Multivariate Discrete Hidden Markov Models for Domain-Based Measurements and Assessment of Risk Factors in Child Development

Many studies in the social and behavioral sciences involve multivariate discrete measurements, which are often characterized by the presence of an underlying individual trait, the existence of clusters such as domains of measurements, and the availability of multiple waves of cohort data. Motivated by an application in child development, we propose a class of extended multivariate discrete hidden Markov models for analyzing domain-based measurements of cognition and behavior. A random effects model is used to capture the long-term trait. Additionally, we develop a model selection criterion based on the Bayes factor for the extended hidden Markov model. The National Longitudinal Survey of Youth (NLSY) is used to illustrate the methods. Supplementary technical details and computer codes are available online.     

隐马尔可夫模型在生物信息学中的应用

隐马尔可夫模型 ( HMM)是一个能够通过可观测的数据很好地捕捉真实空间统计性质的随机模型 ,该模型已成功地运用于语音识别 ,目前 HMM已开始应用于生物信息学 ( bioinformatics) ,已在生物序列分析中得到了广泛的应用 .本文首先介绍了 HMM的基本结构 ,然后着重讨论了 HMM在 DNA序列的多重比对 ,基因发现等生物序列分析中的应用     

Nonparametric Density Estimation in Hidden Markov Models

Let { X n} be a Markov chain that is either f -mixing or satisfies the Poisson equation.In this note we obtain the convergence rate under L 1 -criterion for bounded functions of the X k 's. And in the hidden Markov model setup { (X n ,Y n ) }we study the kernel estimate of the density of the observed variables { Y n }when a 'stable' status is reached.     

Computational Bayesian Analysis of Hidden Markov Models

Abstract

Versions of the Gibbs Sampler are derived for the analysis of data from hidden Markov chains and hidden Markov random fields. The principal new development is to use the pseudolikelihood function associated with the underlying Markov process in place of the likelihood, which is intractable in the case of a Markov random field, in the simulation step for the parameters in the Markov process. Theoretical aspects are discussed and a numerical study is reported.     

Online EM Algorithm for Hidden Markov Models

Online (also called “recursive” or “adaptive”) estimation of fixed model parameters in hidden Markov models is a topic of much interest in times series modeling. In this work, we propose an online parameter estimation algorithm that combines two key ideas. The first one, which is deeply rooted in the Expectation-Maximization (EM) methodology, consists in reparameterizing the problem using complete-data sufficient statistics. The second ingredient consists in exploiting a purely recursive form of smoothing in HMMs based on an auxiliary recursion. Although the proposed online EM algorithm resembles a classical stochastic approximation (or Robbins–Monro) algorithm, it is sufficiently different to resist conventional analysis of convergence. We thus provide limited results which identify the potential limiting points of the recursion as well as the large-sample behavior of the quantities involved in the algorithm. The performance of the proposed algorithm is numerically evaluated through simulations in the case of a noisily observed Markov chain. In this case, the algorithm reaches estimation results that are comparable to those of the maximum likelihood estimator for large sample sizes. The supplemental material for this article available online includes an appendix with the proofs of Theorem 1 and Corollary 1 stated in Section 4 as well as the MATLAB/OCTAVE code used to implement the algorithm in the case of a noisily observed Markov chain considered in Section 5.     

隐马模型及其在基因识别中的应用

生物信息学是一门新兴交叉学科,隐马模型是广泛用于该学科的数学模型.简要介绍了隐马模型的数学原理,并以大肠杆菌和人的基因识别为例说明了它在基因识别中的应用.     

Forgetting the initial distribution for Hidden Markov Models

The forgetting of the initial distribution for discrete Hidden Markov Models (HMM) is addressed: a new set of conditions is proposed, to establish the forgetting property of the filter, at a polynomial and geometric rate. Both a pathwise-type convergence of the total variation distance of the filter started from two different initial distributions, and a convergence in expectation are considered. The results are illustrated using different HMM of interest: the dynamic tobit model, the nonlinear state space model and the stochastic volatility model.     

