resources, the act of measurement itself leads to a change in the value of the quantity one is measuring. To measure the CPU usage of a computer system, for instance, we have to start a new program which collects that information, but that program inevitably also uses the CPU, and therefore changes the conditions of the measurement. These issues are well known in the physical sciences and are captured in principles such as Heisenberg's Uncertainty Principle, Schrbdinger's cat and the use of infinite idealized heat baths in thermodynamics. We can formulate our own verbal expression of this for computer systems: Principle 51 (Uncertainty) The act of measuring a given quantity in a system with finite resources always changes the conditions under which the measurement is made, i.e. the act of measurement changes the system. For instance, to measure the pressure in a tyre, you have to let some of the air out, which reduces the pressure slightly. This is not noticeable on a car tyre, but it can be noticeable on a bicycle. The larger the available resources of the system, compared to the resources required to make the measurement, the smaller the effect on the measurement will be.
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