Academic literature on the topic 'Hierarchical hurdle Gamma model'

ABSTRACTPreservative factors act as hurdles against microorganisms by inhibiting their growth; these are essential control measures for particular food-borne pathogens. Different combinations of hurdles can be quantified and compared to each other in terms of their inhibitory effect (“iso-hurdle”). We present here a methodology for establishing microbial iso-hurdle rules in three steps: (i) developing a predictive model based on existing but disparate data sets, (ii) building an experimental design focused on the iso-hurdles using the model output, and (iii) validating the model and the iso-hurdle rules with new data. The methodology is illustrated withListeria monocytogenes. Existing data from industry, a public database, and the literature were collected and analyzed, after which a total of 650 growth rates were retained. A gamma-type model was developed for the factors temperature, pH, aw, and acetic, lactic, and sorbic acids. Three iso-hurdle rules were assessed (40 logcount curves generated): salt replacement by addition of organic acids, sorbic acid replacement by addition of acetic and lactic acid, and sorbic acid replacement by addition of lactic/acetic acid and salt. For the three rules, the growth rates were equivalent in the whole experimental domain (γ from 0.1 to 0.5). The lag times were also equivalent in the case of mild inhibitory conditions (γ ≥ 0.2), while they were longer in the presence of salt than acids under stress conditions (γ < 0.2). This methodology allows an assessment of the equivalence of inhibitory effects without intensive data generation; it could be applied to develop milder formulations which guarantee microbial safety and stability.

Motivated by a study exploring spatiotemporal trends in emergency department use, we develop a class of two-part hurdle models for the analysis of zero-inflated areal count data. The models consist of two components—one for the probability of any emergency department use and one for the number of emergency department visits given use. Through a hierarchical structure, the models incorporate both patient- and region-level predictors, as well as spatially and temporally correlated random effects for each model component. The random effects are assigned multivariate conditionally autoregressive priors, which induce dependence between the components and provide spatial and temporal smoothing across adjacent spatial units and time periods, resulting in improved inferences. To accommodate potential overdispersion, we consider a range of parametric specifications for the positive counts, including truncated negative binomial and generalized Poisson distributions. We adopt a Bayesian inferential approach, and posterior computation is handled conveniently within standard Bayesian software. Our results indicate that the negative binomial and generalized Poisson hurdle models vastly outperform the Poisson hurdle model, demonstrating that overdispersed hurdle models provide a useful approach to analyzing zero-inflated spatiotemporal data.

For guiding natural language generation, many semantic-driven methods have been proposed. While clearly improving the performance of the end-to-end training task, these existing semantic-driven methods still have clear limitations: for example, (i) they only utilize shallow semantic signals (e.g., from topic models) with only a single stochastic hidden layer in their data generation process, which suffer easily from noise (especially adapted for short-text etc.) and lack of interpretation; (ii) they ignore the sentence order and document context, as they treat each document as a bag of sentences, and fail to capture the long-distance dependencies and global semantic meaning of a document. To overcome these problems, we propose a novel semantic-driven language modeling framework, which is a method to learn a Hierarchical Language Model and a Recurrent Conceptualization-enhanced Gamma Belief Network, simultaneously. For scalable inference, we develop the auto-encoding Variational Recurrent Inference, allowing efficient end-to-end training and simultaneously capturing global semantics from a text corpus. Especially, this article introduces concept information derived from high-quality lexical knowledge graph Probase, which leverages strong interpretability and anti-nose capability for the proposed model. Moreover, the proposed model captures not only intra-sentence word dependencies, but also temporal transitions between sentences and inter-sentence concept dependence. Experiments conducted on several NLP tasks validate the superiority of the proposed approach, which could effectively infer meaningful hierarchical concept structure of document and hierarchical multi-scale structures of sequences, even compared with latest state-of-the-art Transformer-based models.

