A Bayesian hierarchical model for accident and injury surveillance

This article presents a recent study which applies Bayesian hierarchical methodology to model and analyse accident and injury surveillance data. A hierarchical Poisson random effects spatio-temporal model is introduced and an analysis of inter-regional variations and regional trends in hospitalisations due to motor vehicle accident injuries to boys aged 0-24 in the province of British Columbia, Canada, is presented. The objective of this article is to illustrate how the modelling technique can be implemented as part of an accident and injury surveillance and prevention system where transportation and/or health authorities may routinely examine accidents, injuries, and hospitalisations to target high-risk regions for prevention programs, to evaluate prevention strategies, and to assist in health planning and resource allocation. The innovation of the methodology is its ability to uncover and highlight important underlying structure of the data. Between 1987 and 1996, British Columbia hospital separation registry registered 10,599 motor vehicle traffic injury related hospitalisations among boys aged 0-24 who resided in British Columbia, of which majority (89%) of the injuries occurred to boys aged 15-24. The injuries were aggregated by three age groups (0-4, 5-14, and 15-24), 20 health regions (based of place-of-residence), and 10 calendar years (1987 to 1996) and the corresponding mid-year population estimates were used as 'at risk' population. An empirical Bayes inference technique using penalised quasi-likelihood estimation was implemented to model both rates and counts, with spline smoothing accommodating non-linear temporal effects. The results show that (a) crude rates and ratios at health region level are unstable, (b) the models with spline smoothing enable us to explore possible shapes of injury trends at both the provincial level and the regional level, and (c) the fitted models provide a wealth of information about the patterns (both over space and time) of the injury counts, rates and ratios. During the 10-year period, high injury risk ratios evolved from northwest to central-interior and the southeast [corrected].     

Bayesian structural equation modeling method for hierarchical model validation

A building block approach to model validation may proceed through various levels, such as material to component to subsystem to system, comparing model predictions with experimental observations at each level. Usually, experimental data becomes scarce as one proceeds from lower to higher levels. This paper presents a structural equation modeling approach to make use of the lower-level data for higher-level model validation under uncertainty, integrating several components: lower-level data, higher-level data, computational model, and latent variables. The method proposed in this paper uses latent variables to model two sets of relationships, namely, the computational model to system-level data, and lower-level data to system-level data. A Bayesian network with Markov chain Monte Carlo simulation is applied to represent the two relationships and to estimate the influencing factors between them. Bayesian hypothesis testing is employed to quantify the confidence in the predictive model at the system level, and the role of lower-level data in the model validation assessment at the system level. The proposed methodology is implemented for hierarchical assessment of three validation problems, using discrete observations and time-series data.     

The hierarchical Tobit model: A case study in Bayesian computing

In this paper we discuss the potentials of a new Bayesian inference tool, called the Gibbs sampler, for the analysis of the censored regression or Tobit model. Tobit models have a wide range of applications in empirical sciences, like econometrics and biometrics. The estimation results of the simple Tobit model will be compared to a hierarchical Tobit model, and the Gibbs sampling approach to the related classical algorithm of expectation-maximisation (EM). The underlying botanical example of this paper is concerned with the censoring mechanism in plant reproduction and proposes the Bayesian Tobit model for the growth relationship between the reproductive part and the rest of the plant.     

Road network safety evaluation using Bayesian hierarchical joint model

Safety and efficiency are commonly regarded as two significant performance indicators of transportation systems. In practice, road network planning has focused on road capacity and transport efficiency whereas the safety level of a road network has received little attention in the planning stage. This study develops a Bayesian hierarchical joint model for road network safety evaluation to help planners take traffic safety into account when planning a road network. The proposed model establishes relationships between road network risk and micro-level variables related to road entities and traffic volume, as well as socioeconomic, trip generation and network density variables at macro level which are generally used for long term transportation plans. In addition, network spatial correlation between intersections and their connected road segments is also considered in the model.A road network is elaborately selected in order to compare the proposed hierarchical joint model with a previous joint model and a negative binomial model. According to the results of the model comparison, the hierarchical joint model outperforms the joint model and negative binomial model in terms of the goodness-of-fit and predictive performance, which indicates the reasonableness of considering the hierarchical data structure in crash prediction and analysis. Moreover, both random effects at the TAZ level and the spatial correlation between intersections and their adjacent segments are found to be significant, supporting the employment of the hierarchical joint model as an alternative in road-network-level safety modeling as well.     

