In this article, we consider models for time-to-event data obtained from experiments in which stress levels are altered at intermediate stages during the observation period. These experiments, known as step-stress tes...
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In this article, we consider models for time-to-event data obtained from experiments in which stress levels are altered at intermediate stages during the observation period. These experiments, known as step-stress tests, belong to the larger class of accelerated tests used extensively in the reliability literature. The analysis of data from step-stress tests largely relies on the popular cumulative exposure model. However, despite its simple form, the utility of the model is limited, as it is assumed that the hazard function of the underlying distribution is discontinuous at the points at which the stress levels are changed, which may not be very reasonable. Due to this deficiency, Kannan et al. (Journal of Applied Statistics 37 (2010b) 1625-1636) introduced the cumulative risk model, where the hazard function is continuous. In this paper, we propose a class of parametric models based on the cumulative risk model assuming the underlying population contains long-term survivors or 'cured' fraction. An em algorithm to compute the maximum likelihood estimators of the unknown parameters is proposed. This research is motivated by a study on altitude decompression sickness. The performance of different parametric models will be evaluated using data from this study.
Structure learning for Bayesian networks has been made in a heuristic mode in search of an optimal model to avoid an explosive computational burden. In the learning process, a structural error which occurred at a poin...
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Structure learning for Bayesian networks has been made in a heuristic mode in search of an optimal model to avoid an explosive computational burden. In the learning process, a structural error which occurred at a point of learning may deteriorate its subsequent learning. We proposed a remedial approach to this error-for-error process by using marginal model structures. The remedy is made by fixing local errors in structure in reference to the marginal structures. In this sense, we call the remedy a marginally corrective procedure. We devised a new score function for the procedure which consists of two components, the likelihood function of a model and a discrepancy measure in marginal structures. The proposed method compares favourably with a couple of the most popular algorithms as shown in experiments with benchmark data sets.
The detection of underwater objects in a video is a challenging problem particularly when both the camera and the objects are in motion. In this article, this problem has been conceived as an incomplete data problem a...
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The detection of underwater objects in a video is a challenging problem particularly when both the camera and the objects are in motion. In this article, this problem has been conceived as an incomplete data problem and hence the problem is formulated in expectation maximization (em) framework. In the E-step, the frame labels are the maximum a posterior (MAP) estimates, which are obtained using simulated annealing (SA) and the iterated conditional mode (ICM) algorithm. In the M-step, the camera model parameters, both intrinsic and extrinsic, are estimated. In case of parameter estimation, the features are extracted at coarse and fine scale. In order to continuously detect the object in different video frames, em algorithm is repeated for each frame. The performance of the proposed scheme has been compared with other algorithms and the proposed algorithm is found to outperform.
In the general insurance modeling literature, there has been a lot of work based on univariate zero-truncated models, but little has been done in the multivariate zero-truncation cases, for instance a line of insuranc...
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In the general insurance modeling literature, there has been a lot of work based on univariate zero-truncated models, but little has been done in the multivariate zero-truncation cases, for instance a line of insurance business with various classes of policies. There are three types of zero-truncation in the multivariate setting: only records with all zeros are missing, zero counts for one or some classes are missing, or zeros are completely missing for all classes. In this paper, we focus on the first case, the so-called Type I zero-truncation, and a new multivariate zero-truncated hurdle model is developed to study it. The key idea of developing such a model is to identify a stochastic representation for the underlying random variables, which enables us to use the em algorithm to simplify the estimation procedure. This model is used to analyze a health insurance claims dataset that contains claim counts from different categories of claims without common zero observations. (C) 2019 Elsevier B.V. All rights reserved.
This work presents a log-linear model for multivariate Birnbaum-Saunders distribution that can be used in survival analysis to investigate correlated log-lifetimes of two or more units. This model is studied through t...
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This work presents a log-linear model for multivariate Birnbaum-Saunders distribution that can be used in survival analysis to investigate correlated log-lifetimes of two or more units. This model is studied through the use of a generalized multivariate sinh-normal distribution, which is built from the multivariate mixture scale of normal distributions. The marginal and conditional linear regression models of the proposed multivariate Birnbaum-Saunders linear regression model are generalizations of the Birnbaum-Saunders linear regression models of Rieck and Nedelman [A log-linear model for the Birnbaum-Saunders distribution. Technometrics. 1991;33:51-60], which have been used effectively to model lifetime and reliability data. We exploit a nice hierarchical representation of the regression model to propose a fast and accurate em algorithm to compute the maximum likelihood estimates of the model parameters. Hypothesis testing is also performed by the use of the asymptotic normality of the maximum likelihood estimators. Finally, the results of simulation studies as well as an application to a real dataset are displayed, where we also is include a robustness feature of the estimation procedure developed here.