Pricing of repair and maintenance (R&M) contracts is one among the most important processes carried out at Scania. Predictions of repair costs at Scania are carried out using experience-based prediction methods which do not involve statistical methods for the computation of average repair costs for contracts terminated in the recent past. This method is difficult to apply for a reference population of rigid Scania trucks. Hence, the purpose of this study is to perform suitable statistical modelling to predict repair costs of four variants of rigid Scania trucks. The study gathers repair data from multiple sources and performs feature selection using the Akaike Information Criterion (AIC) to extract the most significant features that influence repair costs corresponding to each truck variant. The study proved to show that the inclusion of operational features as a factor could further influence the pricing of contracts. The hurdle Gamma model, which is widely used to handle zero inflations in Generalized Linear Models (GLMs), is used to train the data which consists of numerous zero and non-zero values. Due to the inherent hierarchical structure within the data expressed by individual chassis, a hierarchical hurdle Gamma model is also implemented. These two statistical models are found to perform much better than the experience-based prediction method. This evaluation is done using the mean absolute error (MAE) and root mean square error (RMSE) statistics. A final model comparison is conducted using the AIC to draw conclusions based on the goodness of fit and predictive performance of the two statistical models. On assessing the models using these statistics, the hierarchical hurdle Gamma model was found to perform predictions the best

Approved for public release; distribution unlimited.<br>Combat models often involve target detection times which may vary with different observers due to characteristics of personnel, or detection systems. They may also be affected by different environmental factors such as visual levels, sea states, terrains, etc. There is often interest in quantifying the effects of different observer characteristics and environmental factors on detection times. A hierarchical gammaWeibull regression model is considered which can incorporate observer characteristics and environmental effects which may influence the time to detect targets. Numerical procedures for the estimation of parameters of the hierarchical gammaWeibull model based on maximum likelihood are described. Results of simulation experiments to study small sample behavior of the estimates are reported.

In this work, we study the so-called combined models, generalized linear mixed models with extension to allow for overdispersion, in the context of genetics and breeding. Such flexible models accommodates cluster-induced correlation and overdispersion through two separate sets of random effects and contain as special cases the generalized linear mixed models (GLMM) on the one hand, and commonly known overdispersion models on the other. We use such models while obtaining heritability coefficients for non-Gaussian characters. Heritability is one of the many important concepts that are often quantified upon fitting a model to hierarchical data. It is often of importance in plant and animal breeding. Knowledge of this attribute is useful to quantify the magnitude of improvement in the population. For data where linear models can be used, this attribute is conveniently defined as a ratio of variance components. Matters are less simple for non-Gaussian outcomes. The focus is on time-to-event and count traits, where the Weibull-Gamma-Normal and Poisson-Gamma-Normal models are used. The resulting expressions are sufficiently simple and appealing, in particular in special cases, to be of practical value. The proposed methodologies are illustrated using data from animal and plant breeding. Furthermore, attention is given to the occurrence of negative estimates of variance components in the Poisson-Gamma-Normal model. The occurrence of negative variance components in linear mixed models (LMM) has received a certain amount of attention in the literature whereas almost no work has been done for GLMM. This phenomenon can be confusing at first sight because, by definition, variances themselves are non-negative quantities. However, this is a well understood phenomenon in the context of linear mixed modeling, where one will have to make a choice between a hierarchical and a marginal view. The variance components of the combined model for count outcomes are studied theoretically and the plant breeding study used as illustration underscores that this phenomenon can be common in applied research. We also call attention to the performance of different estimation methods, because not all available methods are capable of extending the parameter space of the variance components. Then, when there is a need for inference on such components and they are expected to be negative, the accuracy of the method is not the only characteristic to be considered.<br>Neste trabalho foram estudados os chamados modelos combinados, modelos lineares generalizados mistos com extensão para acomodar superdispersão, no contexto de genética e melhoramento. Esses modelos flexíveis acomodam correlação induzida por agrupamento e superdispersão por meio de dois conjuntos separados de efeitos aleatórios e contem como casos especiais os modelos lineares generalizados mistos (MLGM) e os modelos de superdispersão comumente conhecidos. Tais modelos são usados na obtenção do coeficiente de herdabilidade para caracteres não Gaussianos. Herdabilidade é um dos vários importantes conceitos que são frequentemente quantificados com o ajuste de um modelo a dados hierárquicos. Ela é usualmente importante no melhoramento vegetal e animal. Conhecer esse atributo é útil para quantificar a magnitude do ganho na população. Para dados em que modelos lineares podem ser usados, esse atributo é convenientemente definido como uma razão de componentes de variância. Os problemas são menos simples para respostas não Gaussianas. O foco aqui é em características do tipo tempo-até-evento e contagem, em que os modelosWeibull-Gama-Normal e Poisson-Gama-Normal são usados. As expressões resultantes são suficientemente simples e atrativas, em particular nos casos especiais, pelo valor prático. As metodologias propostas são ilustradas usando dados de melhoramento animal e vegetal. Além disso, a atenção é voltada à ocorrência de estimativas negativas de componentes de variância no modelo Poisson-Gama- Normal. A ocorrência de componentes de variância negativos em modelos lineares mistos (MLM) tem recebido certa atenção na literatura enquanto quase nenhum trabalho tem sido feito para MLGM. Esse fenômeno pode ser confuso a princípio porque, por definição, variâncias são quantidades não-negativas. Entretanto, este é um fenômeno bem compreendido no contexto de modelagem linear mista, em que a escolha deverá ser feita entre uma interpretação hierárquica ou marginal. Os componentes de variância do modelo combinado para respostas de contagem são estudados teoricamente e o estudo de melhoramento vegetal usado como ilustração confirma que esse fenômeno pode ser comum em pesquisas aplicadas. A atenção também é voltada ao desempenho de diferentes métodos de estimação, porque nem todos aqueles disponíveis são capazes de estender o espaço paramétrico dos componentes de variância. Então, quando há a necessidade de inferência de tais componentes e é esperado que eles sejam negativos, a acurácia do método de estimação não é a única característica a ser considerada.