Model calibration: A hierarchical Bayesian approach

Many geotechnical engineering models are empirical and calibrated based on data gathered from various sites/projects, using optimisation algorithms with criteria like least squared errors or minimising the coefficient of variation of method bias with the constraint of mean bias equal to unity. This paper discusses the use of hierarchical Bayesian regression models for the same purpose. A database of axial capacity of piles in predominantly clay sites and a CPT-based design model, compiled and developed as part of a Joint Industry Project (JIP) led by the Norwegian Geotechnical Institute (NGI), is used for demonstration. The analyses focus on two related areas that the traditional approaches overlook: (i) quantification of uncertainty in the estimated parameters of the model, and (ii) modelling site-dependency of the model parameters (i.e., between-group variation). The former is important in the context of reliability-based design and contributes to establishing confidence in estimated reliability indices, particularly when only limited data are available. The latter expands our understanding regarding the domain of applicability of a model; that is, if a model is broadly applicable or highly site-dependent. The benefits of the proposed Bayesian approach are highlighted with a prediction exercise where the calibrated models are used in conjunction with limited site or project-specific data.     

The substructuring-based topology optimization for maximizing the first eigenvalue of hierarchical lattice structure

This work presents a generalized substructuring-based topology optimization method for the design hierarchical lattice structures to maximize the first eigenvalue. In this method, the macrostructure is assumed to be composed of substructures with a common artificial lattice geometry pattern. And two different yet connected scales are considered through a lattice geometry feature parameter. The feature parameter, which can control the material distribution of the substructure, determines the relative density of corresponding substructure. Each substructure is condensed into a super-element to obtain the associated density-related matrices. A surrogate model using cubic spline interpolation has been particularly built to map the density to stiffness and mass matrices of condensed super-elements. The derivatives of super-element matrices to the associated densities can be evaluated efficiently and accurately. Here, an augmented penalized density for this surrogate model is introduced. And the conventional optimality criteria method is selected as updating method of the density design variables. Numerical examples under two lattice patterns of substructures are shown to validate the correctness and superiority of this substructure-based topology optimization method.     

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.     

A hierarchical model for characterising spatial wafer variations

Silicon wafers are commonly used materials in the semiconductor manufacturing industry. Their geometric quality directly affects the production cost and yield. Therefore, improvement in the quality of wafers is critical for meeting the current competitive market needs. Conventional summary metrics such as total thickness variation, bow and warp can neither fully reflect the local variability within each wafer nor provide useful insight for root cause diagnosis and quality improvement. The advancement of sensing technology enables two-dimensional (2D) data mapping to characterise the geometric shapes of wafers, which provides more information than summary metrics. The objective of this research is to develop a statistical model to characterise the thickness variation of wafers based on 2D data maps. Specifically, the thickness variation of wafers is decomposed into macro-scale and micro-scale variations, which are modelled as a cubic curve and a first-order intrinsic Gaussian Markov random field, respectively. The models can successfully capture both the macro-scale mean trend and the micro-scale local variation, with important engineering implications for process monitoring, fault diagnosis and run-to-run control. A practical case study from a wafer manufacturing process is performed to show the effectiveness of the proposed methodology.     

A model for Bayesian software reliability analysis

Two problems which are of great interest in relation to software reliability are the prediction of future times to failure and the calculation of the optimal release time. An important assumption in software reliability analysis is that the reliability grows whenever bugs are found and removed. In this paper we present a model for software reliability analysis using the Bayesian statistical approach in order to incorporate in the analysis prior assumptions such as the (decreasing) ordering in the assumed constant failure rates of prescribed intervals. We use as prior model the product of gamma functions for each pair of subsequent interval constant failure rates, considering as the location parameter of the first interval the failure rate of the following interval. In this way we include the failure rate ordering information. Using this approach sequentially, we predict the time to failure for the next failure using the previous information obtained. Using also the relevant predictive distributions obtained, we calculate the optimal release time for two different requirements of interest: (a) the probability of an in‐service failure in a prescribed time t; (b) the cost associated with a single or more failures in a prescribed time t. Finally a numerical example is presented. Copyright © 2000 John Wiley & Sons, Ltd.     

A hierarchical combinatorial reliability model for smart home systems

As an application of the Internet of Things, smart home systems have received significant attentions in recent years due to their precedent advantages, eg, in ensuring efficient electricity transmission and integration with renewable energy. This paper proposes a hierarchical and combinatorial methodology for modeling and evaluating reliability of a smart home system. Particularly, the proposed methodology encompasses a multi‐valued decision diagram‐based method for addressing phased‐mission, standby sparing, and functional dependence behaviors in the physical layer; and a combinatorial procedure based on the total probability theorem for addressing probabilistic competing failure behavior with random propagation time in the communication layer. The methods are applicable to arbitrary types of time‐to‐failure and time‐to‐propagation distributions for system components. A detailed case study of an example smart home system is performed to demonstrate applications of the proposed method and effects of different component parameters on the system reliability.     

