In this paper, the maximum likelihood and Bayesian estimation of the parameters of location-scale Rayleigh distribution with partly interval censored data is considered. For computing the maximum likelihood estimators...
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In this paper, the maximum likelihood and Bayesian estimation of the parameters of location-scale Rayleigh distribution with partly interval censored data is considered. For computing the maximum likelihood estimators with partly interval censored data, three methods are used, namely, Newton-Raphson, Expectation-Maximization and Monte-Carlo Expectation-Maximization algorithms. The standard errors of the estimates are computed using the observed information matrix. Also, two types of confidence intervals are constructed using the Wald method and the nonparametric percentile bootstrap confidence intervals. For computing the Bayes estimators, three methods viz Lindley's approximation, Tierney-Kadane approximation and importance sampling methods are used. Highest posterior density (HPD) credible intervals of the two parameters are constructed using importance sampling technique. Monte-Carlo simulation experiments are conducted to investigate the performance of the proposed methods. Finally, the methods are illustrated by using two real data sets, one is related with diabetic patients data set and the other is related to HIV infection data set.
The National Resources Inventory, a longitudinal survey of characteristics related to natural resources and agriculture on nonfederal U.S. land, has increasingly received requests for substate estimates in recent year...
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The National Resources Inventory, a longitudinal survey of characteristics related to natural resources and agriculture on nonfederal U.S. land, has increasingly received requests for substate estimates in recent years. We consider estimation of erosion in subdomains of the Boone-Raccoon River Watershed. This region is of interest for its proximity to intensively cropped areas as well as important waterbodies. The NRI application requires a small area prediction approach that can handle nonlinear relationships and appropriately incorporate survey weights that may have nontrivial relationships to the response variable. Because of the informative design, the conditional distribution required to define a standard empirical Bayes predictor is unknown. We develop a prediction approach that utilizes the approximate distribution of survey weighted score equations arising from a specified two-level superpopulation model. We apply the method to construct estimates of mean erosion in small watersheds. We investigate the robustness of the procedure to an assumption of a constant dispersion parameter and validate the properties of the procedure through simulation.
Collecting a set of classical and emerging methods not available in a single treatment, Foundations of Computational Imaging: A Model-Based Approach is the first book to define a common foundation for the mathematical...
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ISBN:
(数字)9781611977134
ISBN:
(纸本)9781611977127
Collecting a set of classical and emerging methods not available in a single treatment, Foundations of Computational Imaging: A Model-Based Approach is the first book to define a common foundation for the mathematical and statistical methods used in computational imaging. The book brings together a blend of research with applications in a variety of disciplines, including applied math, physics, chemistry, optics, and signal processing, to address a collection of problems that can benefit from a common set of methods.
Readers will find
basic techniques of model-based image processing;
a comprehensive treatment of Bayesian and regularized image reconstruction methods; and
an integrated treatment of advanced reconstruction techniques, such as majorization, constrained optimization, alternating direction method of multipliers (ADMM), and Plug-and-Play methods for model integration.
In this paper, we develop statistical methodology for the analysis of data under nonnormal distributions, in the context of mixed effects models. Although the multivariate normal distribution is useful in many cases, ...
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In this paper, we develop statistical methodology for the analysis of data under nonnormal distributions, in the context of mixed effects models. Although the multivariate normal distribution is useful in many cases, it is not appropriate, for instance, when the data come from skewed and/or heavy-tailed distributions. To analyse data with these characteristics, in this paper, we extend the standard linear mixed effects model, considering the family of generalized hyperbolic distributions. We propose methods for statistical inference based on the likelihood function, and due to its complexity, the em algorithm is used to find the maximum likelihood estimates with the standard errors and the exact likelihood value as a by-product. We use simulations to investigate the asymptotic properties of the expectation-maximization algorithm (em) estimates and prediction accuracy. A real example is analysed, illustrating the usefulness of the proposed methods.
pLSA is a useful method to know the characteristics of customer or item in marketing. In this study, we proposed a method to set the initial values more efficiently than the existing method for the problem that the fi...
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ISBN:
(纸本)9783030776848;9783030776855
pLSA is a useful method to know the characteristics of customer or item in marketing. In this study, we proposed a method to set the initial values more efficiently than the existing method for the problem that the final solution depends on the initial values set in the em algorithm used by pLSA to estimate the solutions. We focused on the dimensional compression and clustering that are the characteristics of pLSA, and thought that the stability of the solution of pLSA would be improved by reflecting it in the initial values. Therefore, first, we performed correspondence analysis and k-means cluster analysis on the original data to express the features of dimensional compression and clustering. Next, we compared the performance of the pLSA results with the initial values of the proposed method and the initial values of the conventional method using random numbers. As a result, it was shown that the proposed method also converges to the same log-likelihood as the conventional method, and that the proposed method is superior in terms of convergence speed and stability.
