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Motion estimation of transparent objects in the frequency domain

SIGNAL PROCESSING 2004年第4期84卷 709-719页

作者： Pingault, M Pellerin, D Inst Natl Polytech Grenoble LIS F-38031 Grenoble France Univ Grenoble 1 Grenoble France

Motion transparency phenomena in image sequences are frequent, but classical methods of motion estimation are unable to deal with them. There is a need for more general techniques in order to solve this important problem. The method described here is based on an image sequence analysis in the frequency domain. It is mainly composed of a Stochastic-Expectation-Maximisation algorithm which provides a new statistical model for this problem. This method, despite its large execution time, offers some interesting results on artificial and natural image sequences. (C) 2003 Elsevier B.V. All rights reserved.

关键词： velocity estimation motion transparency frequency domain statistical model sem algorithm

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Inference based on the Em algorithm for the competing risks model with masked causes of failure

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BIOMETRIKA 2004年第3期91卷 543-558页

作者： Craiu, RV Duchesne, T Univ Toronto Dept Stat Toronto ON M5S 3G3 Canada Univ Laval Dept Math & Stat Ste Foy PQ G1K 7P4 Canada

In this paper we propose inference methods based on the Em algorithm for estimating the parameters of a weakly parameterised competing risks model with masked causes of failure and second-stage data. With a carefully chosen definition of complete data, the maximum likelihood estimation of the cause-specific hazard functions and of the masking probabilities is performed via an Em algorithm. Both the E- and m-steps can be solved in closed form under the full model and under some restricted models of interest. We illustrate the flexibility of the method by showing how grouped data and tests of common hypotheses in the literature on missing cause of death can be handled. The method is applied to a real dataset and the asymptotic and robustness properties of the estimators are investigated through simulation.

关键词： grouped data likelihood ratio test missing data piecewise-constant hazard proportional hazards robustness sem algorithm symmetry assumption time-varying masking probability

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Cluster number selection for a small set of samples using the Bayesian Ying-Yang model

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IEEE TRANSACTIONS ON NEURAL NETWORKS 2002年第3期13卷 757-763页

作者： Guo, P Chen, CLP Lyu, MR Beijing Normal Univ Dept Comp Sci Beijing 100875 Peoples R China Chinese Univ Hong Kong Dept Comp Sci & Engn Shatin Hong Kong Peoples R China Wright State Univ Dept Comp Sci & Engn Dayton OH 45435 USA

One major problem in cluster analysis is the determination of the number of clusters. In this paper, we describe both theoretical and experimental results in determining the cluster number for a small set of samples using the Bayesian-Kullback Ying-Yang (BYY) model selection criterion. Under the second-order approximation, we derive a new equation for estimating the smoothing parameter in the cost function. Finally, we propose a gradient descent smoothing parameter estimation approach that avoids complicated integration procedure and gives the same optimal result.

关键词： bootstrap cluster number selection data smoothing sem algorithm small number sample set smoothing parameter estimation

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Standard errors for EM estimation

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JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY 2000年第2期62卷 257-270页

作者： Jamshidian, M Jennrich, RI Univ Cent Florida Dept Stat Orlando FL 32816 USA Univ Calif Los Angeles Los Angeles CA USA

The EM algorithm is a popular method for computing maximum likelihood estimates. One of its drawbacks is that it does not produce standard errors as a by-product. We consider obtaining standard errors by numerical differentiation. Two approaches are considered. The first differentiates the Fisher score vector to yield the Hessian of the log-likelihood. The second differentiates the EM operator and uses an identity that relates its derivative to the Hessian of the log-likelihood. The well-known sem algorithm uses the second approach. We consider three additional algorithms: one that uses the first approach and two that use the second. We evaluate the complexity and precision of these three and the sem algorithm in seven examples. The first is a single-parameter example used to give insight. The others are three examples in each of two areas of EM application: Poisson mixture models and the estimation of covariance from incomplete data. The examples show that there are algorithms that are much simpler and more accurate than the sem algorithm. Hopefully their simplicity will increase the availability of standard error estimates in EM applications. It is shown that, as previously conjectured, a symmetry diagnostic can accurately estimate errors arising from numerical differentiation. Some issues related to the speed of the EM algorithm and algorithms that differentiate the EM operator are identified.

关键词： asymptotic variance-covariance matrix EM algorithm numerical differentiation observed information precision sem algorithm slow convergence

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Dual screening

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BIOMETRICS 1999年第3期55卷 867-873页

作者： Johnson, WO Pearson, LM Univ Calif Davis Div Stat Davis CA 95616 USA Minnesota State Univ Dept Math & Stat Mankato MN 56002 USA

We discuss the problem of screening a general population for characteristics such as HIV or drug use. Our main approach is Bayesian, which allows for the incorporation of prior information about parameters. In the particular problem we consider, there is currently no information in the data for estimating the sensitivity of the screening test, and consequently, the prevalence of the characteristic among screened negatives cannot be estimated from the collected data alone. Our inferences are straightforward to obtain using Gibbs sampling techniques, and they are valid for large or small samples and for arbitrary prevalence or accuracy of screening tests. We also develop the maximum-likelihood approach using the EM algorithm.