A hierarchical model for the cell loading problem of cellular manufacturing systems

A hierarchical cell loading approach is proposed to solve the production planning problem in cellular manufacturing systems. Our aim is to minimize the variable cost of production subject to production and inventory balance constraints for families and items, and capacity feasibility constraints for group technology cells and resources over the planning horizon. The computational results indicated that the proposed algorithm was very efficient in finding an optimum solution for a set of randomly generated problems.     

Mechanics of hierarchical adhesion structures of geckos

Geckos (Gekko gecko) have evolved elaborate adhesive structures which allow them to move along vertical walls and ceilings against their body weight. There is strong evidence that the adhesion ability of geckos is due to the van der Waals interaction between a contacting surface and hundreds of thousands of keratinous hairs or setae on the gecko’s foot; each seta is 30–130 μm long and contains hundreds of 200–500 nm projections or spatulae. While contact mechanics suggests that the refinement of structure size results in greater adhesive strength, some important questions remain unsolved: What is the significance of nanometer length scale for adhesion? What is the optimum adhesive strength of a structure? How can a structure optimized for attachment simultaneously allow easy detachment, as reversible adhesion is crucial for the animal’s movement? In this paper, we show that the nanometer range of the spatula size of geckos may have evolved to optimize the adhesive strength and maximum tolerance of imperfect adhesion (for robustness). Our analysis also indicates that the asymmetrical structure of the gecko’s seta structure may have been designed to simultaneously allow robust attachment and easy detachment.     

A Bayesian model for the joint optimization of quality and maintenance decisions

We develop a model for the economic design of a Bayesian control chart for monitoring a process mean. The process may randomly suffer failures that result in a non‐operating state, and thus call for an immediate corrective maintenance action, as well as assignable causes that shift the process mean to an undesirable level. Quality shifts, apart from poorer quality outcome and higher operational cost, also result in higher failure rate. Consequently, their removal, besides improving the outcome quality and reducing the quality‐related cost, is also a preventive maintenance action since it reduces the probability of a failure. The proposed Bayesian model allows the determination of the design parameters that minimize the total expected quality and maintenance cost per time unit. The effectiveness of the proposed model is evaluated through the comparison of its expected cost against the optimum expected cost of the simpler variable‐parameter Shewhart chart. Copyright © 2010 John Wiley & Sons, Ltd.     

A Bayesian model for measurements on a set of instruments

A Bayesian model is proposed based on randomizing the systematic errors of the instruments. Conditions are identified under which the randomization reduces the expected bias in estimating a measured quantity. __________ Translated from Izmeritel’naya Tekhnika, No. 3, pp. 22–25, March, 2007.     

A simple thermodynamic model for the doping and alloying of nanoparticles

Impurity incorporation into nanoparticles is modeled using thermodynamics. For small particles, entropically driven impurity incorporation is reduced, rendering doping difficult. We show that the free energy of surface impurities in small nanoparticles is lower than core impurities, surface doping therefore occurs preferentially. A critical size for core doping is identified, below which it is energetically unfavorable. In all cases, core impurity concentration is reduced as particle size decreases. We show larger than bulk impurity concentrations are possible, corresponding to increased alloying.     

A hierarchical model for optimal supplier selection in multiple sourcing contexts

This paper addresses a crucial objective of the strategic purchasing function in supply chains, i.e. optimal supplier selection. We present a hierarchical extension of the data envelopment analysis (DEA), the most widespread method for supplier rating in the literature, for application in a multiple sourcing strategy context. The proposed hierarchical technique is based on three levels. First, a modified DEA approach is used to evaluate the efficiency of each supplier according to some criteria proposed by the buyer. Second, the well known technique for order preference by similarities to ideal solution (TOPSIS) is applied to rank the maximally efficient suppliers given by the previous step. Third and finally, a linear programming problem is stated and solved to find the quantities to order from each maximally efficient supplier in the multiple sourcing context. The presented approach is able to straightforwardly discern between efficient and inefficient partners, avoid the confusion between efficient and effective suppliers and split the supply in a multiple sourcing context. The hierarchical model is applied to the supply of a C class component to show its robustness and effectiveness, while comparing it with the DEA and TOPSIS approaches.