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Geostatistical Modelling Using Non-Gaussian Matern Fields

SCANDINAVIAN JOURNAL OF STATISTICS 2015年第3期42卷 872-890页

作者： Wallin, Jonas Bolin, David Gothenburg Univ Dept Math Sci S-41124 Gothenburg Sweden Chalmers Univ Technol Dept Math Stat SE-41258 Gothenburg Sweden

This work provides a class of non-Gaussian spatial Matern fields which are useful for analysing geostatistical data. The models are constructed as solutions to stochastic partial differential equations driven by generalized hyperbolic noise and are incorporated in a standard geostatistical setting with irregularly spaced observations, measurement errors and covariates. A maximum likelihood estimation technique based on the Monte Carlo expectation-maximization algorithm is presented, and a Monte Carlo method for spatial prediction is derived. Finally, an application to precipitation data is presented, and the performance of the non-Gaussian models is compared with standard Gaussian and transformed Gaussian models through cross-validation.

关键词： Laplace Markov random fields Matern covariances mcem algorithm normal inverse Gaussian SPDE variance Gamma

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Improved Estimation and Uncertainty Quantification Using Monte Carlo-Based Optimization algorithms

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JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS 2015年第3期24卷 771-791页

作者： Xu, Cong Baines, Paul Wang, Jane-Ling Univ Calif Davis Davis CA 95616 USA

In this article, we present a novel method to obtain both improved estimates and reliable stopping rules for stochastic optimization algorithms such as the Monte Carlo EM (mcem) algorithm. By characterizing a stationary point, theta*, of the algorithm as the solution to a fixed point equation, we provide a parameter estimation procedure by solving for the fixed point of the update mapping. We investigate various ways to model the update mapping, including the use of a local linear (regression) smoother. This simple approach allows increased stability in estimating the value of theta* as well as providing a natural quantification of the estimation uncertainty. These uncertainty measures can then also be used to construct convergence criteria that reflect the inherent randomness in the algorithm. We establish convergence properties of our modified estimator. In contrast to existing literature, our convergence results do not require the Monte Carlo sample size to go to infinity. Simulation studies are provided to illustrate the improved stability and reliability of our estimator.

关键词： Stochastic optimization Stopping rules mcem algorithm Local linear smoothing

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An optimal classification rule for multiple interval-screened scale mixture of normal populations

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JOURNAL OF THE KOREAN STATISTICAL SOCIETY 2013年第2期42卷 191-203页

作者： Kim, Hea-Jung Dongguk Univ Seoul Dept Stat Seoul 100715 South Korea

This paper considers a new classification case where K categories of the target variable are defined by disjoint intervals of an underlying variable and proposes an optimal rule for the classification. A parametric classification model, known as interval-screened scale mixture of normal model, is used to derive the rule that classifies individuals into K populations defined by K disjoint intervals of the variable (screening variable). The effectiveness of the rule is verified by the simulation and empirical studies that compare its performance with other existing classification rules. The cross-validation error rate is used as the measure of performance. Necessary theories for deriving the rule, an mcem algorithm for estimating the rule, and the interesting characteristics of the rule are also provided. (C) 2013 The Korean Statistical Society. Published by Elsevier B.V. All rights reserved.

关键词： Classification analysis mcem algorithm Screened scale mixture of normal distribution Optimal rule

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Maximum likelihood estimation of multinomial probit factor analysis models for multivariate t-distribution

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COMPUTATIONAL STATISTICS 2013年第4期28卷 1485-1500页

作者： Jiang, Jie Liu, Xinsheng Yu, Keming Nanjing Univ Aeronaut & Astronaut State Key Lab Mech & Control Mech Struct Inst Nano Sci Nanjing 210016 Peoples R China Nanjing Univ Aeronaut & Astronaut Coll Sci Nanjing 210016 Peoples R China Brunel Univ Dept Math Sci Uxbridge UB8 3PH Middx England Shihezi Univ Sch Business Shihezi 832003 Peoples R China

We propose a model for multinomial probit factor analysis by assuming t-distribution error in probit factor analysis. To obtain maximum likelihood estimation, we use the Monte Carlo expectation maximization algorithm with its M-step greatly simplified under conditional maximization and its E-step made feasible by Monte Carlo simulation. Standard errors are calculated by using Louis's method. The methodology is illustrated with numerical simulations.

