• Nuclear Medicine and Molecular Imaging
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• v.42 no.2
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• pp.118-126
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• 2008

Statistical image reconstruction methods have played an important role in emission computed tomography (ECT) since they accurately model the statistical noise associated with gamma-ray projection data. Although the use of statistical methods in clinical practice in early days was of a difficult problem due to high per-iteration costs and large numbers of iterations, with the development of fast algorithms and dramatically improved speed of computers, it is now inevitably becoming more practical. Some statistical methods are indeed commonly available from nuclear medicine equipment suppliers. In this paper, we first describe a mathematical background for statistical reconstruction methods, which includes assumptions underlying the Poisson statistical model, maximum likelihood and maximum a posteriori approaches, and prior models in the context of a Bayesian framework. We then review a recent progress in developing fast iterative algorithms.

• International Journal of Reliability and Applications
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• v.1 no.1
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• pp.15-26
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• 2000

This paper considers an aperiodic preventive maintenance (PM) model for repairable systems, in which the time intervals between two consecutive preventive maintenances are unequal. To propose such an aperiodic PM model, we assume that each PM reduces the current hazard rate by a certain amount which depends on the number of PMs performed previously. If the system fails between PMs, the minimal repair is performed and the hazard rate remains unchanged after the repair. We give the exact expressions for the hazard rate function for the aperiodic PM model. Based on the proposed aperiodic PM model, we suggest the maximum likelihood method to estimate the parameters characterizing the model and apply the method to the case of Weibull distribution. Numerical examples for estimating the parameters are presented for the purpose of illustration.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.21 no.3
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• pp.155-165
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• 2017

The Hansel-Spittel constitutive model requires a total of nine parameters for flow stress prediction. Typically, the parameters are estimated by least squares methods for given tensile test measurements from a deterministic perspective. In this research we took a different approach, a probabilistic viewpoint, to see through the development of the Hansel-Spittel constitutive model. This perspective change showed that deterministic least squares methods are closely related to statistical maximum likelihood methods via Gaussian noise assumption. More intriguingly, this perspective shift revealed that the Hansel-Spittel constitutive model may leave out deterministic trends in residuals despite nearly perfect agreement with measurements. With tensile test measurements of AA1070 aluminum alloy, we demonstrated this deficiency of the Hansel-Spittel constitutive model, suggesting room for improvement.

• Communications for Statistical Applications and Methods
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• v.17 no.3
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• pp.441-450
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• 2010

In this paper we consider the problem of forecasting binomial time series, modelled by the binomial autoregressive model. This paper considers proposed by McKenzie (1985) and is extended to a higher order by $Wei{\ss}$(2009). Since the binomial autoregressive model is a Markov chain, we can apply the earlier work of Bu and McCabe (2008) for integer valued autoregressive(INAR) model to the binomial autoregressive model. We will discuss how to compute the h-step-ahead forecast of the conditional probabilities of $X_{T+h}$ when T periods are used in fitting. Then we obtain the maximum likelihood estimator of binomial autoregressive model and use it to derive the maximum likelihood estimator of the h-step-ahead forecast of the conditional probabilities of $X_{T+h}$. The methodology is illustrated by applying it to a data set previously analyzed by $Wei{\ss}$(2009).

• Journal of the Korean Statistical Society
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• v.30 no.2
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• pp.179-192
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• 2001

When a statistical model has a hierarchical structure such as multilayer perceptrons in neural networks or Gaussian mixture density representation, the model includes distribution with unidentifiable parameters when the structure becomes redundant. Since the exact structure is unknown, we need to carry out statistical estimation or learning of parameters in such a model. From the geometrical point of view, distributions specified by unidentifiable parameters become a singular point in the parameter space. The problem has been remarked in many statistical models, and strange behaviors of the likelihood ratio statistics, when the null hypothesis is at a singular point, have been analyzed so far. The present paper studies asymptotic behaviors of the maximum likelihood estimator and the Bayesian predictive estimator, by using a simple cone model, and show that they are completely different from regular statistical models where the Cramer-Rao paradigm holds. At singularities, the Fisher information metric degenerates, implying that the cramer-Rao paradigm does no more hold, and that he classical model selection theory such as AIC and MDL cannot be applied. This paper is a first step to establish a new theory for analyzing the accuracy of estimation or learning at around singularities.

• Communications for Statistical Applications and Methods
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• v.21 no.6
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• pp.521-528
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• 2014

A stochastic Gompertz diffusion model for tumor growth is a topic of active interest as cancer is a leading cause of death in Korea. The direct maximum likelihood estimation of stochastic differential equations would be possible based on the continuous path likelihood on condition that a continuous sample path of the process is recorded over the interval. This likelihood is useful in providing a basis for the so-called continuous record or infill likelihood function and infill asymptotic. In practice, we do not have fully continuous data except a few special cases. As a result, the exact ML method is not applicable. In this paper we proposed a method of parameter estimation of stochastic Gompertz differential equation via Markov chain Monte Carlo methods that is applicable for several data structures. We compared a Markov transition data structure with a data structure that have an initial point.

• ETRI Journal
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• v.34 no.5
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• pp.684-689
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• 2012

A mode-singular-value-decomposition (SVD) maximum likelihood (ML) estimation procedure is proposed for the source localization problem under an additive measurement error model. In a practical situation, the noise variance is usually unknown. In this paper, we propose an algorithm that does not require the noise covariance matrix as a priori knowledge. In the proposed method, the weight is derived by the inverse of the noise magnitude square in the ML criterion. The performance of the proposed method outperforms that of the existing methods and approximates the Taylor-series ML and Cram$\acute{e}$r-Rao lower bound.

• Journal of Institute of Control, Robotics and Systems
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• v.4 no.1
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• pp.38-44
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• 1998

The modified maximum likelihood estimation method is used to estimate the nondimensional aerodynamic derivatives of a single turbo-prop aircraft at a specified flight condition for the best deduction of the dynamic characteristics. In wind axes the six degree of freedom equations are algebraically linearized so that the linear state equation contains aerodynamic derivatives in a state-space form and is used in the maximum likelihood method. The simulated data added with the measurement noise is used as a flight test data which is necessary to the estimation of nondimensional aerodynamic derivatives. It is obtained by implementing the 6-DOF nonlinear flight simulation. In the flight simulation, the effects of several control input types, control deflection amplitudes, and the turbulence intensities on the statistical convergence criteria are also examined and quantitative analysis of the results is discussed.

• Communications for Statistical Applications and Methods
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• v.20 no.5
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• pp.405-416
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• 2013

This paper develops a maximum profile likelihood estimator of unknown parameters of the exponentiated Gumbel distribution based on upper record values. We propose an approximate maximum profile likelihood estimator for a scale parameter. In addition, we derive Bayes estimators of unknown parameters of the exponentiated Gumbel distribution using Lindley's approximation under symmetric and asymmetric loss functions. We assess the validity of the proposed method by using real data and compare these estimators based on estimated risk through a Monte Carlo simulation.

• Journal of the Korean Data and Information Science Society
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• v.17 no.4
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• pp.1053-1065
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• 2006

This paper proposes a method in one-way layouts for longitudinal data with informative drop-out. When dropouts are informative, that is, correlated with unobserved data and/or the previous observed data, the simple imputation methods such as 'last observation carried forward' (LOCF) methods would arise the bias of the testing models. The maximum likelihood procedure combined with a logit model for the drop-out process is proposed to test treatment effects for one factorial designs and compared with LOCF method in two examples.