Quantification of the probability of containment failure caused by an in-vessel steam explosion for the Sizewell B PWR

AEA Technology has provided an assessment of the probability of α-mode containment failure for the Sizewell B PWR. After a preliminary review of the methodologies available it was decided to use the probabilistic approach described in the paper, based on an extension of the methodology developed by Theofanous et al. (Nucl. Sci. Eng. 97 (1987) 259–325). The input to the assessment is 12 probability distributions; the bases for the quantification of these distributions are discussed. The α-mode assessment performed for the Sizewell B PWR has demonstrated the practicality of the event-tree method with input data represented by probability distributions. The assessment itself has drawn attention to a number of topics, which may be plant and sequence dependent, and has indicated the importance of melt relocation scenarios. The α-mode failure probability following an accident that leads to core melt relocation to the lower head for the Sizewell B PWR has been assessed as a few parts in 10 000, on the basis of current information. This assessment has been the first to consider elevated pressures (6 MPa and 15 MPa) besides atmospheric pressure, but the results suggest only a modest sensitivity to system pressure.

Understanding the processes governing climate variability and change, climate predictability and the probability of extreme events

The purpose of Research Theme 4 (RT4) was to advance understanding of the basic science issues at the heart of the ENSEMBLES project, focusing on the key processes that govern climate variability and change, and that determine the predictability of climate. Particular attention was given to understanding linear and non-linear feedbacks that may lead to climate surprises,and to understanding the factors that govern the probability of extreme events. Improved understanding of these issues will contribute significantly to the quantification and reduction of uncertainty in seasonal to decadal predictions and projections of climate change. RT4 exploited the ENSEMBLES integrations (stream 1) performed in RT2A as well as undertaking its own experimentation to explore key processes within the climate system. It was working at the cutting edge of problems related to climate feedbacks, the interaction between climate variability and climate change � especially how climate change pertains to extreme events, and the predictability of the climate system on a range of time-scales. The statisticalmethodologies developed for extreme event analysis are new and state-of-the-art. The RT4-coordinated experiments, which have been conducted with six different atmospheric GCMs forced by common timeinvariant sea surface temperature (SST) and sea-ice fields (removing some sources of inter-model variability), are designed to help to understand model uncertainty (rather than scenario or initial condition uncertainty) in predictions of the response to greenhouse-gas-induced warming. RT4 links strongly with RT5 on the evaluation of the ENSEMBLES prediction system and feeds back its results to RT1 to guide improvements in the Earth system models and, through its research on predictability, to steer the development of methods for initialising the ensembles

Calculating the exclusion probability and paternity index for X-chromosomal loci in the presence of substructure

There has been recent interest in the use of X-chromosomal loci for forensic and relatedness testing casework, with many authors developing new X-linked short tandem repeat (STR) loci suitable for forensic use. Here we present formulae for two key quantities in paternity testing, the average probability of exclusion and the paternity index, which are suitable for Xchromosomal loci in the presence of population substructure.

A jackknife variance estimator for unequal probability sampling

The jackknife method is often used for variance estimation in sample surveys but has only been developed for a limited class of sampling designs.We propose a jackknife variance estimator which is defined for any without-replacement unequal probability sampling design. We demonstrate design consistency of this estimator for a broad class of point estimators. A Monte Carlo study shows how the proposed estimator may improve on existing estimators.

Adjusted jackknife for imputation under unequal probability sampling without replacement

Imputation is commonly used to compensate for item non-response in sample surveys. If we treat the imputed values as if they are true values, and then compute the variance estimates by using standard methods, such as the jackknife, we can seriously underestimate the true variances. We propose a modified jackknife variance estimator which is defined for any without-replacement unequal probability sampling design in the presence of imputation and non-negligible sampling fraction. Mean, ratio and random-imputation methods will be considered. The practical advantage of the method proposed is its breadth of applicability.

API-CALC 1.0: a computer program for calculating the average probability of identity allowing for substructure, inbreeding and the presence of close relatives

Individual identification via DNA profiling is important in molecular ecology, particularly in the case of noninvasive sampling. A key quantity in determining the number of loci required is the probability of identity (PIave), the probability of observing two copies of any profile in the population. Previously this has been calculated assuming no inbreeding or population structure. Here we introduce formulae that account for these factors, whilst also accounting for relatedness structure in the population. These formulae are implemented in API-CALC 1.0, which calculates PIave for either a specified value, or a range of values, for F-IS and F-ST.

Probability density function estimation using orthogonal forward regression

Using the classical Parzen window estimate as the target function, the kernel density estimation is formulated as a regression problem and the orthogonal forward regression technique is adopted to construct sparse kernel density estimates. The proposed algorithm incrementally minimises a leave-one-out test error score to select a sparse kernel model, and a local regularisation method is incorporated into the density construction process to further enforce sparsity. The kernel weights are finally updated using the multiplicative nonnegative quadratic programming algorithm, which has the ability to reduce the model size further. Except for the kernel width, the proposed algorithm has no other parameters that need tuning, and the user is not required to specify any additional criterion to terminate the density construction procedure. Two examples are used to demonstrate the ability of this regression-based approach to effectively construct a sparse kernel density estimate with comparable accuracy to that of the full-sample optimised Parzen window density estimate.

Probability density estimation with tunable kernels using orthogonal forward regression

A generalized or tunable-kernel model is proposed for probability density function estimation based on an orthogonal forward regression procedure. Each stage of the density estimation process determines a tunable kernel, namely, its center vector and diagonal covariance matrix, by minimizing a leave-one-out test criterion. The kernel mixing weights of the constructed sparse density estimate are finally updated using the multiplicative nonnegative quadratic programming algorithm to ensure the nonnegative and unity constraints, and this weight-updating process additionally has the desired ability to further reduce the model size. The proposed tunable-kernel model has advantages, in terms of model generalization capability and model sparsity, over the standard fixed-kernel model that restricts kernel centers to the training data points and employs a single common kernel variance for every kernel. On the other hand, it does not optimize all the model parameters together and thus avoids the problems of high-dimensional ill-conditioned nonlinear optimization associated with the conventional finite mixture model. Several examples are included to demonstrate the ability of the proposed novel tunable-kernel model to effectively construct a very compact density estimate accurately.