In this work, we study the odd Lindley Burr XII model initially introduced by Silva et al. [29]. This model has the advantage of being capable of modeling various shapes of aging and failure criteria. Some of its stat...
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In this work, we study the odd Lindley Burr XII model initially introduced by Silva et al. [29]. This model has the advantage of being capable of modeling various shapes of aging and failure criteria. Some of its statistical structural properties including ordinary and incomplete moments, quantile and generating function and order statistics are derived. The odd Lindley Burr XII density can be expressed as a simple linear mixture of Burr XII densities. Useful characterizations are presented. The maximum likelihood method is used to estimate the model parameters. Simulation results to assess the performance of the maximum likelihood estimators are discussed. We prove empirically the importance and flexibility of the new model in modeling various types of data. Bayesian estimation is performed by obtaining the posterior marginal distributions as well as using the simulation method of Markov Chain Monte Carlo (MCMC) by the Metropolis-Hastings algorithm in each step of gibbs algorithm. The trace plots and estimated conditional posterior distributions are also presented.
A regression model with deterministic frontier is considered. This type of model has hardly been studied, partly owing to the difficulty in the application of maximum likelihood estimation since this is a non-regular ...
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A regression model with deterministic frontier is considered. This type of model has hardly been studied, partly owing to the difficulty in the application of maximum likelihood estimation since this is a non-regular model. As an alternative, the Bayesian methodology is proposed and analysed. Through the gibbs algorithm, the inference of the parameters of the model and of the individual efficiencies are relatively straightforward. The results of the simulations indicate that the utilized method performs reasonably well.
The resolution of many large-scale inverse problems using MCMC methods requires a step of drawing samples from a high dimensional Gaussian distribution. While direct Gaussian sampling techniques, such as those based o...
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The resolution of many large-scale inverse problems using MCMC methods requires a step of drawing samples from a high dimensional Gaussian distribution. While direct Gaussian sampling techniques, such as those based on Cholesky factorization, induce an excessive numerical complexity and memory requirement, sequential coordinate sampling methods present a low rate of convergence. Based on the reversible jump Markov chain framework, this paper proposes an efficient Gaussian sampling algorithm having a reduced computation cost and memory usage, while maintaining the theoretical convergence of the sampler. The main feature of the algorithm is to perform an approximate resolution of a linear system with a truncation level adjusted using a self-tuning adaptive scheme allowing to achieve the minimal computation cost per effective sample. The connection between this algorithm and some existing strategies is given and its performance is illustrated on a linear inverse problem of image resolution enhancement.
The multivariate skew-t distribution (J Multivar Anal 79:93-113, 2001;J R Stat Soc, Ser B 65:367-389, 2003;Statistics 37:359-363, 2003) includes the Student t, skew-Cauchy and Cauchy distributions as special cases and...
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The multivariate skew-t distribution (J Multivar Anal 79:93-113, 2001;J R Stat Soc, Ser B 65:367-389, 2003;Statistics 37:359-363, 2003) includes the Student t, skew-Cauchy and Cauchy distributions as special cases and the normal and skew-normal ones as limiting cases. In this paper, we explore the use of Markov Chain Monte Carlo (MCMC) methods to develop a Bayesian analysis of repeated measures, pretest/post-test data, under multivariate null intercept measurement error model (J Biopharm Stat 13(4):763-771, 2003) where the random errors and the unobserved value of the covariate (latent variable) follows a Student t and skew-t distribution, respectively. The results and methods are numerically illustrated with an example in the field of dentistry.
Emerging ecological time series from long-term ecological studies and remote sensing provide excellent opportunities for ecologists to study the dynamic patterns and governing processes of ecological systems. However,...
