Improper and proper posteriors with improper priors in a Poisson-gamma hierarchical model

In Bayesian analysis, Markov chain Monte Carlo techniques have become so easy to use that it is possible to erroneously generate observations from a posterior distribution that is improper. In this paper we discussed the Poisson-gamma hierarchical model. A flexible prior distribution is discussed, one which allows the user to choose improper priors. Necessary and sufficient conditions are given for the posterior distribution to be proper and for the posterior moments to exist. An example using data on brain lesions for multiple sclerosis patients is presented to demonstrate the difficulty in diagnosing whether the posterior is proper.     

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.     

A multivariate Poisson-lognormal regression model for prediction of crash counts by severity, using Bayesian methods

Numerous efforts have been devoted to investigating crash occurrence as related to roadway design features, environmental factors and traffic conditions. However, most of the research has relied on univariate count models; that is, traffic crash counts at different levels of severity are estimated separately, which may neglect shared information in unobserved error terms, reduce efficiency in parameter estimates, and lead to potential biases in sample databases. This paper offers a multivariate Poisson-lognormal (MVPLN) specification that simultaneously models crash counts by injury severity. The MVPLN specification allows for a more general correlation structure as well as overdispersion. This approach addresses several questions that are difficult to answer when estimating crash counts separately. Thanks to recent advances in crash modeling and Bayesian statistics, parameter estimation is done within the Bayesian paradigm, using a Gibbs Sampler and the Metropolis–Hastings (M–H) algorithms for crashes on Washington State rural two-lane highways. Estimation results from the MVPLN approach show statistically significant correlations between crash counts at different levels of injury severity. The non-zero diagonal elements suggest overdispersion in crash counts at all levels of severity. The results lend themselves to several recommendations for highway safety treatments and design policies. For example, wide lanes and shoulders are key for reducing crash frequencies, as are longer vertical curves.     

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].     

Multilevel data and Bayesian analysis in traffic safety

Background

Traditional crash prediction models, such as generalized linear regression model, are incapable of taking into account multilevel data structure. Therefore they suffer from a common underlying limitation that each observation (e.g. a crash or a vehicle involvement) in the estimation procedure corresponds to an individual situation in which the residuals exhibit independence.

Problem

However, this “independence” assumption may often not hold true since multilevel data structures exist extensively because of the traffic data collection and clustering process. Disregarding the possible within-group correlations may lead to production of models with unreliable parameter estimates and statistical inferences.

Proposed theory

In this paper, a 5 × ST-level hierarchy is proposed to represent the general framework of multilevel data structures in traffic safety, i.e. [Geographic region level − Traffic site level − Traffic crash level − Driver-vehicle unit level − Occupant level] × Spatiotemporal level. The involvement and emphasis for different sub-groups of these levels depend on different research purposes and also rely on the heterogeneity examination on crash data employed. To properly accommodate the potential cross-group heterogeneity and spatiotemporal correlation due to the multilevel data structure, a Bayesian hierarchical approach that explicitly specifies multilevel structure and reliably yields parameter estimates is introduced and recommended.

Case studies

Using Bayesian hierarchical models, the results from several case studies are highlighted to show the improvements on model fitting and predictive performance over traditional models by appropriately accounting for the multilevel data structure.     

Investigating different approaches to develop informative priors in hierarchical Bayesian safety performance functions

The Bayesian inference method has been frequently adopted to develop safety performance functions. One advantage of the Bayesian inference is that prior information for the independent variables can be included in the inference procedures. However, there are few studies that discussed how to formulate informative priors for the independent variables and evaluated the effects of incorporating informative priors in developing safety performance functions. This paper addresses this deficiency by introducing four approaches of developing informative priors for the independent variables based on historical data and expert experience. Merits of these informative priors have been tested along with two types of Bayesian hierarchical models (Poisson-gamma and Poisson-lognormal models). Deviance information criterion (DIC), R-square values, and coefficients of variance for the estimations were utilized as evaluation measures to select the best model(s). Comparison across the models indicated that the Poisson-gamma model is superior with a better model fit and it is much more robust with the informative priors. Moreover, the two-stage Bayesian updating informative priors provided the best goodness-of-fit and coefficient estimation accuracies. Furthermore, informative priors for the inverse dispersion parameter have also been introduced and tested. Different types of informative priors’ effects on the model estimations and goodness-of-fit have been compared and concluded. Finally, based on the results, recommendations for future research topics and study applications have been made.     

