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Modelling censored losses using splicing: A global fit strategy with mixed Erlang and extreme value distributions

INSURANCE MATHEMATICS & ECONOMICS 2017年 77卷 65-77页

作者： Reynkens, Tom Verbelen, Roel Beirlant, Jan Antonio, Katrien Katholieke Univ Leuven Dept Math LStat & LRisk Celestijnenlaan 200B B-3001 Leuven Belgium Katholieke Univ Leuven Fac Econ & Business LStat & LRisk Naamsestr 69 B-3000 Leuven Belgium Univ Free State Dept Math Stat & Actuarial Sci POB 339 ZA-9300 Bloemfontein South Africa Univ Amsterdam Fac Econ & Business Roetersstr 11 NL-1018 WB Amsterdam Netherlands

In risk analysis, a global fit that appropriately captures the body and the tail of the distribution of losses is essential. Modelling the whole range of the losses using a standard distribution is usually very hard and often impossible due to the specific characteristics of the body and the tail of the loss distribution. A possible solution is to combine two distributions in a splicing model: a light-tailed distribution for the body which covers light and moderate losses, and a heavy-tailed distribution for the tail to capture large losses. We propose a splicing model with a mixed Erlang (ME) distribution for the body and a Pareto distribution for the tail. This combines the flexibility of the ME distribution with the ability of the Pareto distribution to model extreme values. We extend our splicing approach for censored and/or truncated data. Relevant examples of such data can be found in financial risk analysis. We illustrate the flexibility of this splicing model using practical examples from risk measurement. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Censoring Composite model expectation-maximisation algorithm Risk measurement Tail modelling

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ML modulation classification in presence of unreliable observations

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ELECTRONICS LETTERS 2016年第18期52卷 1569-1570页

作者： Dulek, B. Hacettepe Univ Dept Elect & Elect Engn Beytepe Campus TR-06800 Ankara Turkey

Joint detection and maximum-likelihood (ML) classification of linear modulations based on observations collected over an unknown flat-fading additive Gaussian noise channel is considered. It is assumed that some of the observations are subject to data failures, in which case the receiver acquires only noise. expectation-maximisation algorithm is employed to compute the ML estimates of the unknown channel parameters, which are then substituted into the corresponding likelihood expressions to perform hypothesis testing. Numerical simulations indicate that a suboptimal classifier, which is ignorant to data failures, exhibits extremely poor performance in the presence of high failure rates. On the other hand, the proposed classifier demonstrates comparable performance with that of the clairvoyant classifier which is assumed to have a priori knowledge of the channel parameters and data failures.

关键词： modulation Gaussian noise fading channels maximum likelihood estimation ML modulation classification unreliable observations maximum likelihood classification linear modulations flat fading additive Gaussian noise channel expectation-maximisation algorithm suboptimal classifier data failures channel parameters

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Novel optimal time selection method for synthetic aperture radar data processing via expectation-maximization algorithm

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ELECTRONICS LETTERS 2022年第15期58卷 594-596页

作者： Cao, Rui Wang, Yong Harbin Inst Technol Sch Elect & Informat Engn Harbin Peoples R China

A novel optimal time selection method for synthetic aperture radar (SAR) data processing via the expectation-maximization (EM) algorithm is proposed, which can reduce the computational complexity and improve the image quality simultaneously. First, the Doppler frequency feature after the SAR processing is analyzed from the point of probability. Then, the Doppler frequency is modelled as the Gaussian mixture model (GMM), and the issue of optimal time selection can be implemented by the parameter estimation of GMM. The results of simulated and real measured data are given to demonstrate the effectiveness of the proposed method.

