Robust Variance Components Estimation in the PERG Mixed Distributions of Empirical Variances—PEROBVC Method

A mixed distribution of empirical variances, composed of two distributions the basic and contaminating ones, and referred to as PERG mixed distribution of empirical variances, is considered. In the paper a robust inverse problem solution is given, namely a (new) robust method for estimation of variances of both distributions—PEROBVC Method, as well as the estimates for the numbers of observations for both distributions and, in this way also the estimate of contamination degree.

Joint modelling of location and scale parameters of the skew-normal distribution

Joint location and scale models of the skew-normal distribution provide useful ex- tension for joint mean and variance models of the normal distribution when the data set under consideration involves asymmetric outcomes. This paper focuses on the maximum likelihood estimation of joint location and scale models of the skew-normal distribution. The proposed procedure can simultaneously estimate parameters in the location model and the scale model. Simulation studies and a real example are used to illustrate the proposed methodologies.

Laws of motion of particles in a jigging process

The laws of motion of particle groups in a jigging process are studied. These describe the macroscopic phenomena that occur during jigging. During jigging the heavier and bigger particles concentrate at the bed bottom while lighter and smaller particles move to the upper part of the bed. Particles with equivalent properties tend to concentrate at a certain position centered around the inherent height of their distribution. The particle distribution variance gradually diminishes to some asymptotic value. The state equation group of the jigging bed is deduced and a calculation method, called the λ value judgment method, is proposed. The method is used to calculate the layer number and the inherent height of each particle group. A mathematical expression for the particle distribution variance is also given.

Quantifying the attribution of model bias in simulating summer hot days in China with IAP AGCM 4.1

Using lAP AGCM simulation results for the period 1961-2005, summer hot days in China were calculated and then compared with observations. Generally, the spatial pattern of hot days is reasonably reproduced, with more hot days found in northern China, the Yangtze and Huaihe River basin, the Chuan-Yu region, and southern Xinjiang. However, the model tends to overestimate the number of hot days in the above-mentioned regions, particularly in the Yangtze and Huaihe River basin where the simulated summer-mean hot days is 13 days more than observed when averaged over the whole region, and the maximum overestimation of hot days can reach 23 days in the region. Analysis of the probability distribution of daily maximum temperature （Trnax） suggests that the warm bias in the model-simulated Tmax contributes largely to the overestimation of hot days in the model. Furthermore, the discrepancy in the simulated variance of the Tmax distribution also plays a non- negligible role in the overestimation of hot days. Indeed, the latter can even account for 22% of the total bias of simulated hot days in August in the Yangtze and Huaihe River basin. The quantification of model bias from the mean value and variability can provide more information for further model improvement.

DISTRIBUTED MONITORING SYSTEM RELIABILITY ESTIMATION WITH CONSIDERATION OF STATISTICAL UNCERTAINTY

Taking into account the whole system structure and the component reliability estimation uncertainty, a system reliability estimation method based on probability and statistical theory for distributed monitoring systems is presented. The variance and confidence intervals of the system reliability estimation are obtained by expressing system reliability as a linear sum of products of higher order moments of component reliability estimates when the number of component or system survivals obeys binomial distribution. The eigenfunction of binomial distribution is used to determine the moments of component reliability estimates, and a symbolic matrix which can facilitate the search of explicit system reliability estimates is proposed. Furthermore, a case of application is used to illustrate the procedure, and with the help of this example, various issues such as the applicability of this estimation model, and measures to improve system reliability of monitoring systems are discussed.

Third Order Adjoint Sensitivity and Uncertainty Analysis of an OECD/NEA Reactor Physics Benchmark: III. Response Moments

