A Bayesian alternative to parametric hypothesis testing

Summary A unified approach to parametric hypothesis testing from a decision-theoretical viewpoint is proposed. A measure of the discrepancy between two models is incorporated as part of the utility function. Specifically, the Kullback logarithmic divergence is considered as such a measure. Under certain conditions, when using this measure of discrepancy there is correspondence with the classical solutions.     

A fully Bayesian multivariate approach to before-after safety evaluation

This paper presents a fully Bayesian multivariate approach to before-after safety evaluation. Although empirical Bayes (EB) methods have been widely accepted as statistically defensible safety evaluation tools in observational before-after studies for more than a decade, EB has some limitations such that it requires a development and calibration of reliable safety performance functions (SPFs) and the uncertainty in the EB safety effectiveness estimates may be underestimated when a fairly large reference group is not available. This is because uncertainty (standard errors) of the estimated regression coefficients and dispersion parameter in SPFs is not reflected in the final safety effectiveness estimate of EB.Fully Bayesian (FB) methodologies in safety evaluation are emerging as the state-of-the-art methods that have a potential to overcome the limitations of EB in that uncertainty in regression parameters in the FB approach is propagated throughout the model and carries through to the final safety effectiveness estimate. Nonetheless, there have not yet been many applications of fully Bayesian methods in before-after studies. Part of reasons is the lack of documentation for a step-by-step FB implementation procedure for practitioners as well as an increased complexity in computation. As opposed to the EB methods of which steps are well-documented in the literature for practitioners, the steps for implementing before-after FB evaluations have not yet been clearly established, especially in more general settings such as a before-after study with a comparison group/comparison groups. The objectives of this paper are two-fold: (1) to develop a fully Bayesian multivariate approach jointly modeling crash counts of different types or severity levels for a before-after evaluation with a comparison group/comparison groups and (2) to establish a step-by-step procedure for implementing the FB methods for a before-after evaluation with a comparison group/comparison groups.The fully Bayesian multivariate approach introduced in this paper has additional advantages over the corresponding univariate approaches (whether classical or Bayesian) in that the multivariate approach can recover the underlying correlation structure of the multivariate crash counts and can also lead to a more precise safety effectiveness estimate by taking into account correlations among different crash severities or types for estimation of the expected number of crashes. The new method is illustrated with the multivariate crash count data obtained from expressways in Korea for 13 years to assess the safety effectiveness of decreasing the posted speed limit.     

Some history of the hierarchical Bayesian methodology

Summary A standard technique in subjective “Bayesian” methodology is for a subject (“you”) to make judgements of the probabilities that a physical probability lies in various intervals. In the hierarchical Bayesian technique you make probability judgements (of a higher type, order, level, or stage) concerning the judgements of lower type. The paper will outlinesome of the history of this hierarchical technique with emphasis on the contributions by I. J. Good because I have read every word written by him.     

Prediction of road accidents: A Bayesian hierarchical approach

In this paper a novel methodology for the prediction of the occurrence of road accidents is presented. The methodology utilizes a combination of three statistical methods: (1) gamma-updating of the occurrence rates of injury accidents and injured road users, (2) hierarchical multivariate Poisson-lognormal regression analysis taking into account correlations amongst multiple dependent model response variables and effects of discrete accident count data e.g. over-dispersion, and (3) Bayesian inference algorithms, which are applied by means of data mining techniques supported by Bayesian Probabilistic Networks in order to represent non-linearity between risk indicating and model response variables, as well as different types of uncertainties which might be present in the development of the specific models.     

Uranium dose assessment: a Bayesian approach to the problem of dietary background

Workers are routinely monitored by urinalysis for exposure to uranium at Los Alamos National Laboratory. Urine samples are analysed by alpha spectroscopy for 234U, 235U and 238U. Interpretation of the data is complicated by the presence of natural uranium in the workers' drinking water and diet. Earlier methods used drinking water samples to estimate the dietary component in urine excretion. However, there proved to be insufficient correlation between drinking water concentration and excretion rate. Instead, an iterative calculation is used to identify a typical excretion rate for each individual in the absence of occupational intakes. Bayesian dose-assessment methods, first developed for plutonium bioassay at Los Alamos, have been adapted for uranium. These methods, coupled with an algorithm for identifying each individual's baseline level of uranium from environmental sources, yield improved reliability in the identification of occupational intakes.     

