A Bayesian‐Markov process for reliability prediction

Accurate reliability prediction for large-scale, long lived engineering is a crucial foundation for effective asset risk management and optimal maintenance decision making. However, a lack of failure data for assets that fail infrequently, and changing operational conditions over long periods of time, make accurate reliability prediction for such assets very challenging. To address this issue, we present a Bayesian-Marko best approach to reliability prediction using prior knowledge and condition monitoring data. In this approach, the Bayesian theory is used to incorporate prior information about failure probabilities and current information about asset health to make statistical inferences, while Markov chains are used to update and predict the health of assets based on condition monitoring data. The prior information can be supplied by domain experts, extracted from previous comparable cases or derived from basic engineering principles. Our approach differs from existing hybrid Bayesian models which are normally used to update the parameter estimation of a given distribution such as the Weibull-Bayesian distribution or the transition probabilities of a Markov chain. Instead, our new approach can be used to update predictions of failure probabilities when failure data are sparse or nonexistent, as is often the case for large-scale long-lived engineering assets.

A sequential Monte Carlo algorithm to incorporate model uncertainty in Bayesian sequential design

Here we present a sequential Monte Carlo (SMC) algorithm that can be used for any one-at-a-time Bayesian sequential design problem in the presence of model uncertainty where discrete data are encountered. Our focus is on adaptive design for model discrimination but the methodology is applicable if one has a different design objective such as parameter estimation or prediction. An SMC algorithm is run in parallel for each model and the algorithm relies on a convenient estimator of the evidence of each model which is essentially a function of importance sampling weights. Other methods for this task such as quadrature, often used in design, suffer from the curse of dimensionality. Approximating posterior model probabilities in this way allows us to use model discrimination utility functions derived from information theory that were previously difficult to compute except for conjugate models. A major benefit of the algorithm is that it requires very little problem specific tuning. We demonstrate the methodology on three applications, including discriminating between models for decline in motor neuron numbers in patients suffering from neurological diseases such as Motor Neuron disease.

Use of Bayesian MUNE to show differing rate of loss of motor units in subgroups of ALS

Objectives To evaluate differences among patients with different clinical features of ALS, we used our Bayesian method of motor unit number estimation (MUNE). Methods We performed serial MUNE studies on 42 subjects who fulfilled the diagnostic criteria for ALS during the course of their illness. Subjects were classified into three subgroups according to whether they had typical ALS (with upper and lower motor neurone signs) or had predominantly upper motor neurone weakness with only minor LMN signs, or predominantly lower motor neurone weakness with only minor UMN signs. In all subjects we calculated the half life of MUs, defined as the expected time for the number of MUs to halve, in one or more of the abductor digiti minimi (ADM), abductor pollicis brevis (APB) and extensor digitorum brevis (EDB) muscles. Results The mean half life of MUs was less in subjects who had typical ALS with both upper and lower motor neurone signs than in those with predominantly upper motor neurone weakness or predominantly lower motor neurone weakness. In 18 subjects we analysed the estimated size of the MUs and demonstrated the appearance of large MUs in subjects with upper or lower motor neurone predominant weakness. We found that the appearance of large MUs was correlated with the half life of MUs. Conclusions Patients with different clinical features of ALS have different rates of loss and different sizes of MUs. Significance: These findings could indicate differences in disease pathogenesis.

Condition deterioration prediction of bridge elements using Dynamic Bayesian Networks (DBNs)

The ability of bridge deterioration models to predict future condition provides significant advantages in improving the effectiveness of maintenance decisions. This paper proposes a novel model using Dynamic Bayesian Networks (DBNs) for predicting the condition of bridge elements. The proposed model improves prediction results by being able to handle, deterioration dependencies among different bridge elements, the lack of full inspection histories, and joint considerations of both maintenance actions and environmental effects. With Bayesian updating capability, different types of data and information can be utilised as inputs. Expert knowledge can be used to deal with insufficient data as a starting point. The proposed model established a flexible basis for bridge systems deterioration modelling so that other models and Bayesian approaches can be further developed in one platform. A steel bridge main girder was chosen to validate the proposed model.

Towards semantic search and inference in electronic medical records : an approach using concept-based information retrieval

Background This paper presents a novel approach to searching electronic medical records that is based on concept matching rather than keyword matching. Aim The concept-based approach is intended to overcome specific challenges we identified in searching medical records. Method Queries and documents were transformed from their term-based originals into medical concepts as defined by the SNOMED-CT ontology. Results Evaluation on a real-world collection of medical records showed our concept-based approach outperformed a keyword baseline by 25% in Mean Average Precision. Conclusion The concept-based approach provides a framework for further development of inference based search systems for dealing with medical data.

