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driver can be used to add entropy from Intel s TRNG to the device entropy pool Randomorg and Hotbits are two academic projects supplying large numbers of hardware-generated random bits online (Johnson 2001) Some caution is still warranted with respect to hardware random number generators Often, the exact amount of true entropy supplied by a hardware device is dif cult to determine (see Viega and McGraw 2001) For example, the raw thermal noise collected by the Intel generator is biased, and rmware postprocessing is applied to make the results appear more random (Jun and Kocher 1999) Typically, some forms of TRNG hardware generation are subject to environmental conditions, physical breakage, or incorrect installation.
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This source of uncertainty provides a good example of a low to mediumprobability issue with large impact that does not average out with other issues Such issues either happen or they do not, with a major impact either way relative to the expected outcome For example, assume a 200 million impact in this case with a 010 probability, resulting in an expected cost of 200 million 010 20 million If this issue had been quanti ed and rolled into the analysis used by the corporate board to set the budget for the project, the implicit effect would have been to give the project manager nancial ownership of this issue with a budget of 20 million If the issue was subsequently realized, this budget would not have suf ced and the project manager would have had to go back to the board for more money.
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If the issue was not subsequently realized, the project would have had 20 million to spend on other things that the board would not have appreciated Whatever the outcome, it would not be appropriate for the project to bear the nancial consequences of this kind of issue Responsibility for this issue in nancial terms had to be retained by the board, along with a portfolio of other similar issues associated with other projects It was clearly important for the project team to accept responsibility for physically managing this issue, including developing procedures and plans to avoid the issue being realized and developing contingency plans should it happen It might have been worth indicating to those responsible for avoiding the issue what sort of unpleasant futures might be forthcoming if the issue was realized.
Although most hardware generators check their output using the FIPS 140-1 test suite when the device starts up, these tests are not nearly as rigorous as those supplied by standard test suites for statistical software (see 3) Therefore, some testing of the output of a random number generator is warranted before using it for the rst time 254 Local Search Algorithms We discuss search algorithms and how to choose them in more detail in s 4 and 8 In 3 we show that modern statistical packages are still prone to the problems we describe, and in 10 we discuss some aspects of this problem with respect to nonlinear regression The purpose of this section is to alert researchers to the limitations of these algorithms.
But there was no point in making the project nancially responsible for it with an extra 20 million in the budget..
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Standard techniques for programming an algorithm to nd a local optimum of a function, which may or may not be the global optimum, typically involve examining the numerically calculated or analytic gradients of the likelihood function at the current guess for the solution, and then use these to determine a direction to head uphill Like other algorithms, bugs and oating point inaccuracies may cause problems for nonlinear optimization algorithms, and poorly scaled data can exacerbate inaccuracies in implementation Thus, numerical inaccuracies may prevent the location of local optima, even when the search algorithm itself is mathematically correct More important, nonlinear optimization algorithms suffer from a deeper limitation, that of nding the global optimum The conditions for global optima for some classes of problems are known (eg, quadratic functions).
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