关键词： Multinomial probit model Factor analysis mcem algorithm t-distribution

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A crossed random effects modeling approach for estimating diagnostic accuracy from ordinal ratings without a gold standard

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STATISTICS IN MEDICINE 2013年第20期32卷 3472-3485页

作者： Xie, Yunlong Chen, Zhen Albert, Paul S. Eunice Kennedy Shriver Natl Inst Child Hlth & Hum Biostat & Bioinformat Branch Div Epidemiol Stat & Prevent Res NIH Bethesda MD 20892 USA

In diagnostic studies without a gold standard, the assumption on the dependence structure of the multiple tests or raters plays an important role in model performance. In case of binary disease status, both conditional independence and crossed random effects structure have been proposed and their performance investigated. Less attention has been paid to the situation where the true disease status is ordinal. In this paper, we propose crossed subject-specific and rater-specific random effects to account for the dependence structure and assess the robustness of the proposed model to misspecification in the random effects distributions. We applied the models to data from the Physician Reliability Study, which focuses on assessing the diagnostic accuracy in a population of raters for the staging of endometriosis, a gynecological disorder in women. Using this new methodology, we estimate the probability of a correct classification and show that regional experts can more easily classify the intermediate stage than resident physicians. Copyright (c) 2013 John Wiley & Sons, Ltd.

关键词： random effects models endometriosis mcem algorithm

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Model Selection of Zero-Inflated Generalized Power Series Distribution with Missing Responses

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2012年第6期41卷 1013-1028页

作者： Fu, Ying-Zi Kunming Sci & Technol Univ Sch Sci Kunming 313000 Yunnan Province Peoples R China

Count data with extra zeros are common in many biomedical applications and the zero-inflated generalized power series (ZIGPS) distribution may be appropriate, in which the baseline discrete distribution is a generalized power series distribution, which is a natural extension of power series distribution. In this article, a Monte Carlo EM (mcem) algorithm is proposed to obtain maximum likelihood estimates and standard errors for ZIGPS distribution with missing responses. A Monte Carlo approximation method combining the Gibbs sampler and M-H algorithm is used to implement E-step, whereas the M-step is completed via the method of conditional maximization. As classical model selection procedure such as Akaike's information criterion (AIC) becomes problematic for our considered ZIGPS distribution with incomplete data, some variations on AIC are presented under two different missingness mechanisms, namely, missing at random (MAR) and missing not at random (MNAR), respectively. The most attractive point is that our methods cannot only be used to select distributions and variables, but also can be used to find out whether there exists zero-inflation or not, which is conducted via score test or Bayesian test in previous literature. Finally, a simulation study and a real example are used to illustrate the proposed methodology.

关键词： AIC mcem algorithm Missing data Model selection Zero-inflation

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ParticleCall: A particle filter for base calling in next-generation sequencing systems

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BMC BIOINFORMATICS 2012年第1期13卷 1-10页

作者： Shen, Xiaohu Vikalo, Haris Univ Texas Austin Dept Elect & Comp Engn Austin TX 78712 USA

Background: Next-generation sequencing systems are capable of rapid and cost-effective DNA sequencing, thus enabling routine sequencing tasks and taking us one step closer to personalized medicine. Accuracy and lengths of their reads, however, are yet to surpass those provided by the conventional Sanger sequencing method. This motivates the search for computationally efficient algorithms capable of reliable and accurate detection of the order of nucleotides in short DNA fragments from the acquired data. Results: In this paper, we consider Illumina's sequencing-by-synthesis platform which relies on reversible terminator chemistry and describe the acquired signal by reformulating its mathematical model as a Hidden Markov Model. Relying on this model and sequential Monte Carlo methods, we develop a parameter estimation and base calling scheme called ParticleCall. ParticleCall is tested on a data set obtained by sequencing phiX174 bacteriophage using Illumina's Genome Analyzer II. The results show that the developed base calling scheme is significantly more computationally efficient than the best performing unsupervised method currently available, while achieving the same accuracy. Conclusions: The proposed ParticleCall provides more accurate calls than the Illumina's base calling algorithm, Bustard. At the same time, ParticleCall is significantly more computationally efficient than other recent schemes with similar performance, rendering it more feasible for high-throughput sequencing data analysis. Improvement of base calling accuracy will have immediate beneficial effects on the performance of downstream applications such as SNP and genotype calling. ParticleCall is freely available at https://***/projects/particlecall.