关键词： simulated measured data radar imaging SAR data processing Gaussian mixture model expectation-maximization algorithm Gaussian processes Doppler frequency feature image quality real measured data optimal time selection method synthetic aperture radar computational complexity expectation-maximisation algorithm synthetic aperture radar data processing mixture models parameter estimation

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Neural network segmented CD algorithm-based PET liver image reconstruction

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INTERNATIONAL JOURNAL OF BIOMEDICAL ENGINEERING AND TECHNOLOGY 2015年第3期17卷 276-289页

作者： Prasath, T. Arun Rajasekaran, M. Pallikonda Kannan, S. Kalasalingam Univ Dept Instrumentat & Control Engn Krishnankoil 626126 Tamil Nadu India Kalasalingam Univ Dept Elect & Commun Engn Krishnankoil 626126 Tamil Nadu India Ramco Inst Technol Dept Elect & Elect Engn Rajapalayam 626117 Tamil Nadu India

In this paper, reconstruction of the Positron Emission Tomography (PET) images, a CD algorithm was instigated with NN based image segmentation techniques called Neural Network Segmentation based Coordinate DescentWeighted Least Square (NNCD-WLS). Thus, NNCD-WLS of the function is not quadratic, but natural. The iterative algorithm achieve a fashion equivalent to an analytic derivation of the Maximum Likelihood-expectation maximisation (ML-EM) algorithm, which gives a different minimisation process between two convex sets of matrices. Conversely the distance metric is quite distinct, and more intricate to analyse. This algorithm is similar type, shares many properties acquainted with the ML-EM algorithm. Unlike WLS algorithm, NNCD-WLS method minimises the WLS objective function. The NNCD-WLS algorithm instigates via NN based segmentation process in image reconstruction. Image quality parameter of the PSNR value, NNCD-WLS algorithm and the denoising algorithm is compared. The PET input image is reconstructed and simulated in the MATLAB/Simulink package.

关键词： PET liver image positron emission tomography image reconstruction neural network segmentation WLS weighted least squares CD coordinate descent iterative algorithm EM expectation-maximisation algorithm

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Is the AIDS incubation time changing? A back-calculation approach

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STATISTICS IN MEDICINE 1999年第9期18卷 1031-1047页

作者： Deuffic, S Costagliola, D Fac Med St Antoine INSERM Unite Rech Epidemiol & Sci Informat F-75571 Paris 12 France Fac Med St Antoine INSERM U4444 Unite Rech Epidemiol & Sci Informat F-75571 Paris France

Contradictory literature was recently published on possible changes in AIDS incubation time over the period 1978-1994. The purpose of this work was to test if a change in incubation time (shortening or lengthening) was observed in France, either globally or in specific transmission groups (homosexual-bisexual men, heterosexual subjects), using a back-calculation approach. An age dependent TSI model (time since infection), which took into account a temporary treatment effect and allowed us to test for a change in the incubation time, was applied to the French AIDS cases (Reseau National de Sante Publique). The EM algorithm was used to maximize the likelihood and the best model was selected on the basis of the likelihood ratio statistic. The analysis on all AIDS cases indicated a shortening of the AIDS incubation time estimated to begin in 1983 (95 per cent CI 1982-1984), This shortening of incubation time was also apparent when analysis was restricted to homosexual-bisexual men and to heterosexual subjects, This shortening corresponded to a median incubation time of 9.6 years (95 per cent CI 8.1-10.5) for people infected at 30 years of age in 1983, versus 12.7 years for people infected at 30 years of age before the change. Copyright (C) 1999 John Wiley & Sons, Ltd.

关键词： Acquired Immunodeficiency Syndrome HIV Virus Latency 获得性免疫缺陷综合征病毒潜伏期 Virus Latency expectation-maximisation algorithm Backcalculation incubation time Acquired Immunodeficiency Syndrome Heterosexuals HIV likelihood ratio

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Hidden Markov Modeling with Detailed Balance and Its Application to Single Protein Folding

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BIOPHYSICAL JOURNAL 2016年第10期111卷 2110-2124页

作者： Zhang, Yongli Jiao, Junyi Rebane, Aleksander A. Yale Univ Sch Med Dept Cell Biol New Haven CT 06510 USA Yale Univ Integrated Grad Program Phys & Engn Biol New Haven CT USA Yale Univ Dept Phys New Haven CT USA Yale Univ Nanobiol Inst West Haven CT USA