Severity of driver injury and vehicle damage in traffic crashes at intersections: A Bayesian hierarchical analysis

Most crash severity studies ignored severity correlations between driver-vehicle units involved in the same crashes. Models without accounting for these within-crash correlations will result in biased estimates in the factor effects. This study developed a Bayesian hierarchical binomial logistic model to identify the significant factors affecting the severity level of driver injury and vehicle damage in traffic crashes at signalized intersections. Crash data in Singapore were employed to calibrate the model. Model fitness assessment and comparison using Intra-class Correlation Coefficient (ICC) and Deviance Information Criterion (DIC) ensured the suitability of introducing the crash-level random effects. Crashes occurring in peak time, in good street lighting condition, involving pedestrian injuries are associated with a lower severity, while those in night time, at T/Y type intersections, on right-most lane, and installed with red light camera have larger odds of being severe. Moreover, heavy vehicles have a better resistance on severe crash, while crashes involving two-wheel vehicles, young or aged drivers, and the involvement of offending party are more likely to result in severe injuries.

Hotspot Identification: A Full Bayesian Hierarchical Modeling Approach

This study proposes a full Bayes (FB) hierarchical modeling approach in traffic crash hotspot identification. The FB approach is able to account for all uncertainties associated with crash risk and various risk factors by estimating a posterior distribution of the site safety on which various ranking criteria could be based. Moreover, by use of hierarchical model specification, FB approach is able to flexibly take into account various heterogeneities of crash occurrence due to spatiotemporal effects on traffic safety. Using Singapore intersection crash data(1997-2006), an empirical evaluate was conducted to compare the proposed FB approach to the state-of-the-art approaches. Results show that the Bayesian hierarchical models with accommodation for site specific effect and serial correlation have better goodness-of-fit than non hierarchical models. Furthermore, all model-based approaches perform significantly better in safety ranking than the naive approach using raw crash count. The FB hierarchical models were found to significantly outperform the standard EB approach in correctly identifying hotspots.

The influence of vegetation and soil type on the speciation of iron in soil water

Soluble organic matter derived from exotic Pinus species has been shown to form stronger complexes with iron (Fe) than that derived from most native Australian species. It has also been proposed that the establishment of exotic Pinus plantations in coastal southeast Queensland may have enhanced the solubility of Fe in soils by increasing the amount of organically complexed Fe, but this remains inconclusive. In this study we test whether the concentration and speciation of Fe in soil water from Pinus plantations differs significantly from soil water from native vegetation areas. Both Fe redox speciation and the interaction between Fe and dissolved organic matter (DOM) were considered; Fe - DOM interaction was assessed using the Stockholm Humic Model. Iron concentrations (mainly Fe 2+) were greatest in the soil waters with the greatest DOM content collected from sandy podosols (Podzols), where they are largely controlled by redox potential. Iron concentrations were small in soil waters from clay and iron oxide-rich soils, in spite of similar redox potentials. This condition is related to stronger sorption on to the reactive clay and iron oxide mineral surfaces in these soils, which reduces the amount of DOM available for electron shuttling and microbial metabolism, restricting reductive dissolution of Fe. Vegetation type had no significant influence on the concentration and speciation of iron in soil waters, although DOM from Pinus sites had greater acidic functional group site densities than DOM from native vegetation sites. This is because Fe is mainly in the ferrous form, even in samples from the relatively well-drained podosols. However, modelling suggests that Pinus DOM can significantly increase the amount of truly dissolved ferric iron remaining in solution in oxic conditions. Therefore, the input of ferrous iron together with Pinus DOM to surface waters may reduce precipitation of hydrous ferric oxides (ferrihydrite) and increase the flux of dissolved Fe out of the catchment. Such inputs of iron are most probably derived from podosols planted with Pinus.

A proposed validation framework for expert elicited Bayesian Networks

The popularity of Bayesian Network modelling of complex domains using expert elicitation has raised questions of how one might validate such a model given that no objective dataset exists for the model. Past attempts at delineating a set of tests for establishing confidence in an entirely expert-elicited model have focused on single types of validity stemming from individual sources of uncertainty within the model. This paper seeks to extend the frameworks proposed by earlier researchers by drawing upon other disciplines where measuring latent variables is also an issue. We demonstrate that even in cases where no data exist at all there is a broad range of validity tests that can be used to establish confidence in the validity of a Bayesian Belief Network.

