We describe a general method for analyzing aggregated Bernoulli outcomes. The research is motivated by an epidemiological reproductive study where the outcome was whether pregnancy was detected in a woman's partic...
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We describe a general method for analyzing aggregated Bernoulli outcomes. The research is motivated by an epidemiological reproductive study where the outcome was whether pregnancy was detected in a woman's particular menstrual cycle and the Bernoulli ''trials'' corresponded to days with intercourse during the cycle. Each cycle is either ''viable'' or not, i.e., is or is not susceptible to conception. We develop an em algorithm approach to maximizing the observed-data pseudo-likelihood, based on a set of unobservable latent outcomes linked to the specific days with intercourse. This method is flexible in that it allows one to model effects of covariates on the susceptibility factor and on the latent outcomes. Application of the method to fertility studies enables one to investigate covariates with a long-term or transient effect on the daily conception probability. A complication is that most couples contribute more than one cycle in a prospective study. A generalized estimating equation approach adjusts for the dependency among outcomes within individual couples. The method can be applied in any setting where dependency among Bernoulli trials is induced by a susceptibility factor and the trial outcomes are only observable in the aggregate.
It has recently been shown that the maximum-likelihood estimate of the parameters of a Markov-modulated Poisson process is consistent. In this paper we present an em algorithm for computing such estimates and discuss ...
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It has recently been shown that the maximum-likelihood estimate of the parameters of a Markov-modulated Poisson process is consistent. In this paper we present an em algorithm for computing such estimates and discuss how it may be implemented. We also compare it to the Nelder-Mead downhill simplex algorithm for some numerical examples, and the results show that the number of iterations the em algorithm requires to converge is in general smaller than the number of likelihood evaluations required by the downhill simplex algorithm. An em iteration is more complicated than a likelihood evaluation, though, and thus also implementation aspects must be taken into account to determine the efficiencies of the algorithms.
We show that the nonparametric maximum likelihood estimator (NPMLE) of a survival function may severely underestimate the survival probabilities at very early times for left-truncated and interval-censored data. As an...
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We show that the nonparametric maximum likelihood estimator (NPMLE) of a survival function may severely underestimate the survival probabilities at very early times for left-truncated and interval-censored data. As an alternative, we propose to compute the (nonparametric) MLE under a nondecreasing hazard assumption, the monotone MLE, by a gradient projection algorithm when the assumption holds. The projection step is accomplished via an isotonic regression algorithm, the pool-adjacent-violators algorithm. This gradient projection algorithm is computationally efficient and converges globally. Monte Carlo simulations show superior performance of the monotone MLE over that of the NPMLE in terms of either bias or variance, even for large samples. The methodology is illustrated with the application to the Wisconsin Epidemiological Study of Diabetic Retinopathy data to estimate the probability of incidence of retinopathy.
The paper describes the use of radial basis function neural networks with Gaussian basis functions to classify incomplete feature vectors. The method uses the fact that any marginal distribution of a Gaussian distribu...
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The paper describes the use of radial basis function neural networks with Gaussian basis functions to classify incomplete feature vectors. The method uses the fact that any marginal distribution of a Gaussian distribution can be determined from the mean vector and covariance matrix of the joint distribution. (C) 1998 Published by Elsevier Science B.V. All rights reserved.
It is well-known that the nonparametric maximum likelihood estimator (NPMLE) of a survival function may severely under-estimate the survival probabilities at very early times for left truncated data. This problem migh...
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It is well-known that the nonparametric maximum likelihood estimator (NPMLE) of a survival function may severely under-estimate the survival probabilities at very early times for left truncated data. This problem might be overcome by instead computing a smoothed nonparametric estimator (SNE) via the emS algorithm. The close connection between the SNE and the maximum penalized likelihood estimator is also established. Extensive Monte Carlo simulations demonstrate the superior performance of the SNE over that of the NPMLE, in terms of either bias or variance, even for moderately large samples. The methodology is illustrated with an application to the Massachusetts Health Care Panel Study dataset to estimate the probability of being functionally independent for non-poor male and female groups respectively.
We apply the idea of averaging ensembles of estimators to probability density estimation. In particular, we use Gaussian mixture models which are important components in many neural-network applications, We investigat...
