Suppose that when a unit operates in a certain environment, its lifetime has distribution G, and when the unit operates in another environment, its lifetime has a different distribution, say F. Moreover, suppose the u...
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Suppose that when a unit operates in a certain environment, its lifetime has distribution G, and when the unit operates in another environment, its lifetime has a different distribution, say F. Moreover, suppose the unit is operated for a certain period of time in the first environment and is then transferred to the second environment. Thus we observe a censored lifetime in the first environment and a failure time of a "used" unit in the second environment. We propose an em algorithm approach for obtaining a self-consistent estimator of F using observations from both environments. The case where failure times are subject to right censoring is considered as well. We also establish the maximum likelihood estimator of F when the unit is repairable. Application and simulation studies are presented to illustrate the methods derived.
We consider a new recursive algorithm for parameter estimation from an independent incomplete data sequence. The algorithm can be viewed as a recursive version of the well-known em algorithm, augmented with a Monte-Ca...
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We consider a new recursive algorithm for parameter estimation from an independent incomplete data sequence. The algorithm can be viewed as a recursive version of the well-known em algorithm, augmented with a Monte-Carlo step which restores the missing data. Based on recent results on stochastic algorithms, we give conditions for the a.s. convergence of the algorithm. Moreover, asymptotical variance of this estimator is reduced by a simple averaging. Application to finite mixtures is given with a simulation experiment.
Selective genotyping is a cost-saving strategy in mapping quantitative trait loci (QTLs). When the proportion of individuals selected for genotyping is low, the majority of the individuals are not genotyped, but their...
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Selective genotyping is a cost-saving strategy in mapping quantitative trait loci (QTLs). When the proportion of individuals selected for genotyping is low, the majority of the individuals are not genotyped, but their phenotypic values, if available, are still included in the data analysis to correct the bias in parameter estimation. These ungenotyped individuals do not contribute much information about linkage analysis and their inclusion can substantially increase the computational burden. For multiple trait analysis, ungenotyped individuals may not have a full array of phenotypic measurements. In this case, unbiased estimation of QTL effects using current methods seems to be impossible. In this study, we develop a maximum likelihood method of QTL mapping under selective genotyping using only the phenotypic values of genotyped individuals. Compared with the full data analysis (using all phenotypic values), the proposed method performs well. We derive an expectation-maximization (em) algorithm that appears to be a simple modification of the existing em algorithm for standard interval mapping. The new method can be readily incorporated into a standard QTL mapping software, e.g. MAPMAKER. A general recommendation is that whenever full data analysis is possible, the full maximum likelihood analysis should be performed. If it is impossible to analyse the full data, e.g. sample sizes are too large, phenotypic values of ungenotyped individuals are missing or composite interval mapping is to be performed, the proposed method can be applied.
A problem arising from the study of the spread of a viral infection among potato plants by aphids appears to involve a mixture of two linear regressions on a single predictor variable. The plant scientists studying th...
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A problem arising from the study of the spread of a viral infection among potato plants by aphids appears to involve a mixture of two linear regressions on a single predictor variable. The plant scientists studying the problem were particularly interested in obtaining a 95% confidence upper bound for the infection rate. We discuss briefly the procedure for fitting mixtures of regression models by means of maximum likelihood, effected via the em algorithm. We give general expressions for the implementation of the M-step and then address the issue of conducting statistical inference in this context. A technique due to T. A. Louis may be used to estimate the covariance matrix of the parameter estimates by calculating the observed Fisher information matrix. We develop general expressions for the entries of this information matrix. Having the complete covariance matrix permits the calculation of confidence and prediction bands for the fitted model. We also investigate the testing of hypotheses concerning the number of components in the mixture via parametric and 'semiparametric' bootstrapping. Finally, we develop a method of producing diagnostic plots of the residuals from a mixture of linear regressions.
Many papers (including most of the papers in this issue of Computational Statistics) deal with Markov Chain Monte Carlo (MCMC) methods. This paper will give an introduction to the augmented Gibbs sampler (a special ca...