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.     

Crash risk analysis for Shanghai urban expressways: A Bayesian semi-parametric modeling approach

Urban expressway systems have been developed rapidly in recent years in China; it has become one key part of the city roadway networks as carrying large traffic volume and providing high traveling speed. Along with the increase of traffic volume, traffic safety has become a major issue for Chinese urban expressways due to the frequent crash occurrence and the non-recurrent congestions caused by them. For the purpose of unveiling crash occurrence mechanisms and further developing Active Traffic Management (ATM) control strategies to improve traffic safety, this study developed disaggregate crash risk analysis models with loop detector traffic data and historical crash data. Bayesian random effects logistic regression models were utilized as it can account for the unobserved heterogeneity among crashes. However, previous crash risk analysis studies formulated random effects distributions in a parametric approach, which assigned them to follow normal distributions. Due to the limited information known about random effects distributions, subjective parametric setting may be incorrect. In order to construct more flexible and robust random effects to capture the unobserved heterogeneity, Bayesian semi-parametric inference technique was introduced to crash risk analysis in this study. Models with both inference techniques were developed for total crashes; semi-parametric models were proved to provide substantial better model goodness-of-fit, while the two models shared consistent coefficient estimations. Later on, Bayesian semi-parametric random effects logistic regression models were developed for weekday peak hour crashes, weekday non-peak hour crashes, and weekend non-peak hour crashes to investigate different crash occurrence scenarios. Significant factors that affect crash risk have been revealed and crash mechanisms have been concluded.     

Bayesian system identification of dynamical systems using large sets of training data: A MCMC solution

In the last 20 years the applicability of Bayesian inference to the system identification of structurally dynamical systems has been helped considerably by the emergence of Markov chain Monte Carlo (MCMC) algorithms – stochastic simulation methods which alleviate the need to evaluate the intractable integrals which often arise during Bayesian analysis. In this paper specific attention is given to the situation where, with the aim of performing Bayesian system identification, one is presented with very large sets of training data. Building on previous work by the author, an MCMC algorithm is presented which, through combing Data Annealing with the concept of ‘highly informative training data’, can be used to analyse large sets of data in a computationally cheap manner. The new algorithm is called Smooth Data Annealing.     

A hierarchical modeling approach to accelerated degradation testing data analysis: A case study

In this case study, we investigate the degradation process of light‐emitting diodes (LEDs), which is used as a light source in DNA sequencing machines. Accelerated degradation tests are applied by varying temperature and forward current, and the light outputs are measured by a computerized measuring system. A degradation path model, which connects to the LED function recommended in Mitsuo (1991), is used in describing the degradation process. We consider variations in both measurement errors and degradation paths among individual test units. It is demonstrated that the hierarchical modeling approach is flexible and powerful in modeling a complex degradation process with nonlinear function and random coefficient. After fitting the model by maximum likelihood estimation, the failure time distribution can be obtained by simulation. Copyright © 2010 John Wiley & Sons, Ltd.     

A Bayesian Belief Network modelling of organisational factors in risk analysis: A case study in maritime transportation

The paper presents an innovative approach to integrate Human and Organisational Factors (HOF) into risk analysis. The approach has been developed and applied to a case study in the maritime industry, but it can also be utilised in other sectors. A Bayesian Belief Network (BBN) has been developed to model the Maritime Transport System (MTS), by taking into account its different actors (i.e., ship-owner, shipyard, port and regulator) and their mutual influences. The latter have been modelled by means of a set of dependent variables whose combinations express the relevant functions performed by each actor. The BBN model of the MTS has been used in a case study for the quantification of HOF in the risk analysis carried out at the preliminary design stage of High Speed Craft (HSC). The study has focused on a collision in open sea hazard carried out by means of an original method of integration of a Fault Tree Analysis (FTA) of technical elements with a BBN model of the influences of organisational functions and regulations, as suggested by the International Maritime Organisation's (IMO) Guidelines for Formal Safety Assessment (FSA). The approach has allowed the identification of probabilistic correlations between the basic events of a collision accident and the BBN model of the operational and organisational conditions. The linkage can be exploited in different ways, especially to support identification and evaluation of risk control options also at the organisational level. Conditional probabilities for the BBN have been estimated by means of experts’ judgments, collected from an international panel of different European countries. Finally, a sensitivity analysis has been carried out over the model to identify configurations of the MTS leading to a significant reduction of accident probability during the operation of the HSC.     

