An investigation of estimation performance for a multivariate Poisson-gamma model with parameter dependency

Statistical analysis can be overly reliant on naive assumptions of independence between different data generating processes. This results in having greater uncertainty when estimating underlying characteristics of processes as dependency creates an opportunity to boost sample size by incorporating more data into the analysis. However, this assumes that dependency has been appropriately specified, as mis-specified dependency can provide misleading information from the data. The main aim of this research is to investigate the impact of incorporating dependency into the data analysis. Our motivation for this work is concerned with estimating the reliability of items and as such we have restricted our investigation to study homogeneous Poisson processes (HPP), which can be used to model the rate of occurrence of events such as failures. In an HPP, dependency between rates can occur for numerous reasons. Whether it is similarity in mechanical designs, failure occurrence due to a common management culture or comparable failure count across machines for same failure modes. Multiple types of dependencies are considered. Dependencies can take different forms, such as simple linear dependency measured through the Pearson correlation, rank dependencies which capture non-linear dependencies and tail dependencies where the strength of the dependency may be stronger in extreme events as compared to more moderate one. The estimation of the measure of dependency between correlated processes can be challenging. We develop the research grounded in a Bayes or empirical Bayes inferential framework, where uncertainty in the actual rate of occurrence of a process is modelled with a prior probability distribution. We consider prior distributions to belong to the Gamma distribution given its flexibility and mathematical association with the Poisson process. For dependency modelling between processes we consider copulas which are a convenient and flexible way of capturing a variety of different dependency characteristics between distributions. We use a multivariate Poisson – Gamma probability model. The Poisson process captures aleatory uncertainty, the inherent variability in the data. Whereas the Gamma prior describes the epistemic uncertainty. By pooling processes with correlated underlying mean rate we are able to incorporate data from these processes into the inferential process and reduce the estimation error. There are three key research themes investigated in this thesis. First, to investigate the value in reducing estimation error by incorporating dependency within the analysis via theoretical analysis and simulation experiments. We show that correctly accounting for dependency can significantly reduce the estimation error. The findings should inform analysts a priori as to whether it is worth pursuing a more complex analysis for which the dependency parameter needs to be elicited. Second, to examine the consequences of mis-specifying the degree and form of dependency through controlled simulation experiments. We show the relative robustness of different ways of modelling the dependency using copula and Bayesian methods. The findings should inform analysts about the sensitivity of modelling choices. Third, to show how we can operationalise different methods for representing dependency through an industry case study. We show the consequences for a simple decision problem associated with the provision of spare parts to maintain operation of the industry process when depenency between event rates of the machines is appropriately modelled rather than being treated as independent processes.Statistical analysis can be overly reliant on naive assumptions of independence between different data generating processes. This results in having greater uncertainty when estimating underlying characteristics of processes as dependency creates an opportunity to boost sample size by incorporating more data into the analysis. However, this assumes that dependency has been appropriately specified, as mis-specified dependency can provide misleading information from the data. The main aim of this research is to investigate the impact of incorporating dependency into the data analysis. Our motivation for this work is concerned with estimating the reliability of items and as such we have restricted our investigation to study homogeneous Poisson processes (HPP), which can be used to model the rate of occurrence of events such as failures. In an HPP, dependency between rates can occur for numerous reasons. Whether it is similarity in mechanical designs, failure occurrence due to a common management culture or comparable failure count across machines for same failure modes. Multiple types of dependencies are considered. Dependencies can take different forms, such as simple linear dependency measured through the Pearson correlation, rank dependencies which capture non-linear dependencies and tail dependencies where the strength of the dependency may be stronger in extreme events as compared to more moderate one. The estimation of the measure of dependency between correlated processes can be challenging. We develop the research grounded in a Bayes or empirical Bayes inferential framework, where uncertainty in the actual rate of occurrence of a process is modelled with a prior probability distribution. We consider prior distributions to belong to the Gamma distribution given its flexibility and mathematical association with the Poisson process. For dependency modelling between processes we consider copulas which are a convenient and flexible way of capturing a variety of different dependency characteristics between distributions. We use a multivariate Poisson – Gamma probability model. The Poisson process captures aleatory uncertainty, the inherent variability in the data. Whereas the Gamma prior describes the epistemic uncertainty. By pooling processes with correlated underlying mean rate we are able to incorporate data from these processes into the inferential process and reduce the estimation error. There are three key research themes investigated in this thesis. First, to investigate the value in reducing estimation error by incorporating dependency within the analysis via theoretical analysis and simulation experiments. We show that correctly accounting for dependency can significantly reduce the estimation error. The findings should inform analysts a priori as to whether it is worth pursuing a more complex analysis for which the dependency parameter needs to be elicited. Second, to examine the consequences of mis-specifying the degree and form of dependency through controlled simulation experiments. We show the relative robustness of different ways of modelling the dependency using copula and Bayesian methods. The findings should inform analysts about the sensitivity of modelling choices. Third, to show how we can operationalise different methods for representing dependency through an industry case study. We show the consequences for a simple decision problem associated with the provision of spare parts to maintain operation of the industry process when depenency between event rates of the machines is appropriately modelled rather than being treated as independent processes

ISIPTA'07: Proceedings of the Fifth International Symposium on Imprecise Probability: Theories and Applications

