A Bayesian network to analyse basketball players’ performances: a multivariate copula-based approach

Statistics in sports plays a key role in predicting winning strategies and providing objective performance indicators. Despite the growing interest in recent years in using statistical methodologies in this field, less emphasis has been given to the multivariate approach. This work aims at using the Bayesian networks to model the joint distribution of a set of indicators of players’ performances in basketball in order to discover the set of their probabilistic relationships as well as the main determinants affecting the player’s winning percentage. From a methodological point of view, the interest is to define a suitable model for non-Gaussian data, relaxing the strong assumption on normal distribution in favour of Gaussian copula. Through the estimated Bayesian network, we discovered many interesting dependence relationships, providing a scientific validation of some known results mainly based on experience. At last, some scenarios of interest have been simulated to understand the main determinants that contribute to rising in the number of won games by a player

Analysis of magma flux and eruption intensity during the 2021 explosive activity at the Soufrière of St Vincent, West Indies

Seismic RSAM signals and eruption cloud height measurements were used to estimate peak intensities of 40 explosive events during the 8-22 April 2021 activity of the Soufrière volcano. We estimated magma supply rates and erupted volumes in each explosion, characterized uncertainty by stochastic modelling and identified four eruptive stages. Stage 1 included an intense period of 9.5 hours with 11 explosive events with peak eruption intensity between 2000 and 4000 m3/s and magma supply rate reaching 828 m3/s. 12 high intensity explosions (∼4000 m3/s) occurred in Stage 2 with average magma supply rate of 251 m3/s. Stage 3 involved declining intensity, magma supply rate and lengthening repose periods between explosions. Stage 4 involved 3 much weaker explosions. The total erupted volume of magma is estimated at 38.5 × 106 m3 (90% credible interval: [22.0 .. 61.9] × 106 m3) consistent with independent estimates from analysis of tephra deposits and volcano subsidence sourced at ∼6 km depth. The 150-fold increase in magma supply rate, from the preceding effusive phase to Stage 1 of the explosive phase, is attributed to replacement of very high viscosity degassed magma occupying the shallow conduit system with new lower viscosity volatile-rich magma from the magma chamber. Supplementary material at https://doi.org/10.6084/m9.figshare.c.655800

Mining and visualising ordinal data with non-parametric continuous BBNs

Data mining is the process of extracting and analysing information from large databases. Graphical models are a suitable framework for probabilistic modelling. A Bayesian Belief Net (BBN) is a probabilistic graphical model, which represents joint distributions in an intuitive and efficient way. It encodes the probability density (or mass) function of a set of variables by specifying a number of conditional independence statements in the form of a directed acyclic graph. Specifying the structure of the model is one of the most important design choices in graphical modelling. Notwithstanding their potential, there are only a limited number of applications of graphical models on very complex and large databases. A method for mining ordinal multivariate data using non-parametric BBNs is presented. The main advantage of this method is that it can handle a large number of continuous variables, without making any assumptions about their marginal distributions, in a very fast manner. Once the BBN is learned from data, it can be further used for prediction. This approach allows for rapid conditionalisation, which is a very important feature of a BBN from a user's standpoint. © 2008 Elsevier B.V. All rights reserved

Mining and visualising ordinal data with non-parametric continuous BBNs

Data mining is the process of extracting and analysing information from large databases. Graphical models are a suitable framework for probabilistic modelling. A Bayesian Belief Net (BBN) is a probabilistic graphical model, which represents joint distributions in an intuitive and efficient way. It encodes the probability density (or mass) function of a set of variables by specifying a number of conditional independence statements in the form of a directed acyclic graph. Specifying the structure of the model is one of the most important design choices in graphical modelling. Notwithstanding their potential, there are only a limited number of applications of graphical models on very complex and large databases. A method for mining ordinal multivariate data using non-parametric BBNs is presented. The main advantage of this method is that it can handle a large number of continuous variables, without making any assumptions about their marginal distributions, in a very fast manner. Once the BBN is learned from data, it can be further used for prediction. This approach allows for rapid conditionalisation, which is a very important feature of a BBN from a user's standpoint.

Application of Bayesian Networks to Integrity Management of Energy Pipelines

Metal-loss corrosion and third-party damage (TPD) are the leading threats to the integrity of buried oil and natural gas pipelines. This thesis employs Bayesian networks (BNs) and non-parametric Bayesian networks (NPBNs) to deal with four issues with regard to the reliability-based management program of corrosion and TPD. The first study integrates the quantification of measurement errors of the ILI tools, corrosion growth modeling and reliability analysis in a single dynamic Bayesian network (DBN) model, and employs the parameter learning technique to learn the parameters of the DBN model from the ILI-reported and filed-measured corrosion depths. The second study develops the BN model to estimate the probability of a given pipeline being hit by third-party excavations by taking into account common preventative and protective measures. The parameter learning technique is employed to learn the parameters of the BN model from datasets that consist of individual cases of third-party activities. The ILIs are infeasible for a portion of buried pipelines due to various reasons, which are known as unpiggable pipelines. To assist with the corrosion assessment for the unpiggable pipelines, the third study develops a non-parametric Bayesian network (NPBN) model to predict the corrosion depth on buried pipelines using the pipeline age and local soil properties as the predictors. The last study develops an optimal sample size determination method for collecting samples to reduce the epistemic uncertainties in the probabilistic distributions of basic random variables in the reliability analysis of corroded pipelines

Dynamic multivariate loss and risk assessment of process facilities

Dynamic risk assessments (DRA) are the next generation of risk estimation approaches that help to enable safer operations of complex process systems in changing environments. By incorporating new evidences from systems in the risk assessment process, the DRA techniques ensure estimation of current risk. This thesis investigates the existing knowledge and technological challenges associated with dynamic risk assessment and proposes new methods to improve effective implementation of DRA techniques. Risk is defined as the combination of three attributes: what can go wrong, how bad could it be, and how often might it happen. This research evaluates the limitations of the methodologies that have been developed to answer the latter two questions. Loss functions are used in this work to estimate and model operational loss in process facilities. The application of loss functions provides the following advantages: (i) the stochastic nature of losses is taken into account; and (ii) the estimation of the operational loss in process facilities due to the deviation of key process characteristics (KPC) is conducted. Models to estimate reputational loss and significant elements of business interruption loss, which are usually ignored in the literature, are also provided. This research also presents a methodology to develop multivariate loss functions to measure the operational loss of multivariate process systems. For this purpose, copula functions are used to link the univariate loss functions and develop the multivariate loss functions. Copula functions are also used to address the existing challenge of loss aggregation for multiple-loss scenarios. Regarding the dynamic estimation of the probability of abnormal events, the Bayesian Network (BN) has usually been used in the literature. However, integrated safety analysis of hazardous process facilities calls for an understanding of both stochastic and topological dependencies, going beyond traditional BN analysis to study cause-effect relationships among major risk factors. This work presents a novel model based on the Copula Bayesian Network (CBN) for multivariate safety analysis of process systems, which addresses the main shortcomings of traditional BNs. The proposed CBN model offers great flexibility in probabilistic analysis of individual risk factors while considering their uncertainty and complex stochastic dependence. The research outcomes provide advanced methods for critical operations, such as the offshore operations in harsh environments, to be used in continuous improvement of processes and real-time risk estimation. Application of the proposed dynamic risk assessment framework, along with a proper safety culture, enhances the day-to-day risk-informed decision making process by constantly monitoring, evaluating and improving the process safety performance