Shrinkage for time-varying parameter (TVP) models is investigated within a Bayesian framework, with the aim to automatically reduce time-varying Parameters to staticones, if the model is overfitting. This is achieved through placing the double gamma shrinkage prior on the process variances. An efficient Markov chain Monte Carlo scheme is devel- oped, exploiting boosting based on the ancillarity-sufficiency interweaving strategy. The method is applicable both to TVP models for univariate a swell as multivariate time series. Applications include a TVP generalized Phillips curve for EU area inflation modeling and a multivariate TVP Cholesky stochastic volatility model for joint modeling of the Returns from the DAX-30index.

碩士<br>國立臺灣大學<br>國際企業學研究所<br>93<br>Marketing researchers are always striving for how to identify the customers’ preference structure, and how to predict the customers’ purchase behavior precisely. Due to technology development, the enormous amount of information storage and the ability of data computation enable the researchers to further comprehend the purchases and preferences of consumers more directly. However, on the premise that heterogeneity is existed, if we still continuously use the traditional statistics methods to characterize the consumers’ behavior, then we always face a trade-off: while estimating the behavior of consumers, if based on the information of whole customers, then we may ignore the heterogeneity between them; or if solely based on identical customer, then the estimation may lack efficiency because of insufficient data amount. We construct a prediction model of customer inter-purchase times based on the generalized gamma distribution, which can make the model fit the data more flexible than the other distributions. We also assume the heterogeneity of customer behavior follow the inverse generalized gamma distribution, so that the difference and the instability of consumer behavior between each customer can be reflected clearly. Additionally, our model is formulated with a hierarchical Bayesian framework with demographic variables, which can predict the behavior of new customers without gathering any purchasing information. At last, we estimate the parameters of the model by Bayesian statistics. Because of the integration of prior and sample information, Bayesian statistics can provide individualized estimation of parameters for each customer and also ensure both the heterogeneity of customers and efficiency of parameter estimating at the same time. In order to verify the prediction capability of this hierarchical Bayesian model, the purchase records of a domestic leading petroleum company will be employed in the model and also list the pros and cons with different parameters estimated. Finally, we draw a conclusion, indicate the limitation of this investigation, and suggest the direction to be studied on possible future work.