The (180)3 third-order mixed sensitivities of the leakage response of a polyethylene-reflected plutonium (PERP) experimental benchmark with respect to the benchmark’s 180 microscopic total cross sections have been computed in accompanying works [1] [2]. This work quantifies the contributions of these (180)3 third-order mixed sensitivities to the PERP benchmark’s leakage response distribution moments (expected value, variance and skewness) and compares these contributions to those stemming from the corresponding first- and second-order sensitivities of the PERP benchmark’s leakage response with respect to the total cross sections. The numerical results obtained in this work reveal that the importance of the 3rd-order sensitivities can surpass the importance of the 1st- and 2nd-order sensitivities when the parameters’ uncertainties increase. In particular, for a uniform standard deviation of 10% of the microscopic total cross sections, the 3rd-order sensitivities contribute 80% to the response variance, whereas the contribution stemming from the 1st- and 2nd-order sensitivities amount only to 2% and 18%, respectively. Consequently, neglecting the 3rd-order sensitivities could cause a very large non-conservative error by under-reporting the response variance by a factor of 506%. The results obtained in this work also indicate that the effects of the 3rd-order sensitivities are to reduce the response’s skewness in parameter space, rendering the distribution of the leakage response more symmetric about its expected value. The results obtained in this work are the first such results ever published in reactor physics. Since correlations among the group-averaged microscopic total cross sections are not available, only the effects of typical standard deviations for these cross sections could be considered. Due to this lack of correlations among the cross sections, the effects of the mixed 3rd-order sensitivities could not be quantified exactly at this time. These effects could be quantified only when correlations among the group-averaged microscopic total cross sections would be obtained experimentally by the nuclear physics community.

Third-Order Adjoint Sensitivity Analysis of an OECD/NEA Reactor Physics Benchmark: I. Mathematical Framework

This work extends to third-order previously published work on developing the adjoint sensitivity and uncertainty analysis of the numerical model of a polyethylene-reflected plutonium (acronym: PERP) OECD/NEA reactor physics benchmark. The PERP benchmark comprises 21,976 imprecisely known (uncertain) model parameters. Previous works have used the adjoint sensitivity analysis methodology to compute exactly and efficiently all of the 21,976 first-order and (21,976)2 second-order sensitivities of the PERP benchmark’s leakage response to all of the benchmark’s uncertain parameters, showing that the largest and most consequential 1st- and 2nd-order response sensitivities are with respect to the total microscopic cross sections. These results have motivated extending the previous adjoint-based derivations to third-order, leading to the derivation, in this work, of the exact mathematical expressions of the (180)3 third-order sensitivities of the PERP leakage response with respect to these total microscopic cross sections. The formulas derived in this work are valid not only for the PERP benchmark but can also be used for computing the 3rd-order sensitivities of the leakage response of any nuclear system involving fissionable material and internal or external neutron sources. Subsequent works will use the adjoint-based mathematical expressions obtained in this work to compute exactly and efficiently the numerical values of these (180)3 third-order sensitivities (which turned out to be very large and consequential) and use them for a third-order uncertainty analysis of the PERP benchmark’s leakage response.

High-Sensitivity Transcriptome Data Structure and Implications for Analysis and Biologic Interpretation

Novel microarray technologies such as the AB1700 platform from Applied Biosysterns promise significant increases in the signal dynamic range and a higher sensitivity for weakly expressed transcripts. We have compared a representative set of AB1700 data with a similarly representative Affymetrix HG-U133A dataset. The AB1700 design extends the signal dynamic detection range at the lower bound by one order of magnitude. The lognormal signal distribution profiles of these highsensitivity data need to be represented by two independent distributions. The additional second distribution covers those transcripts that would have gone undetected using the Affymetrix technology. The signal-dependent variance distribution in the AB1700 data is a non-trivial function of signal intensity, describable using a composite function. The drastically different structure of these highsensitivity transcriptome profiles requires adaptation or even redevelopment of the standard microarray analysis methods. Based on the statistical properties, we have derived a signal variance distribution model for AB1700 data that is necessary for such development. Interestingly, the dual lognormal distribution observed in the AB1700 data reflects two fundamentally different biologic mechanisms of transcription initiation.

Generation of Synthetic Transcriptome Data with Defined Statistical Properties for the Development and Testing of New Analysis Methods

We have previously developed a combined signal/variance distribution model that accounts for the particular statistical properties of datasets generated on the Applied Biosystems AB1700 transcriptome system. Here we show that this model can be efficiently used to generate synthetic datasets with statistical properties virtually identical to those of the actual data by aid of the JAVA application ace.map creator 1.0 that we have developed. The fundamentally different structure of AB1700 transcriptome profiles requires re-evaluation, adaptation, or even redevelopment of many of the standard microarray analysis methods in order to avoid misinterpretation of the data on the one hand, and to draw full benefit from their increased specificity and sensitivity on the other hand. Our composite data model and the ace.map creator 1.0 application thereby not only present proof of the correctness of our parameter estimation, but also provide a tool for the generation of synthetic test data that will be useful for further development and testing of analysis methods.