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Data-recursive smoother formulae for partially observed discrete-time markov chains

STOCHASTIC ANALYSIS AND APPLICATIONS 2006年第3期24卷 579-597页

作者： Elliott, RJ Malcolm, WP Natl ICT Australia Canberra ACT 2601 Australia Univ Calgary Haskayne Sch Business Calgary AB Canada

In this article we consider HMM parameter estimation in the context of a filter and smoother based expectation maximization (EM) algorithms. The models we study are discrete time Markov chains observed in Gaussian noise. New formulae for updating smoothed estimates are given for these models. Our formulae are computed by exploiting a duality between a forward in time unnormalized probability process and its dual, and do not require complete recalculation upon the arrival of new measurements. That is, parameter estimates can be updated with new observations, without complete recalculation from the origin. This important feature is in contrast to more classical HMM techniques, (see, for example, [10]), which require the entire log likelihood function to be recalculated upon the arrival of new measurements. Filter-based and smoother-based EM algorithms are computed for the models studied and computer simulations are provided.

关键词： expectation maximization algorithm Martingales parameter estimation reference probability

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On the use of the modified power series family of distributions in a cure rate model context

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STATISTICAL METHODS IN MEDICAL RESEARCH 2020年第7期29卷 1831-1845页

作者： Gallardo, Diego I. Gomez, Yolanda M. Gomez, Hector W. de Castro, Mario Univ Atacama Fac Ingn Dept Matemat Copiapo Chile Univ Antofagasta Fac Ciencias Basicas Dept Matemat Ave Angamos 601 Antofagasta Chile Univ Sao Paulo Inst Ciencias Matem & Comp Sao Paulo Brazil

In this paper, we propose a generalization of the power series cure rate model for the number of competing causes related to the occurrence of the event of interest. The model includes distributions not yet used in the cure rate models context, such as the Borel, Haight and Restricted Generalized Poisson distributions. The model is conveniently parameterized in terms of the cure rate. Maximum likelihood estimation based on the expectation maximization algorithm is discussed. A simulation study designed to assess some properties of the estimators is carried out, showing the good performance of the proposed estimation procedure in finite samples. Finally, an application to a bone marrow transplant data set is presented.

关键词： expectation maximization algorithm long-term survival models maximum likelihood promotion time cure rate model survival analysis

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Modelling the patient accrual with truncated Gaussian mixture distribution for the accurate estimation of sample size in survival trials

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STATISTICAL METHODS IN MEDICAL RESEARCH 2020年第10期29卷 2972-2987页

作者： Hu, Haixia Wang, Ling Li, Chen Ge, Wei Wu, Kejian Xia, Jielai Air Force Med Univ Fac Prevent Med Dept Hlth Stat 169 Changle West Rd Xian 710032 Peoples R China Air Force Med Univ Sch Basic Med Dept Math & Phys Xian Peoples R China

In survival trials with fixed trial length, the patient accrual rate has a significant impact on the sample size estimation or equivalently, on the power of trials. A larger sample size is required for the staggered patient entry. During enrollment, the patient accrual rate changes with the recruitment publicity effect, disease incidence and many other factors and fluctuations of the accrual rate occur frequently. However, the existing accrual models are either over-simplified for the constant rate assumption or complicated in calculation for the subdivision of the accrual period. A more flexible accrual model is required to represent the fluctuant patient accrual rate for accurate sample size estimation. In this paper, inspired by the flexibility of the Gaussian mixture distribution in approximating continuous densities, we propose the truncated Gaussian mixture distribution accrual model to represent different variations of accrual rate by different parameter configurations. The sample size calculation formula and the parameter setting of the proposed accrual model are discussed further.