La méthode que nous présentons pour modéliser des données dites de "comptage" ou données de Poisson est basée sur la procédure nommée Modélisation multi-niveau et interactive de la régression de Poisson (PRIMM) développée par Christiansen et Morris (1997). Dans la méthode PRIMM, la régression de Poisson ne comprend que des effets fixes tandis que notre modèle intègre en plus des effets aléatoires. De même que Christiansen et Morris (1997), le modèle étudié consiste à faire de l'inférence basée sur des approximations analytiques des distributions a posteriori des paramètres, évitant ainsi d'utiliser des méthodes computationnelles comme les méthodes de Monte Carlo par chaînes de Markov (MCMC). Les approximations sont basées sur la méthode de Laplace et la théorie asymptotique liée à l'approximation normale pour les lois a posteriori. L'estimation des paramètres de la régression de Poisson est faite par la maximisation de leur densité a posteriori via l'algorithme de Newton-Raphson. Cette étude détermine également les deux premiers moments a posteriori des paramètres de la loi de Poisson dont la distribution a posteriori de chacun d'eux est approximativement une loi gamma. Des applications sur deux exemples de données ont permis de vérifier que ce modèle peut être considéré dans une certaine mesure comme une généralisation de la méthode PRIMM. En effet, le modèle s'applique aussi bien aux données de Poisson non stratifiées qu'aux données stratifiées; et dans ce dernier cas, il comporte non seulement des effets fixes mais aussi des effets aléatoires liés aux strates. Enfin, le modèle est appliqué aux données relatives à plusieurs types d'effets indésirables observés chez les participants d'un essai clinique impliquant un vaccin quadrivalent contre la rougeole, les oreillons, la rub\'eole et la varicelle. La régression de Poisson comprend l'effet fixe correspondant à la variable traitement/contrôle, ainsi que des effets aléatoires liés aux systèmes biologiques du corps humain auxquels sont attribués les effets indésirables considérés.<br>We propose a method for analysing count or Poisson data based on the procedure called Poisson Regression Interactive Multilevel Modeling (PRIMM) introduced by Christiansen and Morris (1997). The Poisson regression in the PRIMM method has fixed effects only, whereas our model incorporates random effects. As well as Christiansen and Morris (1997), the model studied aims at doing inference based on adequate analytical approximations of posterior distributions of the parameters. This avoids the use of computationally expensive methods such as Markov chain Monte Carlo (MCMC) methods. The approximations are based on the Laplace's method and asymptotic theory. Estimates of Poisson mixed effects regression parameters are obtained through the maximization of their joint posterior density via the Newton-Raphson algorithm. This study also provides the first two posterior moments of the Poisson parameters involved. The posterior distributon of these parameters is approximated by a gamma distribution. Applications to two datasets show that our model can be somehow considered as a generalization of the PRIMM method since it also allows clustered count data. Finally, the model is applied to data involving many types of adverse events recorded by the participants of a drug clinical trial which involved a quadrivalent vaccine containing measles, mumps, rubella and varicella. The Poisson regression incorporates the fixed effect corresponding to the covariate treatment/control as well as a random effect associated with the biological system of the body affected by the adverse events.

This paper presents a methodology to evaluate the reliability of corroding pipelines by simultaneously considering the growth and generation of corrosion defects. The non-homogeneous Poisson process is employed to model the generation of corrosion defects, whereas the non-homogeneous gamma process is used to characterize the growth of corrosion defects once generated. The parameters included in the non-homogeneous Poisson process and non-homogeneous gamma process are evaluated from the inline inspection data using a hierarchical Bayesian model. The measurement errors associated with the inline inspection tools are taken into account in the Bayesian updating. The time-dependent failure probability of the corroding pipeline is evaluated using the Monte Carlo simulation technique. The methodology is illustrated using a natural gas pipeline that has been subjected to multiple inline inspections over a period of time. The results illustrate the necessity to incorporate the generation of new corrosion defects in the reliability analysis of corroding pipelines.

BACKGROUND: Daily diary measurements are a common way to assess substance use behaviours, however researchers and clinicians are often cognizant of assessment reactivity (or “reactivity”) in daily substance use measurement. Reactivity involves changes to behaviours that result simply from self-monitoring those behaviours. When reactivity to substance use measurement has been found to exist, it has been identified both as a possible confound in daily diary research and a potential intervention tool in clinical practice. Reactivity to daily self-monitoring of alcohol and tobacco use has been investigated in prior research, however this research has been inconsistent. Reactivity to daily self-monitoring of cannabis use quantity has yet to be documented at all. METHOD: The current study involved secondary analyses of data from N=88 women who self-monitored their cannabis use for 32 consecutive days (Joyce et al., under review). We examined objective reactivity of cannabis use to daily self-monitoring both for the probability of use each day as well as the quantity of cannabis used on each cannabis-using day. At study completion, participants were asked the degree to which they felt self-monitoring impacted their cannabis use (i.e., subjective reactivity). We explored the reported degree of subjective reactivity, and we examined correspondence between objective and subjective reactivity. RESULTS: Hurdle models were the best fit for the data. Participants’ probability of daily cannabis use and the quantity of cannabis use did not change significantly over the study period. For subjective reactivity, many respondents (45%) reported no subjective reactivity, though a majority (55%) reported some degree of subjective reactivity with 24% reporting moderate or more reactivity. A three-step hierarchical linear model was used to investigate the relationship between objective and subjective reactivity. Time was the only predictor in the first step, subjective reactivity was added as a predictor in the second step, and the time x subjective reactivity interaction was explored in the final step. Subjective reactivity was not found to moderate the relationship between time and cannabis use, although there was a significant relationship between self-reported subjective reactivity and variability of cannabis use across the data collection period. CONCLUSIONS: This study determined that participants who report greater subjective reactivity to cannabis measurement are more likely to demonstrate variability in their cannabis usage. While this study did not find a significant change in cannabis scores over time because of reactivity, the non-significant results are valuable from both a research and a clinical standpoint. For research, the lack of change is an indicator that reactivity is likely not a confounding factor in studies involving cannabis daily diary research. From a clinical perspective, the non-significant change indicates that simply self-monitoring cannabis is unlikely to provide standalone benefits when daily self-monitoring is used in clinical practice. It is relevant to note that our study involved a non-help-seeking sample, and future research could benefit from determining whether cannabis reactivity may be moderated by help-seeking behaviours or motivations to change.