关键词： Hide Markov Model Particle Filter Hide Markov Model Model Parameter Estimation Scheme mcem algorithm

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Semiparametric analysis of longitudinal zero-inflated count data

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JOURNAL OF MULTIVARIATE ANALYSIS 2011年第1期102卷 61-72页

作者： Feng, Jiarui Zhu, Zhongyi Fudan Univ Dept Stat Shanghai 200433 Peoples R China

In this article, we consider a semiparametric zero-inflated Poisson mixed model that postulates a possible nonlinear relationship between the natural logarithm of the mean of the counts and a particular covariate in the longitudinal studies. A penalized log-likelihood function is proposed and Monte Carlo expectation-maximization algorithm is used to derive the estimates. Under some mild conditions, we establish the consistency and asymptotic normality of the resulting estimators. Simulation studies are carried out to investigate the finite sample performance of the proposed method. For illustration purposes, the method is applied to a data set from a pharmaceutical company where the variable of interest is the number of episodes of side effects after the patient has taken the treatments. (C) 2010 Elsevier Inc. All rights reserved.

关键词： ZIP regression Mixed model Penalized spline mcem algorithm

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Extended mixture factor analysis model with covariates for mixed binary and continuous responses

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STATISTICS IN MEDICINE 2011年第21期30卷 2634-2647页

作者： An, Xinming Bentler, Peter M. Univ Calif Los Angeles Dept Psychol Los Angeles CA 90024 USA

Finite mixture factor analysis provides a parsimonious model to explore latent group structures of high-dimensional data. In this modeling framework, we can explore latent structures for continuous responses. However, dichotomous items are often used to define latent domains in practice. This paper proposes an extended finite mixture factor analysis model with covariates to model mixed continuous and binary responses. We use a Monte Carlo expectation-maximization (mcem) algorithm to estimate the model. In the E step, closed-form solutions are not available for the conditional expectation of complete data log likelihood, so it is approximated by sample means, which are in turn generated by the Gibbs sampler from the joint conditional distribution of latent variables. To monitor the convergence of the mcem algorithm, we use bridge sampling to calculate the log likelihood ratio of two successive iterations. We adopt a diagnostic plot of the log likelihood ratio against iterations for monitoring the convergence of the mcem algorithm. We compare different models based on BIC, in which we approximate the observed data log likelihood by using a Monte Carlo method. We investigate the computational properties of the mcem algorithm by simulation studies. We use a real data example to illustrate the practical usefulness of the model. Finally, we discuss limitations and possible extensions. Copyright (C) 2011 John Wiley & Sons, Ltd.

关键词： finite mixture model factor analysis model mcem algorithm Gibbs sampler

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Nonlinear structural equation modeling with distribution-free method

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Model Assisted Statistics and Applications 2011年第1期6卷 39-46页

作者： Zhao, Yan D. Rahardja, Dewi Department of Clinical Sciences Simmons Cancer Center UT Southwestern Medical Center Dallas TX United States Department of Clinical Sciences UT Southwestern Medical Center Dallas TX United States Dallas TX 75390-8590 5323 Harry Hines Blvd United States

Structural equation models (SEM) are widely used in many fields including economics and social science. Typical nonlinear SEMs consist of two parts: a linear measurement model relating observed measurements to underlying latent variables, and a nonlinear structural model describing relationships among the latent variables. For such models, we propose a pseudo likelihood approach based on a hypothetical normal mixture assumption on the latent variables. To obtain pseudo likelihood parameter estimates, a Monte Carlo EM algorithm is developed. Standard errors for the structural parameter estimates are obtained by combining an empirical observed information matrix and a bootstrap estimated covariance matrix. For nonlinear SEMs with latent variables with various distributions, we conduct simulations to show our approach produced unbiased parameter estimates and confidence intervals with nominal coverage. © 2011 - IOS Press and the authors. All rights reserved.

关键词： Bootstrap deconvolution latent variable modeling mcem algorithm normal mixture standard error estimation

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