Variable Selection in Varying-Coefficient Models Using P-Splines

In this article, we consider nonparametric smoothing and variable selection in varying-coefficient models. Varying-coefficient models are commonly used for analyzing the time-dependent effects of covariates on responses measured repeatedly (such as longitudinal data). We present the P-spline estimator in this context and show its estimation consistency for a diverging number of knots (or B-spline basis functions). The combination of P-splines with nonnegative garrote (which is a variable selection method) leads to good estimation and variable selection. Moreover, we consider APSO (additive P-spline selection operator), which combines a P-spline penalty with a regularization penalty, and show its estimation and variable selection consistency. The methods are illustrated with a simulation study and real-data examples. The proofs of the theoretical results as well as one of the real-data examples are provided in the online supplementary materials.     

Importance Sampling for Continuous Time Markov Chains and Applications to Fluid Models*

In this paper we determine the asymptotically efficient change of intensity for some problems of Monte Carlo simulation involving a finite state continuous time Markov process. Firstly, the computation of probabilities of large deviations of empirical averages from their asymptotic mean; second, the computation of probabilities of crossing a large level for the corresponding additive process. We are motivated by the study of overflows in a buffer whose input is modeled as a Markov fluid.     

Generalized Nonparametric Mixed-Effect Models: Computation and Smoothing Parameter Selection

Generalized linear mixed-effect models are widely used for the analysis of correlated non-Gaussian data such as those found in longitudinal studies. In this article, we consider extensions with nonparametric fixed effects and parametric random effects. The estimation is through the penalized likelihood method, and our focus is on the efficient computation and the effective smoothing parameter selection. To assist efficient computation, the joint likelihood of the observations and the latent variables of the random effects is used instead of the marginal likelihood of the observations. For the selection of smoothing parameters and correlation parameters, direct cross-validation techniques are employed; the effectiveness of cross-validation with respect to a few loss functions are evaluated through simulation studies. Real data examples are presented to illustrate potential applications of the methodology. Open-source R code is demonstrated in the Appendix.     

State Estimation Schemes for Independent Component Coupled Hidden Markov Models

Conventional Hidden Markov models generally consist of a Markov chain observed through a linear map corrupted by additive noise. This general class of model has enjoyed a huge and diverse range of applications, for example, speech processing, biomedical signal processing and more recently quantitative finance. However, a lesser known extension of this general class of model is the so-called Factorial Hidden Markov Model (FHMM). FHMMs also have diverse applications, notably in machine learning, artificial intelligence and speech recognition [13 Ghahramani , Z. , and Jordan , M. 1997 . Factorial hidden Markov models . Machine Learning 29 : 245 – 273 .[Crossref], [Web of Science ®] , [Google Scholar], 17 Logan , B. , and Moreno , P.J. 1997 . Factorial Hidden Markov Models for Speech Recognition: Preliminary Experiments. Cambridge Research Laboratory, Technical Report CRL 97/7, September.  [Google Scholar]]. FHMMs extend the usual class of HMMs, by supposing the partially observed state process is a finite collection of distinct Markov chains, either statistically independent or dependent. There is also considerable current activity in applying collections of partially observed Markov chains to complex action recognition problems, see, for example, [6 Brand , M. , Oliver , N. , and Pentland , A. 1997 . Coupled hidden Markov models for complex action recognition . IEEE Conference on Computer Vision and Pattern Recognition , San Juan , Puerto Rico . [Google Scholar]].

In this article we consider the Maximum Likelihood (ML) parameter estimation problem for FHMMs. Much of the extant literature concerning this problem presents parameter estimation schemes based on full data log-likelihood EM algorithms. This approach can be slow to converge and often imposes heavy demands on computer memory. The latter point is particularly relevant for the class of FHMMs where state space dimensions are relatively large.

The contribution in this article is to develop new recursive formulae for a filter-based EM algorithm that can be implemented online. Our new formulae are equivalent ML estimators, however, these formulae are purely recursive and so, significantly reduce numerical complexity and memory requirements. A computer simulation is included to demonstrate the performance of our results.     