关键词： Truncated Gaussian mixture distribution accrual model expectation maximization algorithm sample size estimation survival trials

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POINT PROCESS MODELING OF DRUG OVERDOSES WITH HETEROGENEOUS AND MISSING DATA

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ANNALS OF APPLIED STATISTICS 2021年第1期15卷 88-101页

作者： Liu, Xueying Carter, Jeremy Ray, Brad Mohler, George Indiana Univ Purdue Univ Indianapolis Dept Comp & Informat Sci Indianapolis IN 46202 USA Indiana Univ Purdue Univ Indianapolis ONeill Sch Publ & Environm Affairs Indianapolis IN USA

Opioid overdose rates have increased in the United States over the past decade and reflect a major public health crisis. Modeling and prediction of drug and opioid hotspots, where a high percentage of events fall in a small percentage of space-time, could help better focus limited social and health services. In this work we present a spatial-temporal point process model for drug overdose clustering. The data input into the model comes from two heterogeneous sources: (1) high volume emergency medical calls for service (EMS) records containing location and time but no information on the type of nonfatal overdose, and (2) fatal overdose toxicology reports from the coroner containing location and high-dimensional information from the toxicology screen on the drugs present at the time of death. We first use nonnegative matrix factorization to cluster toxicology reports into drug overdose categories, and we then develop an EM algorithm for integrating the two heterogeneous data sets, where the mark corresponding to overdose category is inferred for the EMS data and the high volume EMS data is used to more accurately predict drug overdose death hotspots. We apply the algorithm to drug overdose data from Indianapolis, showing that the point process defined on the integrated data out-performs point processes that use only coroner data (AUC improvement 0.81 to 0.85). We also investigate the extent to which overdoses are contagious, as a function of the type of overdose, while controlling for exogenous fluctuations in the background rate that might also contribute to clustering. We find that drug and opioid overdose deaths exhibit significant excitation with branching ratio ranging from 0.72 to 0.98.

关键词： Point process expectation maximization algorithm semisupervised learning nonnegative matrix factorization opioid overdose

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Using Case-parent Triads to Estimate Relative Risks Associated with a Candidate Haplotype

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ANNALS OF HUMAN GENETICS 2009年第3期73卷 346-359页

作者： Shi, Min Umbach, David M. Weinberg, Clarice R. NIEHS Biostat Branch NIH DHHS Res Triangle Pk NC 27709 USA

Estimating haplotype relative risks in a family-based study is complicated by phase ambiguity and the many parameters needed to quantify relative risks for all possible diplotypes. This problem becomes manageable if a particular haplotype has been implicated previously as relevant to risk. We fit log-linear models to estimate the risks associated with a candidate haplotype relative to the aggregate of other haplotypes. Our approach uses existing haplotype-reconstruction algorithms but requires assumptions about the distribution of haplotypes among triads in the source population. We consider three levels of stringency for those assumptions: Hardy-Weinberg Equilibrium (HWE), random mating, and no assumptions at all. We assessed our method's performance through simulations encompassing a range of risk haplotype frequencies, missing data patterns, and relative risks for either offspring or maternal genetic effects. The unconstrained model provides robustness to bias from population structure but requires excessively large sample sizes unless there are few haplotypes. Assuming HWE accommodates many more haplotypes but sacrifices robustness. The model assuming random mating is intermediate, both in the number of haplotypes it can handle and in robustness. To illustrate, we reanalyze data from a study of orofacial clefts to investigate a 9-SNP candidate haplotype of the IRF6 gene.

关键词： Log-linear model candidate haplotype phase ambiguity expectation maximization algorithm Hardy-Weinberg equilibrium maternal genetic effects Yin-Yang haplotypes

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Identification of base-excited structures using output-only parameter estimation

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EARTHQUAKE ENGINEERING & STRUCTURAL DYNAMICS 2004年第1期33卷 133-155页

作者： Pridham, BA Wilson, JC McMaster Univ Dept Civil Engn Hamilton ON L8S 4L7 Canada