Hidden Markov modeling (HMM) has revolutionized kinetic studies of macromolecules. However, results from HMM often violate detailed balance when applied to the transitions under thermodynamic equilibrium, and the consequence of such violation has not been well understood. Here, to our knowledge, we developed a new HMM method that satisfies detailed balance (HMM-DB) and optimizes model parameters by gradient search. We used free energy of stable and transition states as independent fitting parameters and considered both normal and skew normal distributions of the measurement noise. We validated our method by analyzing simulated extension trajectories that mimicked experimental data of single protein folding from optical tweezers. We then applied HMM-DB to elucidate kinetics of regulated SNARE zippering containing degenerate states. For both simulated and measured trajectories, we found that HMM-DB significantly reduced overfitting of short trajectories compared to the standard HMM based on an expectation-maximization algorithm, leading to more accurate and reliable model fitting by HMM-DB. We revealed how HMM-DB could be conveniently used to derive a simplified energy landscape of protein folding. Finally, we extended HMM-DB to correct the baseline drift in single-molecule trajectories. Together, we demonstrated an efficient, versatile, and reliable method of HMM for kinetics studies of macromolecules under thermodynamic equilibrium.

关键词： THERMODYNAMIC EQUILIBRIUM macromolecules baseline wander expectation-maximisation algorithm Noise measurement mode matching Kinetics detailed balancing trajectory Hidden Markov models Protein Folding Optical Tweezers

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Assessing the strength of directed influences among neural signals: An approach to noisy data

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JOURNAL OF NEUROSCIENCE METHODS 2015年第0期239卷 47-64页

作者： Sommerlade, Linda Thiel, Marco Mader, Malenka Mader, Wolfgang Timmer, Jens Platt, Bettina Schelter, Bjoern Univ Aberdeen Kings Coll Inst Complex Syst & Math Biol Old Aberdeen AB24 3UE England Univ Aberdeen Kings Coll Inst Pure & Appl Math Old Aberdeen AB24 3UE England Univ Freiburg Freiburg Ctr Data Anal & Modeling FDM D-79104 Freiburg Germany Univ Freiburg Inst Phys D-79104 Freiburg Germany Univ Freiburg Freiburg Inst Adv Studies FRIAS D-79104 Freiburg Germany Univ Med Ctr Freiburg Dept Neuropediat & Muscular Dis D-79106 Freiburg Germany Univ Freiburg BIOSS Ctr Biol Signalling Studies D-79104 Freiburg Germany Univ Aberdeen Inst Med Sci Aberdeen AB25 2ZD Scotland

Background: Measurements in the neurosciences are afflicted with observational noise. Granger-causality inference typically does not take this effect into account. We demonstrate that this leads to false positives conclusions and spurious causalities. New method: State space modelling provides a convenient framework to obtain reliable estimates for Granger-causality. Despite its previous application in several studies, the analytical derivation of the statistics for parameter estimation in the state space model was missing. This prevented a rigorous evaluation of the results. Results: In this manuscript we derive the statistics for parameter estimation in the state space model. We demonstrate in an extensive simulation study that our novel approach outperforms standard approaches and avoids false positive conclusions about Granger-causality. Comparison with existing methods: In comparison with the naive application of Granger-causality inference, we demonstrate the superiority of our novel approach. The wide-spread applicability of our procedure provides a statistical framework for future studies. The application to mice electroencephalogram data demonstrates the immediate applicability of our approach. Conclusions: The analytical derivation of the statistics presented in this manuscript enables a rigorous evaluation of the results of Granger causal network inference. It is noteworthy that the statistics can be readily applied to various measures for Granger causality and other approaches that are based on vector autoregressive models. (C) 2014 Elsevier B.V. All rights reserved.