A novel Bayesian approach to reliability modeling: The benefits of uncertainty evaluation in the model selection procedure

This paper proposes a different likelihood formulation within the Bayesian paradigm for parameter estimation of reliability models. Moreover, the assessment of the uncertainties associated with parameters, the goodness of fit, and the model prediction of reliability are included in a systematic framework for better aiding the model selection procedure. Two case studies are appraised to highlight the contributions of the proposed method and demonstrate the differences between the proposed Bayesian formulation and an existing Bayesian formulation.     

A case study in engineering model validation using new wavelet‐based methods

Simulation model validation is an important part of simulation development and use. An emerging challenge is the examination of functional data systems and the validation of the simulations built to represent them. While validation methods do exist, there is a gap in the engineering and statistical approaches used for functional model validation. This case study demonstrates the use of recently developed methods based on the use of wavelets to bridge the engineering‐statistical gap in functional simulation model validation. Two methods are used to provide insight regarding model validity, and a third method is used to identify areas of system‐simulation disagreement when model validity fails to hold.     

The application of SVR model in the improvement of QbD: a case study of the extraction of podophyllotoxin

In order to make a further optimization of process design via increasing the stability of design space, we brought in the model of Support Vector Regression (SVR). In this work, the extraction of podophyllotoxin was researched as a case study based on Quality by Design (QbD). We compared the fitting effect of SVR and the most used quadratic polynomial model (QPM) in QbD, and an analysis was made between the two design spaces obtained by SVR and QPM. As a result, the SVR stayed ahead of QPM in prediction accuracy, the stability of model and the generalization ability. The introduction of SVR into QbD made the extraction process of podophyllotoxin well designed and easier to control. The better fitting effect of SVR improved the application effect of QbD and the universal applicability of SVR, especially for non-linear, complicated and weak-regularity problems, widened the application field of QbD.     

Fatigue and crashes: The case of freight transport in Colombia

Truck drivers have been involved in a significant number of road fatalities in Colombia. To identify variables that could be associated with crashes in which truck drivers are involved, a logistic regression model was constructed. The model had as the response variable a dichotomous variable that included the presence or absence of a crash during a specific trip. As independent variables the model included information regarding a driver's work shift, with variables that could be associated with driver's fatigue. The model also included potential confounders related with road conditions. With the model, it was possible to determine the odds ratio of a crash in relation to several variables, adjusting for confounding. To collect the information about the trips included in the model, a survey among truck drivers was conducted. The results suggest strong associations between crashes (i.e., some of them statistically significant) with the number of stops made during the trip, and the average time of each stop. Survey analysis allowed us to identify the practices that contribute to generating fatigue and unhealthy conditions on the road among professional drivers. A review of national regulations confirmed the lack of legislation on this topic.     

Forward and backward risk assessment throughout a system life cycle using dynamic Bayesian networks: A case in a petroleum refinery

In this paper, risk modeling was conducted based on the defined risk elements of a conceptual risk framework. This model allows for the estimation of a variety of risks, including human error probability, operational risk, financial risk, technological risk, commercial risk, health risk, and social and environmental risks. Bayesian network (BN) structure learning techniques were used to determine the relationships among the model variables. By solving a bi-objective optimization problem applying the genetic algorithm (GA) with the Pareto ranking approach, the network structure was learned. Then, risk modeling was performed for a petroleum refinery focusing on HydroDeSulfurization (HDS) technology throughout its life cycle. To extend the model horizontally and make it possible to evaluate the risk trend throughout the technology life cycle, we developed a dynamic Bayesian network (DBN) with three-time slices. A two-way forward and backward approach was used to analyze the model. The model validation was performed by applying the leave-one-out cross-validation method.     