This paper presents a new identification technique for the extraction of modal parameters of structural systems subjected to base excitation. The technique uses output-only measurements of the structural response. A combined subspace-maximum likelihood algorithm is developed and applied to a three-degree-of-freedom simulation model. Five ensembles of synthetically generated input signals, representing varying input characteristics, are employed in Monte Carlo simulations to illustrate the applicability of the method. The technique is able to circumvent some of the difficulties arising from short data sets by employing the expectation maximization (EM) algorithm to refine the subspace state estimates. This approach is motivated by successful application by previous authors on speech signals. Results indicate that, for certain system characteristics, more accurate pole estimates can be identified using the combined subspace-EM formulation. In general, the damping ratios of the system are difficult to identify accurately due to limitations on data set length. The applicability of the technique to structural vibration signals is illustrated through the identification of seismic response data from the Vincent Thomas Bridge. Copyright (C) 2003 John Wiley Sons, Ltd.

关键词： system identification base excitation subspace methods expectation maximization algorithm modal parameters Vincent Thomas Bridge

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Application of Bayesian Model Averaging Approach to Multimodel Ensemble Hydrologic Forecasting

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JOURNAL OF HYDROLOGIC ENGINEERING 2013年第11期18卷 1426-1436页

作者： Liang, Zhongmin Wang, Dong Guo, Yan Zhang, Yu Dai, Rong Hohai Univ Coll Hydrol & Water Resources Nanjing 210098 Jiangsu Peoples R China Northwest Hydro Consulting Engn CHECC Xian 710065 Peoples R China

Bayesian model averaging (BMA) is a statistical method that can synthesize the advantages of different models or methods. The objective of this research is to explore the use of BMA to forecast combinations among several hydrological models. BMA is a statistical scheme that infers the posterior distribution of forecasting variables by weighing individual posterior distributions based on their probabilistic likelihood measures, with the better performing predictions receiving higher weights than the worse predictions. The Topographic Kinematic Approximation and Integration and Xin'anjiang models were applied to the Dongwan basin, Yellow River, China, for flood simulation. Observed and simulated discharge time series were transformed into normally distributed variables through the normal quantile transform. The Gaussian mixture model was constructed by weighing the posterior distribution of individual hydrological models in the transformed space. The posterior probability measuring samples belonging to each specific hydrological model were treated as the weights. The parameters of the Gaussian mixture model and the weight of each hydrological model were estimated by the expectation maximization algorithm. Thus, the forecast combination in the catchment was obtained from the two hydrological models. For flood forecasting, the results provided not only the mean discharge values, but also quantitative evaluation of forecasting uncertainties (e.g.,standard deviation and confidence interval), because the BMA approach calculated the estimation of the probability distribution of forecasted variables. (C) 2013 American Society of Civil Engineers.

关键词： Bayesian analysis Hydrology Forecasting algorithms Uncertainty principles Bayesian model averaging Multimodel ensemble hydrologic forecasting Hydrological model Normal quantile transform Gaussian mixture model expectation maximization algorithm Forecasting uncertainty

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Estimating the accuracy of polymerase chain reaction-based tests using endpoint dilution

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BIOMETRICS 2003年第3期59卷 505-511页

作者： Hughes, JP Totten, P Univ Washington Dept Biostat 357232 Seattle WA 98195 USA Univ Washington Dept Med Seattle WA USA

Polymerase chain reaction (PCR)-based tests for various microorganisms or target DNA sequences are generally acknowledged to be highly "sensitive," yet the concept of sensitivity is ill-defined in the literature on these tests. We propose that sensitivity should be expressed as a function of the number of target DNA molecules in the sample (or specificity, when the target number is 0). However, estimating this "sensitivity curve" is problematic, since it is difficult to construct samples with a fixed number of targets. Nonetheless, using serially diluted replicate aliquots of a known concentration of the target DNA sequence, we show that it is possible to disentangle random variations in the number of target DNA molecules from the underlying test sensitivity. We develop parametric, nonparametric, and semiparametric (spline-based) models for the sensitivity curve. The methods are compared on a new test for M. genitalium.