关键词： Granger-causality Observational noise Statistics expectation-maximisation algorithm Kalman filter Incomplete data likelihood Analytical covariance matrix

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Statistical estimation and pedigree analysis of CCR2-CCR5 haplotypes

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HUMAN GENETICS 2001年第6期108卷 484-493页

作者： Clark, VJ Metheny, N Dean, M Peterson, RJ NCI Lab Genom Divers Frederick MD 21702 USA Celadon Labs Inc College Pk MD 20742 USA

As more SNP marker data becomes available, researchers have used haplotypes of markers, rather than individual polymorphisms, for association analysis of candidate genes. In order to perform haplotype analysis in a population-based case-control study, haplotypes must be determined by estimation in the absence of family information or laboratory methods for establishing phase. Here, we test the accuracy of the expectation-Maximization (EM) algorithm for estimating haplotype state and frequency in the CCR2-CCR5 gene region by comparison with haplotype state and frequency determined by pedigree analysis. To do this, we have characterized haplotypes comprising alleles at seven biallelic loci in the CCR2-CCR5 chemokine receptor gene region, a span of 20 kb on chromosome 3p21. Three-generation CEPH families (n=40), totaling 489 individuals, were genotyped by the 5 ' nuclease assay (TaqMan). Haplotype states and frequencies were compared in 103 grandparents who were assumed to have mated at random. Both pedigree analysis and the EM algorithm yielded the same small number of haplotypes for which linkage disequilibrium was nearly maximal. The haplotype frequencies generated by the two methods were nearly identical. These results suggest that the EM algorithm estimation of haplotype states, frequency, and linkage disequilibrium analysis will be an effective strategy in the CCR2-CCR5 gene region. For genetic epidemiology studies, CCR2-CCR5 allele and haplotype frequencies were determined in African-American (n=30), Hispanic (n=24) and European-American (n=34) populations.

关键词： Haplotypes Receptors CCR5 Chemokine CC chemokine receptor-2 单元型受体趋化因子 CCR5 Receptors CCR2 Receptors Chemokines expectation-maximisation algorithm Statistical Estimation Haplotypes Linkage Disequilibrium pedigree analysis Receptor

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The concave-convex procedure

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NEURAL COMPUTATION 2003年第4期15卷 915-936页

作者： Yuille, AL Rangarajan, A Smith Kettlewell Eye Res Inst San Francisco CA 94115 USA Univ Florida Dept Comp & Informat Sci & Engn Gainesville FL 32611 USA

The concave-convex procedure (CCCP) is a way to construct discrete-time iterative dynamical systems that are guaranteed to decrease global optimization and energy functions monotonically. This procedure can be applied to almost any optimization problem, and many existing algorithms can be interpreted in terms of it. In particular, we prove that all expectation-maximization algorithms and classes of Legendre minimization and variational bounding algorithms can be reexpressed in terms of CCCR We show that many existing neural network and mean-field theory algorithms are also examples of CCCR The generalized iterative scaling algorithm and Sinkhorn's algorithm can also be expressed as CCCP by changing variables. CCCP can be used both as a new way to understand, and prove the convergence of, existing optimization algorithms and as a procedure for generating new algorithms.

关键词： expectation-maximisation algorithm Optimization algorithms algorithms Carbonyl Cyanide m-Chlorophenyl Hydrazone Road Global optimization

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Conjugate Mixture Models for Clustering Multimodal Data

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NEURAL COMPUTATION 2011年第2期23卷 517-557页

作者： Khalidov, Vasil Forbes, Florence Horaud, Radu INRIA Grenoble Rhone Alpes F-38330 Montbonnot St Martin France

The problem of multimodal clustering arises whenever the data are gathered with several physically different sensors. Observations from different modalities are not necessarily aligned in the sense there there is no obvious way to associate or compare them in some common space. A solution may consist in considering multiple clustering tasks independently for each modality. The main difficulty with such an approach is to guarantee that the unimodal clusterings are mutually consistent. In this letter, we show that multimodal clustering can be addressed within a novel framework: conjugate mixture models. These models exploit the explicit transformations that are often available between an unobserved parameter space (objects) and each of the observation spaces (sensors). We formulate the problem as a likelihood maximization task and derive the associated conjugate expectation-maximization algorithm. The convergence properties of the proposed algorithm are thoroughly investigated. Several local and global optimization techniques are proposed in order to increase its convergence speed. Two initialization strategies are proposed and compared. A consistent model selection criterion is proposed. The algorithm and its variants are tested and evaluated within the task of 3D localization of several speakers using both auditory and visual data.

关键词： Converge variants letter expectation-maximisation algorithm model selection Sensors Loudspeakers Global optimization Cluster Analysis

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