Bayesian methodology to estimate and update safety performance functions under limited data conditions: A sensitivity analysis

In road safety studies, decision makers must often cope with limited data conditions. In such circumstances, the maximum likelihood estimation (MLE), which relies on asymptotic theory, is unreliable and prone to bias. Moreover, it has been reported in the literature that (a) Bayesian estimates might be significantly biased when using non-informative prior distributions under limited data conditions, and that (b) the calibration of limited data is plausible when existing evidence in the form of proper priors is introduced into analyses. Although the Highway Safety Manual (2010) (HSM) and other research studies provide calibration and updating procedures, the data requirements can be very taxing. This paper presents a practical and sound Bayesian method to estimate and/or update safety performance function (SPF) parameters combining the information available from limited data with the SPF parameters reported in the HSM. The proposed Bayesian updating approach has the advantage of requiring fewer observations to get reliable estimates. This paper documents this procedure. The adopted technique is validated by conducting a sensitivity analysis through an extensive simulation study with 15 different models, which include various prior combinations. This sensitivity analysis contributes to our understanding of the comparative aspects of a large number of prior distributions. Furthermore, the proposed method contributes to unification of the Bayesian updating process for SPFs. The results demonstrate the accuracy of the developed methodology. Therefore, the suggested approach offers considerable promise as a methodological tool to estimate and/or update baseline SPFs and to evaluate the efficacy of road safety countermeasures under limited data conditions.     

An approach for using risk assessment in risk-informed decisions on plant-specific changes to the licensing basis

This paper discusses an acceptable approach that the US Nuclear Regulatory Commission staff has proposed for using Probabilistic Risk Assessment in making decisions on changes to the licensing basis of a nuclear power plant. First, the overall philosophy of risk-informed decision-making, and the process framework are described. The philosophy is encapsulated in five principles, one of which states that, if the proposed change leads to an increase in core damage frequency or risk, the increases must be small and consistent with the intent of the Nuclear Regulatory Commission's Safety Goal Policy Statement. The second part of the paper discusses the use of PRA to demonstrate that this principle has been met. The discussion focuses on the acceptance guidelines, and on comparison of the PRA results with those guidelines. The difficulties that arise because of limitations in scope and analytical uncertainties are discussed and approaches to accommodate these difficulties in the decision-making are described.     

An approach for the Bayesian estimation in the case of ordered piecewise constant failure rates

In this paper we present an approach for the Bayesian estimation of piecewise constant failure rates under the constraint that the constant value of the failure rate in an interval of time is greater than a function of its values in the prior intervals. We apply this approach to the estimation of piecewise constant failure rates for conditional IFR, IFRA and NBU distributions. The prior distribution for the failure rate in each interval is specified through gamma distributions with functions of the failure rate values corresponding to the rest of the intervals as location parameters. Using this approach the prior distribution parameters have interpretations through prior means and variances of the values of the piecewise constant failure rate. The posterior distributions and expected values can be found in terms of gamma functions, without the necessity of numerical integrations. We apply this approach to a model for reliability estimation when two operational modes exists and the number of failures in each operational mode is unknown. Finally a numerical example is presented in which simulations of posterior densities are carried out.     

A macroscopic approach to the problem of heteroepitaxy

Based on the concepts of classical nucleation theory, a macroscopic criterion of heteroepitaxy is derived for layer-substrate systems in which no intermediate phases are formed. The criterion relates the epitaxial growth temperature to the associated interfacial energies, lattice mismatch, elastic constants of the layer, and supersaturation of the parent phase with the deposited substance.     

A combined approach to solve the redundancy optimization problem for multi-state systems under repair policies

This paper combines universal moment generating function technique with stochastic Petri nets to solve the redundancy optimization problem for multi-state systems under repair policies. Redundant elements are included in order to achieve a desirable level of production availability. The elements of the system are characterized by their cost, performance and availability. These elements are chosen from a list of products available on the market. The number of repair teams is less than the number of reparable elements, and a repair policy specifies the maintenance priorities between the system elements. A heuristic is proposed to determine the minimal cost system configuration under availability constraints. This heuristic, first applies universal moment generating function technique to evaluate the system availability, assuming unlimited maintenance resources. Once a preliminary solution is found by the optimization algorithm, stochastic Petri nets are used to model different repair policies, and to find the best system configuration (architecture and number of repairmen) in terms of global performance (availability and cost). This combined procedure is applied to a reference example.     

Some implications of an event-based definition of exposure to the risk of road accident

This paper proposes a new definition of exposure to the risk of road accident as any event, limited in space and time, representing a potential for an accident to occur by bringing road users close to each other in time or space of by requiring a road user to take action to avoid leaving the roadway. A typology of events representing a potential for an accident is proposed. Each event can be interpreted as a trial as defined in probability theory. Risk is the proportion of events that result in an accident. Defining exposure as events demanding the attention of road users implies that road users will learn from repeated exposure to these events, which in turn implies that there will normally be a negative relationship between exposure and risk. Four hypotheses regarding the relationship between exposure and risk are proposed. Preliminary tests support these hypotheses. Advantages and disadvantages of defining exposure as specific events are discussed. It is argued that developments in vehicle technology are likely to make events both observable and countable, thus ensuring that exposure is an operational concept.     