Discriminating stromatolite formation modes using rare earth element geochemistry: Trapping and binding versus in situ precipitation of stromatolites from the Neoproterozoic Bitter Springs Formation, Northern Territory, Australia

Stromatolites consist primarily of trapped and bound ambient sediment and/or authigenic mineral precipitates, but discrimination of the two constituents is difficult where stromatolites have a fine texture. We used laser ablation-inductively coupled plasma-mass spectrometry to measure trace element (rare earth element – REE, Y and Th) concentrations in both stromatolites (domical and branched) and closely associated particulate carbonate sediment in interspaces (spaces between columns or branches) from bioherms within the Neoproterozoic Bitter Springs Formation, central Australia. Our high resolution sampling allows discrimination of shale-normalised REE patterns between carbonate in stromatolites and immediately adjacent, fine-grained ambient particulate carbonate sediment from interspaces. Whereas all samples show similar negative La and Ce anomalies, positive Gd anomalies and chondritic Y/Ho ratios, the stromatolites and non-stromatolite sediment are distinguishable on the basis of consistently elevated light REEs (LREEs) in the stromatolitic laminae and relatively depleted LREEs in the particulate sediment samples. Additionally, concentrations of the lithophile element Th are higher in ambient sediment samples than in stromatolites, consistent with accumulation of some fine siliciclastic detrital material in the ambient sediment but a near absence in the stromatolites. These findings are consistent with the stromatolites consisting dominantly of in situ carbonate precipitates rather than trapped and bound ambient sediment. Hence, high resolution trace element (REE + Y, Th) geochemistry can discriminate fine-grained carbonates in these stromatolites from coeval non-stromatolitic carbonate sediment and demonstrates that the sampled stromatolites formed primarily from in situ precipitation, presumably within microbial mats/biofilms, rather than by trapping and binding of ambient sediment. Identification of the source of fine carbonate in stromatolites is significant, because if it is not too heavily contaminated by trapped ambient sediment, it may contain geochemical biosignatures and/or direct evidence of the local water chemistry in which the precipitates formed.

Integrated health prediction of bridge systems using dynamic object oriented Bayesian networks (DOOBNS)

The serviceability and safety of bridges are crucial to people’s daily lives and to the national economy. Every effort should be taken to make sure that bridges function safely and properly as any damage or fault during the service life can lead to transport paralysis, catastrophic loss of property or even casualties. Nonetheless, aggressive environmental conditions, ever-increasing and changing traffic loads and aging can all contribute to bridge deterioration. With often constrained budget, it is of significance to identify bridges and bridge elements that should be given higher priority for maintenance, rehabilitation or replacement, and to select optimal strategy. Bridge health prediction is an essential underpinning science to bridge maintenance optimization, since the effectiveness of optimal maintenance decision is largely dependent on the forecasting accuracy of bridge health performance. The current approaches for bridge health prediction can be categorised into two groups: condition ratings based and structural reliability based. A comprehensive literature review has revealed the following limitations of the current modelling approaches: (1) it is not evident in literature to date that any integrated approaches exist for modelling both serviceability and safety aspects so that both performance criteria can be evaluated coherently; (2) complex system modelling approaches have not been successfully applied to bridge deterioration modelling though a bridge is a complex system composed of many inter-related bridge elements; (3) multiple bridge deterioration factors, such as deterioration dependencies among different bridge elements, observed information, maintenance actions and environmental effects have not been considered jointly; (4) the existing approaches are lacking in Bayesian updating ability to incorporate a variety of event information; (5) the assumption of series and/or parallel relationship for bridge level reliability is always held in all structural reliability estimation of bridge systems. To address the deficiencies listed above, this research proposes three novel models based on the Dynamic Object Oriented Bayesian Networks (DOOBNs) approach. Model I aims to address bridge deterioration in serviceability using condition ratings as the health index. The bridge deterioration is represented in a hierarchical relationship, in accordance with the physical structure, so that the contribution of each bridge element to bridge deterioration can be tracked. A discrete-time Markov process is employed to model deterioration of bridge elements over time. In Model II, bridge deterioration in terms of safety is addressed. The structural reliability of bridge systems is estimated from bridge elements to the entire bridge. By means of conditional probability tables (CPTs), not only series-parallel relationship but also complex probabilistic relationship in bridge systems can be effectively modelled. The structural reliability of each bridge element is evaluated from its limit state functions, considering the probability distributions of resistance and applied load. Both Models I and II are designed in three steps: modelling consideration, DOOBN development and parameters estimation. Model III integrates Models I and II to address bridge health performance in both serviceability and safety aspects jointly. The modelling of bridge ratings is modified so that every basic modelling unit denotes one physical bridge element. According to the specific materials used, the integration of condition ratings and structural reliability is implemented through critical failure modes. Three case studies have been conducted to validate the proposed models, respectively. Carefully selected data and knowledge from bridge experts, the National Bridge Inventory (NBI) and existing literature were utilised for model validation. In addition, event information was generated using simulation to demonstrate the Bayesian updating ability of the proposed models. The prediction results of condition ratings and structural reliability were presented and interpreted for basic bridge elements and the whole bridge system. The results obtained from Model II were compared with the ones obtained from traditional structural reliability methods. Overall, the prediction results demonstrate the feasibility of the proposed modelling approach for bridge health prediction and underpin the assertion that the three models can be used separately or integrated and are more effective than the current bridge deterioration modelling approaches. The primary contribution of this work is to enhance the knowledge in the field of bridge health prediction, where more comprehensive health performance in both serviceability and safety aspects are addressed jointly. The proposed models, characterised by probabilistic representation of bridge deterioration in hierarchical ways, demonstrated the effectiveness and pledge of DOOBNs approach to bridge health management. Additionally, the proposed models have significant potential for bridge maintenance optimization. Working together with advanced monitoring and inspection techniques, and a comprehensive bridge inventory, the proposed models can be used by bridge practitioners to achieve increased serviceability and safety as well as maintenance cost effectiveness.