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Emerging ecological time series from long-term ecological studies and remote sensing provide excellent opportunities for ecologists to study the dynamic patterns and governing processes of ecological systems. However, signal extraction from long-term time series often requires system learning (e.g., estimation of true system state) to process the large amount of information, to reconstruct system state, to account for measurement error, and to handle missing data. State-space models (SSMs) are a natural choice for these tasks and thus have received increasing attention in ecological and environmental studies. Data-based learning using SSMs that connect ecological processes to the measurement of system state becomes a useful technique in the ecological informatics toolkit. The present Study illustrates the use of the Kalman filter (KF), an estimator of SSMs, with case studies of population dynamics. The examples of the SSM applications include the reconstruction of system state using the KF method and Markov chain Monte Carlo methods, estimation of measurement-error variances in the estimates of animal population abundance using basic structural models (BSMs), and estimation of missing values using the KF and Kalman smoother. Estimation of measurement-error variances by BSMs does not require knowledge of the functional form that generates the time series data. Instead, BSMs approximate the trajectory or deterministic skeleton of a system dynamics in a semi-parametric fashion, and provide a robust estimator of measurement-error variances. The present study also compares Bayesian SSMs with non-Bayesian SSMs. The joint use of the KF method or its extensions and Markov chain Monte Carlo (MCMC) methods is a promising approach to the parameter estimation of SSMS. (C) 2009 Elsevier B.V. All rights reserved.
Non-linear mixed models defined by stochastic differential equations (SDEs) are considered: the parameters of the diffusion process are random variables and vary among the individuals. A maximum likelihood estimation ...
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Skew-normal distribution is a class of distributions that includes the normal distributions as a special case. In this paper, we explore the use of Markov Chain Monte Carlo (MCMC) methods to develop a Bayesian analysi...
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Skew-normal distribution is a class of distributions that includes the normal distributions as a special case. In this paper, we explore the use of Markov Chain Monte Carlo (MCMC) methods to develop a Bayesian analysis in a multivariate, null intercept, measurement error model [R. Aoki, H. Bolfarine, J.A. Achcar, and D. Leao Pinto Jr, Bayesian analysis of a multivariate null intercept error-in -variables regression model, J. Biopharm. Stat. 13(4) (2003b), pp. 763-771] where the unobserved value of the covariate (latent variable) follows a skew-normal distribution. The results and methods are applied to a real dental clinical trial presented in [A. Hadgu and G. Koch, Application of generalized estimating equations to a dental randomized clinical trial, J. Biopharm. Stat. 9 (1999), pp. 161-178].
In this paper, we establish upper and lower bounds for some statistical estimation problems through concise information-theoretic arguments. Our upper bound analysis is based on a simple yet general inequality which w...
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In this paper, we establish upper and lower bounds for some statistical estimation problems through concise information-theoretic arguments. Our upper bound analysis is based on a simple yet general inequality which we call the information exponential inequality. We show that this inequality naturally leads to a general randomized estimation method, for which performance upper bounds can be obtained. The lower bounds, applicable for all statistical estimators, are obtained by original applications of some well known information-theoretic inequalities, and approximately match the obtained upper bounds for various important problems. Moreover, our framework can be regarded as a natural generalization of the standard minimax framework, in that we allow the performance of the estimator to vary for different possible underlying distributions according to a predefined prior.
Complex hierarchical models lead to a complicated likelihood and then, in a Bayesian analysis, to complicated posterior distributions. To obtain Bayes estimates such as the posterior mean or Bayesian confidence region...
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Complex hierarchical models lead to a complicated likelihood and then, in a Bayesian analysis, to complicated posterior distributions. To obtain Bayes estimates such as the posterior mean or Bayesian confidence regions, it is therefore necessary to simulate the posterior distribution using a method such as an MCMC algorithm. These algorithms often get slower as the number of observations increases, especially when the latent variables are considered. To improve the convergence of the algorithm, we propose to decrease the number of parameters to simulate at each iteration by using a Laplace approximation on the nuisance parameters. We provide a theoretical study of the impact that such an approximation has on the target posterior distribution. We prove that the distance between the true target distribution and the approximation becomes of order O(N-a) with a is an element of (0,1), a close to 1, as the number of observations N increases. A simulation study illustrates the theoretical results. The approximated MCMC algorithm behaves extremely well on an example which is driven by a study on HIV patients.
In 2003, Xu obtained remarkably precise estimates of QTL positions despite the many markers simultaneously in his Bayesian model. We extend his model and gibbs algorithm to ensure a valid posterior distribution and co...
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In 2003, Xu obtained remarkably precise estimates of QTL positions despite the many markers simultaneously in his Bayesian model. We extend his model and gibbs algorithm to ensure a valid posterior distribution and convergence to it, without changing the attractiveness of the method.
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