This paper describes a non-homogeneous gamma process-based model to characterize the growth of the depth of corrosion defect on oil and gas pipelines. All the parameters in the growth model are assumed to be uncertain; the probabilistic characteristics of these parameters are evaluated using the hierarchical Bayesian methodology by incorporating the defect information reported by the multiple in-line inspections (ILIs) as well as the prior knowledge about these parameters. The bias and random measurement error associated with the ILI tools as well as the correlation between the measurement errors associated with different ILI tools are taken into account in the analysis. The application of the model is illustrated using an example involving real ILI data on a pipeline that is currently in service. The results suggest that the model in general can predict the growth of corrosion defects reasonably well. The proposed model can be used to facilitate the development and application of reliability-based pipeline corrosion management.

Abstract Well placement with geosteering can get very complex in reservoirs with formation change not simply addressed by changes in the gamma ray log response. This paper uses data mining to characterize complex reservoirs for optimum well placement. The objective of this paper is to develop a data mining process to evaluate non-trivial geologic settings for geosteering reservoir well placement. The well logs’ data was collected from multiple wells in a Norwegian North Sea field, where the reservoir rocks are characterized with high heterogeneities. Principal component analysis was used to recognize data pattern and extract underlying features. The extracted features are then into distinct groups using Hierarchical clustering (HC) analysis. A classification model, that is based on the deviance analysis, was constructed to build a criterion to identify each cluster within a set of well log data. The results show that the data mining approach sufficiently identified highly heterogeneous formations and can be used for geosteering applications. Classification trees defined quantitative decision criterion for the identified clusters. The approach is capable of distinguishing between potential and non-potential steering clusters, as the identified clusters have distinct decision criteria and effectively explain the variations within a section, as verified with the lithology described from core analysis.

In-line inspection (ILI) data is commonly used in corrosion growth models (CGMs) to predict the corrosion growth in energy pipelines. A hierarchical stochastic corrosion growth model is considered in this paper which considers the variations in the corrosion growth, both spatially and temporally, the inherent measurement error of the ILI tools as well as the model uncertainties. These uncertainties are represented as unknown model variables and are often inferred using a Bayesian method [1], [2] and samples of the unknown parameters’ posterior probability density functions (PDFs) are obtained using Markov Chain Monte Carlo (MCMC) sampling techniques [3]. ILIs can result in massive data sets. In order for MCMC-based inference techniques to yield reasonably accurate results, many samples (approaching infinity) are required. This fact in addition to the massive data sets exponentially increases the scale of the inference problem from an attainable solution to a potentially impossible one that is limited by today’s computing power. For this reason, MCMC-based inference techniques can become inefficient in the cases where ILI datasets are large. The objective is to propose variational inference (VI) as an alternative to MCMC to determine a Bayesian solution for the unknown parameters in complex stochastic CGMs. VI produces approximations of the posterior PDFs by treating the inference as an optimization problem. Variational inference emerged from machine learning for Bayesian inference of large data sets; therefore, it is an appropriate tool to use in the analysis of mass pipeline inspection data[4]–[7]. This paper introduces VI to solve the inference problem and provide a solution for a hierarchical stochastic CGM to describe the defect-specific corrosion growth experienced in pipelines based on excessively large ILI datasets. To gauge the accuracy of the VI implementation in the model, the results are compared to a set of values generated using a stochastic gamma process that represents the corrosion growth process experienced by the pipe.