The purpose of this application paper is to apply the Stein-Chen (SC) method to provide a Poisson-based approximation and corresponding total variation distance bounds in a time series context. The SC method that is u...The purpose of this application paper is to apply the Stein-Chen (SC) method to provide a Poisson-based approximation and corresponding total variation distance bounds in a time series context. The SC method that is used approximates the probability density function (PDF) defined on how many times a pattern such as <em>I<sub>t</sub></em>,<em>I<sub>t</sub></em><sub>+1</sub>,<em>I<sub>t</sub></em><sub>+2</sub> = {1 0 1} occurs starting at position t in a time series of length N that has been converted to binary values using a threshold. The original time series that is converted to binary is assumed to consist of a sequence of independent random variables, and could, for example, be a series of residuals that result from fitting any type of time series model. Note that if {1 0 1} is known to not occur, for example, starting at position <em>t</em> = 1, then this information impacts the probability that {1 0 1} occurs starting at position <em>t</em> = 2 or <em>t</em> = 3, because the trials to obtain {1 0 1} are overlapping and thus not independent, so the Poisson distribution assumptions are not met. Nevertheless, the results shown in four examples demonstrate that Poisson-based approximation (that is strictly correct only for independent trials) can be remarkably accurate, and the SC method provides a bound on the total variation distance between the true and approximate PDF.展开更多
Several nondestructive assay (NDA) methods to quantify special nuclear materials use calibration curves that are linear in the predictor, either directly or as an intermediate step. The linear response model is also o...Several nondestructive assay (NDA) methods to quantify special nuclear materials use calibration curves that are linear in the predictor, either directly or as an intermediate step. The linear response model is also often used to illustrate the fundamentals of calibration, and is the usual detector behavior assumed when evaluating detection limits. It is therefore important for the NDA community to have a common understanding of how to implement a linear calibration according to the common method of least squares and how to assess uncertainty in inferred nuclear quantities during the prediction stage following calibration. Therefore, this paper illustrates regression, residual diagnostics, effect of estimation errors in estimated variances used for weighted least squares, and variance propagation in a form suitable for implementation. Before the calibration can be used, a transformation of axes is required;this step, along with variance propagation is not currently explained in available NDA standard guidelines. The role of systematic and random uncertainty is illustrated and expands on that given previously for the chosen practical NDA example. A listing of open-source software is provided in the Appendix.展开更多
One of the simplest tests of a radiation portal monitor (RPM) is a series of n repeats (a vehicle drive-through) in which the ith repeat records a total number of counts Xi and alarms if Xi ≥ T where T is an alarm th...One of the simplest tests of a radiation portal monitor (RPM) is a series of n repeats (a vehicle drive-through) in which the ith repeat records a total number of counts Xi and alarms if Xi ≥ T where T is an alarm threshold. The RPM performance tests we consider use n repeats to estimate the probability p = P(Xi ≥ T). This paper addresses criterion A for testing RPMs, where criterion A is: for specified source strength, we must be at least 95% confident that p ≥ 0.5. To assess criterion A, we consider a distribution-free test and a test relying on assuming the counts Xi have approximately a Poisson distribution. Both test options require tolerance interval construction.展开更多
文摘The purpose of this application paper is to apply the Stein-Chen (SC) method to provide a Poisson-based approximation and corresponding total variation distance bounds in a time series context. The SC method that is used approximates the probability density function (PDF) defined on how many times a pattern such as <em>I<sub>t</sub></em>,<em>I<sub>t</sub></em><sub>+1</sub>,<em>I<sub>t</sub></em><sub>+2</sub> = {1 0 1} occurs starting at position t in a time series of length N that has been converted to binary values using a threshold. The original time series that is converted to binary is assumed to consist of a sequence of independent random variables, and could, for example, be a series of residuals that result from fitting any type of time series model. Note that if {1 0 1} is known to not occur, for example, starting at position <em>t</em> = 1, then this information impacts the probability that {1 0 1} occurs starting at position <em>t</em> = 2 or <em>t</em> = 3, because the trials to obtain {1 0 1} are overlapping and thus not independent, so the Poisson distribution assumptions are not met. Nevertheless, the results shown in four examples demonstrate that Poisson-based approximation (that is strictly correct only for independent trials) can be remarkably accurate, and the SC method provides a bound on the total variation distance between the true and approximate PDF.
文摘Several nondestructive assay (NDA) methods to quantify special nuclear materials use calibration curves that are linear in the predictor, either directly or as an intermediate step. The linear response model is also often used to illustrate the fundamentals of calibration, and is the usual detector behavior assumed when evaluating detection limits. It is therefore important for the NDA community to have a common understanding of how to implement a linear calibration according to the common method of least squares and how to assess uncertainty in inferred nuclear quantities during the prediction stage following calibration. Therefore, this paper illustrates regression, residual diagnostics, effect of estimation errors in estimated variances used for weighted least squares, and variance propagation in a form suitable for implementation. Before the calibration can be used, a transformation of axes is required;this step, along with variance propagation is not currently explained in available NDA standard guidelines. The role of systematic and random uncertainty is illustrated and expands on that given previously for the chosen practical NDA example. A listing of open-source software is provided in the Appendix.
文摘One of the simplest tests of a radiation portal monitor (RPM) is a series of n repeats (a vehicle drive-through) in which the ith repeat records a total number of counts Xi and alarms if Xi ≥ T where T is an alarm threshold. The RPM performance tests we consider use n repeats to estimate the probability p = P(Xi ≥ T). This paper addresses criterion A for testing RPMs, where criterion A is: for specified source strength, we must be at least 95% confident that p ≥ 0.5. To assess criterion A, we consider a distribution-free test and a test relying on assuming the counts Xi have approximately a Poisson distribution. Both test options require tolerance interval construction.