Finite mixtures are a flexible modeling tool for irregularly shaped densities and samples from heterogeneous populations. When modeling with mixtures using an exchangeable prior on the component features, the componen...
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Finite mixtures are a flexible modeling tool for irregularly shaped densities and samples from heterogeneous populations. When modeling with mixtures using an exchangeable prior on the component features, the component labels are arbitrary and are indistinguishable in posterior analysis. This makes it impossible to attribute any meaningful interpretation to the marginal posterior distributions of the component features. We propose a model in which a small number of observations are assumed to arise from some of the labeled component densities. The resulting model is not exchangeable, allowing inference on the component features without post-processing. Our method assigns meaning to the component labels at the modeling stage and can be justified as a data-dependent informative prior on the labelings. We show that our method produces interpretable results, often (but not always) similar to those resulting from relabeling algorithms, with the added benefit that the marginal inferences originate directly from a well specified probability model rather than a post hoc manipulation. We provide asymptotic results leading to practical guidelines for model selection that are motivated by maximizing prior information about the class labels and demonstrate our method on real and simulated data.
We consider the problem of detection of features in the presence of clutter for spatio-temporal point patterns. In previous studies, related to the spatial context, Kth nearest-neighbor distances to classify points be...
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We consider the problem of detection of features in the presence of clutter for spatio-temporal point patterns. In previous studies, related to the spatial context, Kth nearest-neighbor distances to classify points between clutter and features. In particular, a mixture of distributions whose parameters were estimated using an expectation-maximization algorithm. This paper extends this methodology to the spatio-temporal context by considering the properties of the spatio-temporal Kth nearest-neighbor distances. For this purpose, we make use of a couple of spatio-temporal distances, which are based on the Euclidean and the maximum norms. We show close forms for the probability distributions of such Kth nearest-neighbor distances and present an intensive simulation study together with an application to earthquakes.
One of the challenges in cluster analysis is the evaluation of the obtained clustering results without using auxiliary information. To this end, a common approach is to use internal validity criteria. For mixtures of ...
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One of the challenges in cluster analysis is the evaluation of the obtained clustering results without using auxiliary information. To this end, a common approach is to use internal validity criteria. For mixtures of linear regressions whose parameters are estimated by maximum likelihood, we propose a three-term decomposition of the total sum of squares as a starting point to define some internal validity criteria. In particular, three types of mixtures of regressions are considered: with fixed covariates, with concomitant variables, and with random covariates. A ternary diagram is also suggested for easier joint interpretation of the three terms of the proposed decomposition. Furthermore, local and overall coefficients of determination are respectively defined to judge how well the model fits the data group-by-group but also taken as a whole. Artificial data are considered to find out more about the proposed decomposition, including violations of the model assumptions. Finally, an application to real data illustrates the use and the usefulness of these proposals.
Doubly censored failure time data occur when the failure time of interest represents the elapsed time between two events, an initial event and a subsequent event, and the observations on both events may suffer censori...
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Doubly censored failure time data occur when the failure time of interest represents the elapsed time between two events, an initial event and a subsequent event, and the observations on both events may suffer censoring. A well-known example of such data is given by the acquired immune deficiency syndrome (AIDS) cohort study in which the two events are HIV infection and AIDS diagnosis, and several inference methods have been developed in the literature for their regression analysis. However, all of them only apply to limited situations or focus on a single model. In this paper, we propose a marginal likelihood approach based on a general class of semiparametric transformation models, which can be applied to much more general situations. For the implementation, we develop a two-step procedure that makes use of both the multiple imputation technique and a novel em algorithm. The asymptotic properties of the resulting estimators are established by using the modern empirical process theory, and the simulation study conducted suggests that the method works well in practical situations. An application is also provided.
Data augmentation (DA) turns seemingly intractable computational problems into simple ones by augmenting latent missing data. In addition to computational simplicity, it is now well-established that DA equipped with a...
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Data augmentation (DA) turns seemingly intractable computational problems into simple ones by augmenting latent missing data. In addition to computational simplicity, it is now well-established that DA equipped with a deterministic transformation can improve the convergence speed of iterative algorithms such as an em algorithm or Gibbs sampler. In this article, we outline a framework for the transformation-based DA, which we call data transforming augmentation (DTA), allowing augmented data to be a deterministic function of latent and observed data, and unknown parameters. Under this framework, we investigate a novel DTA scheme that turns heteroscedastic models into homoscedastic ones to take advantage of simpler computations typically available in homoscedastic cases. Applying this DTA scheme to fitting linear mixed models, we demonstrate simpler computations and faster convergence rates of resulting iterative algorithms, compared with those under a non-transformation-based DA scheme. We also fit a Beta-Binomial model using the proposed DTA scheme, which enables sampling approximate marginal posterior distributions that are available only under homoscedasticity. are available online.
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