A Bayesian Neural Network approach to estimating the Energy Equivalent Speed

To reduce the number and the gravity of accidents, it is necessary to analyse and reconstruct them. Accident modelling requires the modelling of the impact which in turn requires the estimation of the deformation energy. There are several tools available to evaluate the deformation energy absorbed by a vehicle during an impact. However, there is a growing demand for more precise and more powerful tools. In this work, we express the deformation energy absorbed by a vehicle during a crash as a function of the Energy Equivalent Speed (EES). The latter is a difficult parameter to estimate because the structural response of the vehicle during an impact depends on parameters concerning the vehicle, but also parameters concerning the impact. The objective of our work is to design a model to estimate the EES by using an original approach combining Bayesian and Neural Network approaches. Both of these tools are complementary and offer significant advantages, such as the guarantee of finding the optimal model and the implementation of error bars on the computed output. In this paper, we present the procedure for implementing this Bayesian Neural Network approach and the results obtained for the modelling of the EES: our model is able to estimate the EES of the car with a mean error of 1.34 m s(-1). Furthermore, we built a sensitivity analysis to study the relevance of model's inputs.     

A genetic algorithm approach to the integrated inventory-distribution problem

We introduce a new genetic algorithm (GA) approach for the integrated inventory distribution problem (IIDP). We present the developed genetic representation and use a randomized version of a previously developed construction heuristic to generate the initial random population. We design suitable crossover and mutation operators for the GA improvement phase. The comparison of results shows the significance of the designed GA over the construction heuristic and demonstrates the capability of reaching solutions within 20% of the optimum on sets of randomly generated test problems.     

A new approach to the d-MC problem

Many real-world systems (such as cellular telephones, transportation, etc.) are multistate-node acyclic network (MNAN) composed of multistate-nodes. Such network has a source node (position) where the signal source is located, a number of sink nodes that only receive the signal, and a number of intermediate nodes that retransmit the received signal to some other nodes. The non-sink node has different states determined by a set of nodes receiving the signal directly from it. The reliability of MNAN can be computed in terms of minimal trees (MTs). Based on the Branch-and-Bound algorithm, we developed an intuitive algorithm that is simpler than the best-known existing method. The computational complexity of the proposed algorithm is also analyzed. One example is illustrated to show how all MTs are generated by the proposed algorithm. The reliability of this example is then computed.     

A DNA-based approach to the carbon nanotube sorting problem

Carbon nanotube sorting, i.e., the separation of a mixture of tubes into different electronic types and further into species with a specific chirality, is a fascinating problem of both scientific and technological importance. It is one of those problems that are easy to describe but difficult to solve. Single-stranded DNA forms stable complexes with carbon nanotubes and disperses them effectively in water. A particular DNA sequence of alternating guanine (G) and thymine (T) nucleotides ((GT) _n , with n = 10 to 45) self-assembles into an ordered supramolecular structure around an individual nanotube, in such a way that the electrostatic properties of the DNA-carbon nanotube hybrid depend on tube structure, enabling nanotube separation by anion-exchange chromatography. This review provides a summary of the separation of metallic and semiconducting tubes, and purification of single (n, m) tubes using the DNA-wrapping approach. We will present our current understanding of the DNA-carbon nanotube hybrid structure and separation mechanisms, and predict future developments of the DNA-based approach. This article is published with open access at Springerlink.com     

Fatigue life of 2017(A) aluminum alloy under proportional constant-amplitude bending with torsion in the energy approach

We present the results obtained for 2017(A) aluminum alloy under the conditions of pure bending with constant amplitude, pure torsion, and two combinations of proportional bending with torsion. All results can be described by a single criterion based on the parameter of strain-energy density in the critical plane. The critical plane is defined as the plane where the parameter attains its maximum value. The fatigue life is affected by the sum of the densities of normal and shear strain energies in the accepted critical plane. The results are presented in a scatter band with coefficient equal to three for the case of pure bending. Published in Fizyko-Khimichna Mekhanika Materialiv, Vol. 44, No. 4, pp. 68–74, July–August, 2008.     

A cross-entropy approach to the single row facility layout problem

The single row facility layout problem is to arrange a given number of facilities along a straight line so as to minimise the total cost associated with the interactions between the facilities. In this paper, a metaheuristic algorithm based on the cross-entropy method, incorporating a local search procedure and symmetry-breaking techniques, is developed to solve this problem. The proposed algorithm has been tested on some widely used benchmark instances. The computational results show that the proposed algorithm has found the optimal or the best solutions known so far for the instances of size with up to 100 facilities and is competitive with some existing algorithms.     

A bottleneck assignment approach to the multiple container loading problem

The container loading problem addresses the question of how to store several three dimensional, rectangular items (e.g. boxes) in one or more containers in such a way that maximum use is made of the container space. The multiple container problem concentrates on the situation where the consignment to be loaded cannot be accommodated in a single container. To minimize the number of required containers the repeated application of a single container approach is often suggested in the literature. In contrast, in this paper an approach based on a set partitioning formulation of the problem is presented. Within this approach a single container algorithm is used to produce alternative loading patterns. This approach easily allows introducing additional aspects, e.g. separation of boxes or complete shipment of boxes.