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We apply the idea of averaging ensembles of estimators to probability density estimation. In particular, we use Gaussian mixture models which are important components in many neural-network applications, We investigate the performance of averaging using three data sets. For comparison, we employ two, traditional regularization approaches, i.e., a maximum penalized likelihood approach and a Bayesian approach. In the maximum penalized likelihood approach we use penalty functions derived from conjugate Bayesian priors such that an expectation maximization (em) algorithm can be used for training. In all experiments, the maximum penalized likelihood approach and averaging improved performance considerably if compared to a maximum likelihood approach. In two of the experiments, the maximum penalized likelihood approach outperformed averaging. In one experiment averaging was clearly superior, Our conclusion is that maximum penalized likelihood gives good results if the penalty term in the cost function is appropriate for the particular problem. If this is not the case, averaging is superior since it shows greater robustness by not relying on any particular prior assumption, The Bayesian approach worked very web on a low-dimensional toy problem but failed to give good performance in higher dimensional problems.
The iterative convex minorant (ICM) algorithm (Groeneboom and Wellner, 1992) is widely believed to be much faster than the em algorithm (Turnbull, 1976) in computing the NPMLE of the distribution function for interval...
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The iterative convex minorant (ICM) algorithm (Groeneboom and Wellner, 1992) is widely believed to be much faster than the em algorithm (Turnbull, 1976) in computing the NPMLE of the distribution function for interval censored data. Our formulation of the ICM helps to explore its connection with the gradient projection (GP) method that is commonly used in the constrained optimization area. Difficulties in extending the ICM to left truncated and interval censored data are also explained. Simulations were conducted to assess the performance of these methods. In particular, the GP is shown to be much faster than the em. Due to its generality and simplicity the GP method is easily applied to the Cox proportional hazards model with left truncated and interval censored data. The methodology is illustrated by using the Massachusetts Health Care Panel Study dataset. (C) 1998 Elsevier Science B.V. All rights reserved.
A frailty model for multivariate correlated life times is considered. The model both extends, in a rather straight-forward way, ordinary survival analysis with its emphasis on hazard modeling and incorporates well-kno...
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A frailty model for multivariate correlated life times is considered. The model both extends, in a rather straight-forward way, ordinary survival analysis with its emphasis on hazard modeling and incorporates well-known variance components models to account for the dependence between events of related individuals. Different approaches to estimation and inference are considered. An example from an ongoing study of genetic and environmental influences on premature death in adults serves to motivate and illustrate the model. Multivariate frailty models offer a conceptually simple and promising framework for analysis of correlated event times data, even if current knowledge is too sparse for such models to be tested critically.
In this paper, we present an efficient parallel system with an interconnection network customized for Positron emission Tomography (PET) image reconstruction. The proposed parallel reconstruction system has two distin...
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In this paper, we present an efficient parallel system with an interconnection network customized for Positron emission Tomography (PET) image reconstruction. The proposed parallel reconstruction system has two distinguished features. On feature is that the interconnection network is optimal for both filtered backprojection and em algorithms, rather than only for one of them. The other feature is that with only four-connectivity in contrast to log N-connectivity for a hypercube, the proposed parallel algorithms may accomplish the same performance in terms of order statistics as achieved by the optimal algorithms on a hypercube. The proposed parallel system has been realized using transputers. (C) 1998 Elsevier Science B.V. All rights reserved.
We consider the probabilistic neural network (PNN) that is a mixture of Gaussian basis functions having different variances. Such a Gaussian heteroscedastic PNN is more economic, in terms of the number of kernel funct...
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We consider the probabilistic neural network (PNN) that is a mixture of Gaussian basis functions having different variances. Such a Gaussian heteroscedastic PNN is more economic, in terms of the number of kernel functions required, than the Gaussian mixture PNN of a common variance. The expectation-maximisation (em) algorithm, although a powerful technique for constructing maximum likelihood (ML) homoscedastic PNNs, often encounters numerical difficulties when training heteroscedastic PNNs. We combine a robust statistical technique known as the Jack-knife with the em algorithm to provide a robust ML training algorithm. An artificial-data case, the two-dimensional XOR problem, and a real-data case, success or failure prediction of UK private construction companies, are used to evaluate the performance of this robust learning algorithm. (C) 1998 Elsevier Science Ltd. All rights reserved.
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