Bayesian experimental design for models with intractable likelihoods

In this paper we present a methodology for designing experiments for efficiently estimating the parameters of models with computationally intractable likelihoods. The approach combines a commonly used methodology for robust experimental design, based on Markov chain Monte Carlo sampling, with approximate Bayesian computation (ABC) to ensure that no likelihood evaluations are required. The utility function considered for precise parameter estimation is based upon the precision of the ABC posterior distribution, which we form efficiently via the ABC rejection algorithm based on pre-computed model simulations. Our focus is on stochastic models and, in particular, we investigate the methodology for Markov process models of epidemics and macroparasite population evolution. The macroparasite example involves a multivariate process and we assess the loss of information from not observing all variables.

Marginal reversible jump Markov chain Monte Carlo with application to motor unit number estimation

Motor unit number estimation (MUNE) is a method which aims to provide a quantitative indicator of progression of diseases that lead to loss of motor units, such as motor neurone disease. However the development of a reliable, repeatable and fast real-time MUNE method has proved elusive hitherto. Ridall et al. (2007) implement a reversible jump Markov chain Monte Carlo (RJMCMC) algorithm to produce a posterior distribution for the number of motor units using a Bayesian hierarchical model that takes into account biological information about motor unit activation. However we find that the approach can be unreliable for some datasets since it can suffer from poor cross-dimensional mixing. Here we focus on improved inference by marginalising over latent variables to create the likelihood. In particular we explore how this can improve the RJMCMC mixing and investigate alternative approaches that utilise the likelihood (e.g. DIC (Spiegelhalter et al., 2002)). For this model the marginalisation is over latent variables which, for a larger number of motor units, is an intractable summation over all combinations of a set of latent binary variables whose joint sample space increases exponentially with the number of motor units. We provide a tractable and accurate approximation for this quantity and also investigate simulation approaches incorporated into RJMCMC using results of Andrieu and Roberts (2009).

Eigenvoice modeling for cross likelihood ratio based speaker clustering : a Bayesian approach

This paper proposes the use of Bayesian approaches with the cross likelihood ratio (CLR) as a criterion for speaker clustering within a speaker diarization system, using eigenvoice modeling techniques. The CLR has previously been shown to be an effective decision criterion for speaker clustering using Gaussian mixture models. Recently, eigenvoice modeling has become an increasingly popular technique, due to its ability to adequately represent a speaker based on sparse training data, as well as to provide an improved capture of differences in speaker characteristics. The integration of eigenvoice modeling into the CLR framework to capitalize on the advantage of both techniques has also been shown to be beneficial for the speaker clustering task. Building on that success, this paper proposes the use of Bayesian methods to compute the conditional probabilities in computing the CLR, thus effectively combining the eigenvoice-CLR framework with the advantages of a Bayesian approach to the diarization problem. Results obtained on the 2002 Rich Transcription (RT-02) Evaluation dataset show an improved clustering performance, resulting in a 33.5% relative improvement in the overall Diarization Error Rate (DER) compared to the baseline system.

Towards Bayesian experimental design for nonlinear models that require a large number of sampling times

The use of Bayesian methodologies for solving optimal experimental design problems has increased. Many of these methods have been found to be computationally intensive for design problems that require a large number of design points. A simulation-based approach that can be used to solve optimal design problems in which one is interested in finding a large number of (near) optimal design points for a small number of design variables is presented. The approach involves the use of lower dimensional parameterisations that consist of a few design variables, which generate multiple design points. Using this approach, one simply has to search over a few design variables, rather than searching over a large number of optimal design points, thus providing substantial computational savings. The methodologies are demonstrated on four applications, including the selection of sampling times for pharmacokinetic and heat transfer studies, and involve nonlinear models. Several Bayesian design criteria are also compared and contrasted, as well as several different lower dimensional parameterisation schemes for generating the many design points.