Default Times in a Continuous Time Markov Chain Economy

Abstract

A continuous time financial market is considered where randomness is modelled by a finite state Markov chain. Using the chain, a stochastic discount factor is defined. The probability distributions of default times are shown to be given by solutions of a system of coupled partial differential equations.     

离散型广义非线性纵向数据模型中偏离名义离差的检验及其功效模拟

离散型广义非线性模型包括Poisson,二项,负二项模型.本文讨论离散型广义非线性纵向数据模型中偏离名义离差的检验问题,得到了检验的score统计量,并利用MonteCarlo方法研究了检验统计量的性质.最后,利用杀虫剂数据说明了检验方法的应用.     

Superposition of Spatially Interacting Aggregated Continuous Time Markov Chains

A system s{ X(t)} = {X ₁(t),X ₂(t),..., X _N(t)} of N interacting time reversible continuous time Markov chains is considered. The state space of each of the processes {X _i(t)} (i = 1, 2,...,N) is partitioned into two aggregates. Interaction between the processes {X _i(t)},{X ₂(t)},...,{X _N(t)} is introduced by allowing the transition rates of an individual process at time t to depend on the configuration of aggregates occupied by the other N - 1 processes at that time. The motivation for this work comes from ion channel modeling, where {(X}(t)} describes the gating mechanisms of N channels and the partitioning of the state space of {X _i(t)} correspond to whether the channel is conducting or not. Let S(t) denote the number of conducting channels at time t. For a time-reversible class of such processes, expressions are derived for the mean and probability density function of the sojourns of {S(t)} at its different levels when {X(t)} is in equilibrium. Particular attention is paid to the situation when the N channels are located on a circle with nearest neighbor interaction. Necessary and sufficient conditions for a general co-operative multiple channel system to be time reversible are derived.     

半马氏环境连续时间马氏决策过程：平均准则

本文讨论半马氏环境连续时间马氏决策过程中的平均准则．首先讨论了半马氏报酬过程中的逼近问题，进而讨论平均目标函数逼近问题。     

Parameter Estimation in Hidden Markov Models With Intractable Likelihoods Using Sequential Monte Carlo

We propose sequential Monte Carlo-based algorithms for maximum likelihood estimation of the static parameters in hidden Markov models with an intractable likelihood using ideas from approximate Bayesian computation. The static parameter estimation algorithms are gradient-based and cover both offline and online estimation. We demonstrate their performance by estimating the parameters of three intractable models, namely the α-stable distribution, g-and-k distribution, and the stochastic volatility model with α-stable returns, using both real and synthetic data.     

Biclustering Three-Dimensional Data Arrays With Plaid Models

Three-dimensional data arrays (collections of individual data matrices) are increasingly prevalent in modern data and pose unique challenges to pattern extraction and visualization. This article introduces a biclustering technique for exploration and pattern detection in such complex structured data. The proposed framework couples the popular plaid model together with tools from functional data analysis to guide the estimation of bicluster responses over the array. We present an efficient algorithm that first detects biclusters that exhibit strong deviations for some data matrices, and then estimates their responses over the entire data array. Altogether, the framework is useful to home in on and display underlying structure and its evolution over conditions/time. The methods are scalable to large datasets, and can accommodate a variety of dynamic patterns. The proposed techniques are illustrated on gene expression data and bilateral trade networks. Supplementary materials are available online.     

隐Markov模型的强马氏性

引入隐Markov模型强马氏性的概念,并进一步研究了隐Markov模型在强马氏性方面的一些性质.     

非齐次隐马尔可夫模型随机变换的若干强极限定理

利用鞅方法讨论了非齐次隐马尔可夫模型变换的强极限定理,作为特殊情形,将随机选择的概念拓展到非齐次隐马尔可夫模型中,得到了关于有限非齐次隐马尔可夫模型随机选择与随机公平比的若干极限定理.