B

Methodology for Assessing Reliability Growth Using Multiple Information Sources

The research presented here examines the assessment of the reliability of a system or product utilizing multiple data sources available throughout the different stages of its development. The assessment of the reliability as it changes throughout the development of a system is traditionally referred to as reliability growth, which refers to the discovery and mitigation of failure modes within the system, thereby improving the underlying reliability. Traditional models for assessing reliability growth work with test data from individual test events to assess the system reliability at the current stage of development. These models track or project the reliability of the system as it matures subject to the specific assumptions of the models. The contributions of this research are as follows. A new Bayesian reliability growth assessment technique is introduced for continuous-use systems under general corrective action strategies. The technique differs from those currently in the literature due to the allowance for arbitrary times for corrective actions. It also provides a probabilistic treatment of the various parameters within the model, accounting for the uncertainty present in the assessment. The Bayesian reliability growth assessment model is then extended to include results from operational testing. The approach considers the posterior distribution from the reliability growth assessment of the prior for the operational reliability assessment. The developmental and operational testing environments are not a priori assumed to be equivalent, and the change in environments is accounted for in a probabilistic manner within the model. A Bayesian reliability growth planning model is also presented that takes advantage of the reduced uncertainty in the combined operational assessment. The approach allows for reductions in the amount of demonstration testing necessary for a given level of uncertainty in the assessment, and it can also be used to reduce high design goals that often result from traditional operating characteristic curve applications. The final part of this research involves combining various sources of reliability information to obtain prior distributions on the system reliability. The approach presents a general framework for utilizing information such as component/subsystem testing, historical component reliability data, and physics-based modeling of specific component failure mechanisms

Optimal treatment allocations in space and time for on-line control of an emerging infectious disease

A key component in controlling the spread of an epidemic is deciding where, whenand to whom to apply an intervention.We develop a framework for using data to informthese decisionsin realtime.We formalize a treatment allocation strategy as a sequence of functions, oneper treatment period, that map up-to-date information on the spread of an infectious diseaseto a subset of locations where treatment should be allocated. An optimal allocation strategyoptimizes some cumulative outcome, e.g. the number of uninfected locations, the geographicfootprint of the disease or the cost of the epidemic. Estimation of an optimal allocation strategyfor an emerging infectious disease is challenging because spatial proximity induces interferencebetween locations, the number of possible allocations is exponential in the number oflocations, and because disease dynamics and intervention effectiveness are unknown at outbreak.We derive a Bayesian on-line estimator of the optimal allocation strategy that combinessimulation–optimization with Thompson sampling.The estimator proposed performs favourablyin simulation experiments. This work is motivated by and illustrated using data on the spread ofwhite nose syndrome, which is a highly fatal infectious disease devastating bat populations inNorth America

Mixing Bayes and empirical Bayes inference to anticipate the realization of engineering concerns about variant system designs

Mixing Bayes and Empirical Bayes inference provides reliability estimates for variant system designs by using relevant failure data – observed and anticipated – about engineering changes arising due to modification and innovation. A coherent inference framework is proposed to predict the realization of engineering concerns during product development so that informed decisions can be made about the system design and the analysis conducted to prove reliability. The proposed method involves combining subjective prior distributions for the number of engineering concerns with empirical priors for the non-parametric distribution of time to realize these concerns in such a way that we can cross-tabulate classes of concerns to failure events within time partitions at an appropriate level of granularity. To support efficient implementation, a computationally convenient hypergeometric approximation is developed for the counting distributions appropriate to our underlying stochastic model. The accuracy of our approximation over first-order alternatives is examined, and demonstrated, through an evaluation experiment. An industrial application illustrates model implementation and shows how estimates can be updated using information arising during development test and analysis

Mixing Bayes and empirical Bayes inference to anticipate the realization of engineering concerns about variant system designs

Mixing Bayes and Empirical Bayes inference provides reliability estimates for variant system designs by using relevant failure data – observed and anticipated – about engineering changes arising due to modification and innovation. A coherent inference framework is proposed to predict the realization of engineering concerns during product development so that informed decisions can be made about the system design and the analysis conducted to prove reliability. The proposed method involves combining subjective prior distributions for the number of engineering concerns with empirical priors for the non-parametric distribution of time to realize these concerns in such a way that we can cross-tabulate classes of concerns to failure events within time partitions at an appropriate level of granularity. To support efficient implementation, a computationally convenient hypergeometric approximation is developed for the counting distributions appropriate to our underlying stochastic model. The accuracy of our approximation over first-order alternatives is examined, and demonstrated, through an evaluation experiment. An industrial application illustrates model implementation and shows how estimates can be updated using information arising during development test and analysis

New Fundamental Technologies in Data Mining

The progress of data mining technology and large public popularity establish a need for a comprehensive text on the subject. The series of books entitled by "Data Mining" address the need by presenting in-depth description of novel mining algorithms and many useful applications. In addition to understanding each section deeply, the two books present useful hints and strategies to solving problems in the following chapters. The contributing authors have highlighted many future research directions that will foster multi-disciplinary collaborations and hence will lead to significant development in the field of data mining

Untangling hotel industry’s inefficiency: An SFA approach applied to a renowned Portuguese hotel chain

The present paper explores the technical efficiency of four hotels from Teixeira Duarte Group - a renowned Portuguese hotel chain. An efficiency ranking is established from these four hotel units located in Portugal using Stochastic Frontier Analysis. This methodology allows to discriminate between measurement error and systematic inefficiencies in the estimation process enabling to investigate the main inefficiency causes. Several suggestions concerning efficiency improvement are undertaken for each hotel studied.info:eu-repo/semantics/publishedVersio