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Many papers (including most of the papers in this issue of Computational Statistics) deal with Markov Chain Monte Carlo (MCMC) methods. This paper will give an introduction to the augmented Gibbs sampler (a special case of MCMC), illustrated using the random intercept model. A 'nonstandard' application of the augmented Gibbs sampler will be discussed to give an illustration of the power of MCMC methods. Furthermore, it will be illustrated that the posterior sample resulting from an application of MCMC can be used for more than determination of convergence and the computation of simple estimators like the a posteriori expectation and standard deviation. Posterior samples give access to many other inferential possibilities. Using a simulation study, the frequency properties of some of these possibilities will be evaluated.
Introduces a series of articles on the developments in iterative image reconstruction for positron-emission tomography (PET) and single proton emission computer tomography (SPECT).
Introduces a series of articles on the developments in iterative image reconstruction for positron-emission tomography (PET) and single proton emission computer tomography (SPECT).
Recently the authors introduced a general Bayesian statistical method for modeling and analysis in linear inverse problems involving certain types of count data. emission-based tomography in medical imaging is a parti...
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ISBN:
(纸本)0819437646
Recently the authors introduced a general Bayesian statistical method for modeling and analysis in linear inverse problems involving certain types of count data. emission-based tomography in medical imaging is a particularly important and common example of this type of problem. In this paper we provide an overview of the methodology and illustrate its application to problems in emission tomography through a series of simulated and real-data examples. The framework rests on the special manner in which a multiscale representation of recursive dyadic partitions (essentially an unnormalized Haar analysis) interacts with the statistical likelihood of data with Poisson noise characteristics. In particular, the likelihood function permits a factorization, with respect to location-scale indexing, analogous to the manner in which, say, an arbitrary signal allows a wavelet transform. Recovery of an object from tomographic data is then posed as a problem involving the statistical estimation of a multiscale parameter vector. A type of statistical shrinkage estimation is used, induced by careful choice of a Bayesian prior probability structure for the parameters. Finally, the ill-posedness of the tomographic imaging problem is accounted for by embedding the above-described framework within a larger, but simpler statistical estimation problem, via the so-called Expectation-Maximization (em) approach. The resulting image reconstruction algorithm is iterative in nature, entailing the calculation of two closed-form algebraic expressions at each iteration. Convergence of the algorithm to a unique solution, under appropriate choice of Bayesian prior, can be assured.
Information derived from interim sacrifices or on cause of death is routinely used in the statistical analyses of carcinogenicity experiments involving occult tumours. The authors describe a simple semiparametric mode...
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Information derived from interim sacrifices or on cause of death is routinely used in the statistical analyses of carcinogenicity experiments involving occult tumours. The authors describe a simple semiparametric model which does not require this information. Natural deaths during the experiment and the usual terminal sacrifice provide sufficient information to ensure that the tumour incidence rates, which are of primary interest in occult-tumour studies, can be estimated nonparametrically. The advantages of this semiparametric approach to the analysis of survival/sacrifice experiments are illustrated using data from a study on benzyl acetate conducted under the U. S. National Toxicology Program. The results derived compare favourably with those obtained using a previously published approach to the analysis of tumorigenicity data.
Ambroise et al. (1996) have proposed a clustering algorithm that is well-suited for dealing with spatial data. This algorithm, derived from the em algorithm (Dempster et al., 1977), has been designed for penalized lik...
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Ambroise et al. (1996) have proposed a clustering algorithm that is well-suited for dealing with spatial data. This algorithm, derived from the em algorithm (Dempster et al., 1977), has been designed for penalized likelihood estimation in situations with unobserved class labels. Some very satisfactory empirical results lead us to believe that this algorithm converges (Ambroise et al., 1996). However, this convergence has not been proven theoretically. In this paper, we present sufficient conditions and proof of the convergence. A practical application illustrates the use of this algorithm. (C) 1998 Published by Elsevier Science B.V. All rights reserved.
Suppose that some components are initially operated in a certain condition and then switched to operating in a different condition. Working hours of the components in condition 1 and condition 2 air respectively obser...
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Suppose that some components are initially operated in a certain condition and then switched to operating in a different condition. Working hours of the components in condition 1 and condition 2 air respectively observed. Of interest is the lifetime distribution F of the component in the second condition only, i.e., the distribution without the prior exposure to the first condition. In this paper, we propose a method to transform the lifetime obtained in condition 1 to an equivalent lifetime in condition 2 and then use the transformed data to estimate F. Both parametric and nonparametric approaches each with complete and censored data are discussed. Numerical studies are presented to investigate the performance of the method. (C) 2000 John Wiley & Sons, Inc.
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