关键词： drug screening EM algorithm Gibbs sampling HIV screening predictive value positive prevalence sem algorithm sensitivity

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An Akaike information criterion for model selection in the presence of incomplete data

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JOURNAL OF STATISTICAL PLANNING AND INFERENCE 1998年第1期67卷 45-65页

作者： Cavanaugh, JE Shumway, RH Univ Missouri Dept Stat Columbia MO 65211 USA Univ Calif Davis Div Stat Livermore CA 95616 USA

We derive and investigate a variant of AIC, the Akaike information criterion, for model selection in settings where the observed data is incomplete. Our variant is based on the motivation provided for the PDIO ('predictive divergence for incomplete observation models') criterion of Shimodaira (1994, in: Selecting Models from Data: Artificial Intelligence and Statistics IV, Lecture Notes in Statistics, vol. 89, Springer, New York, pp. 21-29). However, our variant differs from PDIO in its 'goodness-of-fit' term. Unlike AIC and PDIO, which require the computation of the observed-data empirical log-likelihood, our criterion can be evaluated using only complete-data tools, readily available through the EM algorithm and the sem ('supplemented' EM) algorithm of Meng and Rubin (Journal of the American Statistical Association 86 (1991) 899-909). We compare the performance of our AIC variant to that of both AIC and PDIO in simulations where the data being modeled contains missing values. The results indicate that our criterion is less prone to overfitting than AIC and less prone to underfitting than PDIO. (C) 1998 Elsevier Science B.V. All rights reserved.

关键词： AIC EM algorithm information theory Kullback-Leibler information model selection criteria PDIO criterion sem algorithm

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Information matrix computation from conditional information via normal approximation

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BIOMETRIKA 1998年第4期85卷 973-979页

作者： Liu, CH AT&T Bell Labs Lucent Technol Murray Hill NJ 07974 USA

This paper provides a method for computing the asymptotic covariance matrix from a likelihood function with known maximum likelihood estimate of the parameters. Philosophically, the basic idea is to assume that the likelihood function should be well approximated by a normal density when asymptotic results about the maximum likelihood estimate are applied for statistical inference. Technically, the method makes use of two facts: the information for a one-dimensional parameter can be well computed when the loglikelihood is approximately quadratic over the range corresponding to a small positive confidence interval;and the covariance matrix of a normal distribution can be obtained from its one-dimensional conditional distributions whose sample spaces span the sample space of the joint distribution. We illustrate the method with its application to a linear mixed-effects model.

关键词： conditional information EM algorithm Fisher information maximum likelihood Q-Q plot sem algorithm

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An EM algorithm Fitting First-Order Conditional Autoregressive Models to Longitudinal Data

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Journal of the American Statistical Association 1996年第435期91卷 1322-1330页

作者： Schmid, Christopher H

Presents an EM algorithm that fits a state-space formulation of the longitudinal regression model. Lagged response of both time-dependent and time-independent covariates; Dependence of the baseline response on covaria... 详细信息

关键词： Fixed-interval smoothing algorithm Kalman filter Measurement error Pulmonary function sem algorithm State-space model

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A METHOD FOR CALIBRATING FALSE-MATCH RATES IN RECORD LINKAGE

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JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION 1995年第430期90卷 694-707页

作者： BELIN, TR RUBIN, DB HARVARD UNIV DEPT STAT CAMBRIDGE MA 02138 USA US BUR CENSUS RECORD LINKAGE STAFF WASHINGTON DC 20233 USA

Specifying a record-linkage procedure requires both (1) a method for measuring closeness of agreement between records, typically a scalar weight, and (2) a rule for deciding when to classify records as matches or nonmatches based on the weights. Here we outline a general strategy for the second problem, that is, for accurately estimating false-match rates for each possible cutoff weight. The strategy uses a model where the distribution of observed weights are viewed as a mixture of weights for true matches and weights for false matches. An EM algorithm for fitting mixtures of transformed-normal distributions is used to find posterior modes;associated posterior variability is due to uncertainty about specific normalizing transformations as well as uncertainty in the parameters of the mixture model the latter being calculated using the sem algorithm. This mixture-model calibration method is shown to perform well in an applied setting with census data. Further, a simulation experiment reveals that, across a wide variety of settings not satisfying the model's assumptions, the procedure is slightly conservative on average in the sense of overstating false-match rates, and the one-sided confidence coverage (i.e., the proportion of times that these interval estimates cover or overstate the actual false-match rate) is very close to the nominal rate.

关键词： BOX-COX TRANSFORMATION CANDIDATE MATCHED PAIRS EM algorithm MIXTURE MODEL sem algorithm WEIGHTS

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Handling “Don't Know” Survey Responses: The Case of the Slovenian Plebiscite

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Quarterly Publications of the American Statistical Association 1995年第431期90卷 822-828页

The critical step in the drive toward an independent Slovenia was the plebiscite held in December 1990, at which the citizens of Slovenia voted overwhelmingly in favor of a sovereign and independent state. The Slovenian Public Opinion (SPO) survey of November/December 1990 was used by the government of Slovenia to prepare for the plebiscite. Because the plebiscite counted as “YES voters” only those voters who attended and voted for independence (nonvoters counted as “NO voters”), “Don't Know” survey responses can be thought of as missing data—the true intention of the voter is unknown but must be either “YES” or “NO.” An analysis of the survey data under the missing-at-random assumption for the missing responses provides remarkably accurate estimates of the eventual plebiscite outcome, substantially better than ad hoc methods and a nonignorable model that allows nonresponse to depend on the intended vote.

关键词： Contingency table ECM algorithm EM algorithm Ignorable nonresponse Missing at random Missing data Nonignorable nonresponse sem algorithm

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