We propose a novel iterative algorithm for solving a large sparse linear system. The method is based on the em algorithm. If the system has a unique solution, the algorithm guarantees convergence with a geometric rate...
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We propose a novel iterative algorithm for solving a large sparse linear system. The method is based on the em algorithm. If the system has a unique solution, the algorithm guarantees convergence with a geometric rate. Otherwise, convergence to a minimal Kullback-Leibler divergence point is guaranteed. The algorithm is easy to code and competitive with other iterative algorithms.
This paper presents a method of exercises recommendation based on machine learning. This method can recommend more suitable exercises to students according to the category they belong to. Firstly, we use linear regres...
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ISBN:
(纸本)9781665441063
This paper presents a method of exercises recommendation based on machine learning. This method can recommend more suitable exercises to students according to the category they belong to. Firstly, we use linear regression and em algorithm to accurately model the students' mastery of each knowledge point. For each knowledge point, students are divided into several categories according to their mastery of the knowledge point and their average mastery of all knowledge points. For each knowledge point, according to the student history answer record, find out the exercise that can make each kind of student get bigger promotion respectively. For the students who need to recommend the exercises that contain the specified knowledge points, we first use the k-nearest neighbor algorithm to classify the students, and then recommend the exercises suitable for the students. It has been proved by experiments that this method can help students to achieve greater improvement in the same number of exercises.
Concerning the real-time monitoring of important component contents during a fermentation process of 1,3-propanediol,a near-infrared(NIR) spectral calibration modeling method is proposed based on a semi-supervised lea...
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ISBN:
(数字)9789887581581
ISBN:
(纸本)9798350366907
Concerning the real-time monitoring of important component contents during a fermentation process of 1,3-propanediol,a near-infrared(NIR) spectral calibration modeling method is proposed based on a semi-supervised learning *** solve the problems of high dimensionality and serious information overlap of NIR spectra,a binary mayfly optimization algorithm(BMA) is proposed to select the characteristic wavenumbers of the measured spectra for model *** address the issue of insufficient labeled sample dataset,a robust semi-supervised probabilistic principal component regression(RSSPPCR) modeling method is presented based on the expectation maximization(em) algorithm,which could fully utilize all labeled and unlabeled spectral *** student t-distribution is introduced into the modeling to improve the model tolerance of outliers,so as to ensure the reliability of simultaneous detection of multiple components during the fermentation *** experimental results show that the proposed model can effectively predict the important contents of glycerol(substrate),1,3-propanediol(product),and biomass during a fermentation process of 1,3-propanediol.
The use of the first two moments of the truncated multivariate Student-t distribution has attracted increasing attention from a wide range of applications. This paper develops recurrence relations for integrals that i...
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The use of the first two moments of the truncated multivariate Student-t distribution has attracted increasing attention from a wide range of applications. This paper develops recurrence relations for integrals that involve the density of multivariate Student-t distributions. The proposed techniques allow for fast computation of arbitrary-order product moments of folded and truncated multivariate Student-t distributions and offer explicit expressions of low-order moments of folded and truncated multivariate Student-t distributions. A real data example containing positive censored responses is applied to illustrate the effectiveness and importance of the proposed methods. An R MomTrunc package is developed and publicly available on the CRAN repository.
Skew -t regression models have been widely used to model and analyze asymmetric heavy-tailed data. Moreover, observations in this kind of data can be missing or subject to some upper and/or lower detection limits beca...
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Skew -t regression models have been widely used to model and analyze asymmetric heavy-tailed data. Moreover, observations in this kind of data can be missing or subject to some upper and/or lower detection limits because of the restriction of the experimental apparatus. We propose a novel robust regression model for multiple censored or missing data based on the multivariate skew -t distribution for such data structures. This approach allows us to model data with great flexibility, simultaneously accommodating heavy tails and skewness. We develop an analytically simple yet effi-cient em-type algorithm to conduct maximum likelihood estimation of the parameters. The algorithm has closed-form expressions at the E-step that rely on formulas for the mean and variance of truncated multivariate Student's-t, skew -t, and extended skew -t distributions. Furthermore, a general information-based method for approximating the asymptotic covariance matrix of the estimators is also presented. Results obtained from the analysis of both simulated and real datasets are reported to demonstrate the effectiveness of the proposed method.(c) 2023 Elsevier Inc. All rights reserved.
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