A model for optimal armature maintenance in electric haul truck wheel motors: a case study

The objective of the work presented in this paper is the determination of an optimal age-based maintenance strategy for wheel motor armatures of a fleet of Komatsu haul trucks in a mining application in Chile. For such purpose, four years of maintenance data of these components were analyzed to estimate their failure distribution and a model was created to simulate the maintenance process and its restrictions. The model incorporates the impact of successive corrective (on-failure) and preventive maintenance on necessary new component investments. The analysis of the failure data showed a significant difference in failure distribution of new armatures versus armatures that had already undergone one or several preventive maintenance actions. Finally, the model was applied to calculate estimated costs per unit time for different preventive maintenance intervals. From the resulting relationship an optimal preventive maintenance interval was determined and the operational and economical consequences and effects with respect to the actual strategy were quantified. The application of the model resulted in the optimal preventive maintenance interval of 14,500 operational hours. Considering the failure distribution of the armatures, this optimal strategy is very close to a run-to-failure scenario.     

An AHP-based multi-criteria model for assessment of the social sustainability of technology management process: A case study in banking industry

The abrupt development of technology has confronted different industries' managers with crucial decision points. The scope of their decisions' impact goes beyond their companies' borders. Sustainable assessment of technology investigates the economic, environmental, and social effects of technologies on firms and their environment. Nonetheless, the technology management process includes different steps (such as technology acquisition and exploitation) which need a comprehensive decision-making tool toward sustainable development targets. This paper aims to propose an integrated decision-making model to investigate the social sustainability of the technology management process. Considering three main steps of the technology management process (technology selection, technology acquisition, and technology exploitation), we constructed our model utilizing the Analytic Hierarchy Process (AHP) as one of the most popular decision-making tools. In order to evaluate the efficiency of the model, we implemented it for E-banking technologies in one of the oldest banks of Iran (Iran's AgriBank). The results indicated that internet banking, internal R&D, and internal exploitation are the best decision alternatives among the technology management process from the social sustainability perspective. The results were validated by calculating the Consistency Rate (CR) and performing scenario-based sensitivity analysis.     

The optimization of the geometric cross-section dimensions of raised pedestrian crosswalks: A case study in Qazvin

This study attempts to optimize the geometric cross-section dimensions of raised pedestrian crosswalks (RPC), employing safety and comfort measures which reflect environmental conditions and drivers behavioral patterns in Qazvin, Iran. Geometric characteristics including street width, ramp lengths, top flat crown length and height, and 4672 spot speed observations of 23 implemented RPCs were considered. The authors established geometric and analytical equations to satisfactorily express the discomfort that vehicle occupants experience while traversing an RPC and the crossing risk to pedestrians. Artificial neural networks (ANN) are reputed for their capability to learn and generalize complex engineering phenomena and were therefore adopted to cope with the highly nonlinear relationship between the before-RPC spot speeds, the geometric characteristics, and spot speeds on the RPC. This on-RPC spot speed has been utilized for computing the above-mentioned criteria. Combining these criteria, a new judgment index was created to identify the optimum RPC which fulfills the highest comfort and safety levels. It was observed that the variable with the highest impact is the second ramp length, followed by the first ramp length, top flat crown length, before-RPC spot speed, height, and street width, in order of magnitude.     

The relationship between the travelling speed and motorcycle styles in urban settings: A case study in Belgrade

This report examines the difference in the distribution of the speeds of different motorcycle styles and the difference in the distribution of speeds of particular motorcycle styles and cars. The relationship between the speed of motorcycles that possess and those that do not possess vehicle registration plates was also explored. The speed was measured at six different locations on main roads in the city of Belgrade, Serbia. The study confirmed that, on average, motorcyclists drive faster than drivers of cars, but extreme speeding is recorded 2.3 times more often by motorcyclists than by car drivers. In this research, the styles of motorcycles were divided into three different groups according to their average speeds. The first group consists of sport motorcycles, which were faster than the other styles. The second group consists of scooter motorcycles, which were slower. The third group consists of conventional, touring, enduro, and chopper motorcycles with speeds that were statistically not significantly different. According to the differences of the mean speed of motorcyclists who use and do not use vehicle registration plates, the use of the registration plates can be considered a significant indicator of traffic safety. By classifying motorcycles in the three different groups, the issue of “generalizing” motorcyclists as a unique group is avoided and can be taken into consideration for future studies of motorcyclist safety.