关键词： expectation maximization algorithm endpoint dilution isotonic estimation monotone smoothing spline polymerase chain reaction sensitivity specificity

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Linear mixed-effects model for multivariate longitudinal compositional data

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NEUROCOMPUTING 2019年 335卷 48-58页

作者： Wang, Zhichao Wang, Huiwen Wang, Shanshan Beihang Univ Sch Econ & Management Beijing 100191 Peoples R China Beijing Key Lab Emergence Support Simulat Technol Beijing 100191 Peoples R China Beijing Adv Innovat Ctr Big Data & Brain Comp Beijing 100191 Peoples R China

Compositional data analysis is becoming increasing important in economic research, where the variables of interest may be structural indicators, such as the investment proportion of industries. In many applications, the measurements of these indicators are collected from countries/regions on a yearly/monthly basis, which falls into the paradigm of longitudinal data. Typically, data from the same individual may show potential association due to unobserved shared factors. To incorporate the dependence within the individual, we investigate the linear mixed-effects model for multivariate longitudinal compositional data. We develop and implement a maximum likelihood estimation procedure through the expectation maximization algorithm. We also investigate the statistical inferences of fixed effects coefficients and the selection of random effects via a proposed Bayesian information criterion. The proposed method shows desirable properties and performs well in finite samples, as comprehensive numerical studies indicate. We further illustrate the practical utility of the proposed method in a real data study based on China's industrial structure, and show that it can improve the performance and enhance the interpretability of the regression on multivariate compositional data. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Longitudinal compositional data Linear mixed-effects model expectation maximization algorithm Structural economic indicator

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Segmentation of Plaques in Sequences of Ultrasonic B-Mode Images of Carotid Arteries Based on Motion Estimation and a Bayesian Model

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IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING 2011年第8期58卷 p2202-2211页

作者： Destrempes, Francois Meunier, Jean Giroux, Marie-France Soulez, Gilles Cloutier, Guy Univ Montreal Hosp Res Ctr CRCHUM Lab Biorheol & Med Ultrason Montreal PQ H2L 2W5 Canada Univ Montreal Dept Radiol Radiooncol & Nucl Med Montreal PQ H3T 1J4 Canada Univ Montreal Inst Biomed Engn Montreal PQ H3T 1J4 Canada Univ Montreal Dept Comp Sci & Operat Res DIRO Montreal PQ H3C 3J7 Canada Univ Montreal Hosp Ctr CHUM Dept Radiol Montreal PQ H2L 4M1 Canada

The goal of this paper is to perform a segmentation of atherosclerotic plaques in view of evaluating their burden and to provide boundaries for computing properties such as the plaque deformation and elasticity distribution (elastogram and modulogram). The echogenicity of a region of interest comprising the plaque, the vessel lumen, and the adventitia of the artery wall in an ultrasonic B-mode image was modeled by mixtures of three Nakagami distributions, which yielded the likelihood of a Bayesian segmentation model. The main contribution of this paper is the estimation of the motion field and its integration into the prior of the Bayesian model that included a local geometrical smoothness constraint, as well as an original spatiotemporal cohesion constraint. The Maximum A Posteriori of the proposed model was computed with a variant of the exploration/selection algorithm. The starting point is a manual segmentation of the first frame. The proposed method was quantitatively compared with manual segmentations of all frames by an expert technician. Various measures were used for this evaluation, including the mean point-to-point distance and the Hausdorff distance. Results were evaluated on 94 sequences of 33 patients (for a total of 8988 images). We report a mean point-to-point distance of 0.24 +/- 0.08 mm and a Hausdorff distance of 1.24 +/- 0.40 mm. Our tests showed that the algorithm was not sensitive to the degree of stenosis or calcification.

关键词： B-Mode Bayesian methods Bayesian model Carotid arteries carotid artery Computational modeling expectation maximization algorithm exploration selection algorithm Image segmentation mixtures of Nakagami distributions motion estimation Motion segmentation Pixel plaque segmentation stochastic optimization tracking ultrasound Video sequences

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