三状态隐马氏模型观测过程的可逆性(英文)

对于连续时间和离散时间三状态隐马氏模型,给出了观测过程直到三维的似然函数流的显式表达.作为一个应用,证明了观测过程可逆性的充分必要条件.     

基于二维真实隐马氏模型的手写体文字识别算法

近几年来，人们采用各种方法试图将1D隐马氏模型(HMM)^[2]推广到2D隐马氏模型。令人失望的是由于在建立合适的2D模型及其计算上的复杂度问题上存在困难，前面的尝试都没有得到一个真实的2DHMM．本文对于应用真实2D隐马氏模型(隐马氏网格随机场HMMRF)^[1,4]进行手写字符识别问题提出新的框架，针对文献[1]中的单点最优算法给出局部最优的译码算法。HMMRF模型是1D隐马氏模型到2D的扩展，能更好的描述字符的2D特性。HMMRF在字符识别中的应用具有两个相——学习相和译码相。在学习相和译码相中我们的最优标准是基于极大边缘后验概率的。不过，在涉及到2D模型中的计算问题时，对模型做出某些简单化的假设是必要的。本文用到的方法对于在合理的模型假设下解决手写字符识别问题呈现了很大的潜力。     

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。     

盈余过程的马氏性与索赔到达间隔分布为离散型的连续时间风险模型

本文研究广泛的一类连续时间风险模型盈余过程的马氏性,得到了盈余过程成为马氏过程的充分必要条件．首次建立了索赔到达间隔为离散型分布的连续时间风险模型．并对两个基本特例得到了破产概率的准确表达式．     

基于动态规划的高阶隐马氏模型推广的Viterbi算法

首先通过Hadar等价变换方法将高阶隐马氏模型转换为与之等价的一阶向量值隐马氏模型,然后利用动态规划原理建立了一阶向量值隐马氏模型的Viterbi算法,最后通过高阶隐马氏模型和一阶向量值隐马氏模型之间的等价关系建立了高阶隐马氏模型基于动态规划推广的Viterbi算法．研究结果在一定程度上推广了几乎所有隐马氏模型文献中所涉及到的解码问题的Viterbi算法,从而进一步丰富和发展了高阶隐马氏模型的算法理论．     

可修系统中半马氏过程的稳态分布

众所周知,可修系统是可靠性理论中讨论的一类非常重要的系统,也是可靠性数学主要研究对象之一,研究可修系统的主要数学工具是马氏理论.当构成系统各部件的寿命分布和故障后的修理时间分布,及其出现的有关分布均为指数分布时,只要适当的定义系统的状态,这样的系统总可以用马氏过程来描述.大部分学者为了方便,均是在马氏框架下研究问题的.但是在实践中经常遇到部件的寿命或修理时间分布不是指数分布的情形,这时可修系统所构成的随机过程是半马氏过程,用现有的马氏理论无法解决相关问题.目前,关于半马氏的理论研究的研究又很少,基于此,针对半马氏的随机模型给出了与马氏理论相平行的稳态分布的求解方法.     

具有摄动的两类马氏决策规则

在状态空间和行动集均有限的条件下,[1-5]讨论了时间离散的,平稳的马氏决策规划的摄动模型,其中,[1,3,4]讨论了单摄动模型,[5]讨论了具有加权准则的摄动模型,[6,7]讨论了时间离散的,平稳的马氏报酬过程的摄动模型,但[6,7]仅考虑了摄动对最优值的影响,而没有考虑摄动对最优策略的影响,本文将讨论具有摄动的非平衡平均马氏均策规划和连续时间折扣马氏决策规划。     

连续时间马氏链中拟平稳分布和不变分布之间的关系

Van Doorn(1991)说明了一个有吸收态的生灭过程中,如何有过程的转移概率来确定拟平衡分布,Nair和Pollett(1933)把它推广到由一个不可约类C和一个吸收态0。并且0从可可到不可约类C的连续时间马氏链,本对一个连续时间马氏连讨论了拟平稳分布与不变分布之间的关系。     

报酬无界的连续时间折扣马氏决策规划

本文讨论了报酬函数夫界，转移速率族一致有界，状态空间和行动集均可数的连续时间折扣马氏决策规划，文中引入了一为新的无界报酬函数，并在一新的马氏策略类中，证明了有界报酬下成立的所有结果。讨论了最优策略的结构，得到了该模型策略为最优的一个充要条件。     

离散型冲击折扣半马氏决策过程

本文讨论离散型冲击折扣半马氏决策过程，在建立模型后，我们将它化成了一个等价的离散时间马氏决策过程．     

Classroom note: Building simple hidden Markov models

Hidden Markov models (HMMs) are widely used in bioinformatics, speech recognition and many other areas. This note presents HMMs via the framework of classical Markov chain models. A simple example is given to illustrate the model. An estimation method for the transition probabilities of the hidden states is also discussed.     

Efficient sensitivity analysis in hidden markov models

Sensitivity analysis in hidden Markov models (HMMs) is usually performed by means of a perturbation analysis where a small change is applied to the model parameters, upon which the output of interest is re-computed. Recently it was shown that a simple mathematical function describes the relation between HMM parameters and an output probability of interest; this result was established by representing the HMM as a (dynamic) Bayesian network. To determine this sensitivity function, it was suggested to employ existing Bayesian network algorithms. Up till now, however, no special purpose algorithms for establishing sensitivity functions for HMMs existed. In this paper we discuss the drawbacks of computing HMM sensitivity functions, building only upon existing algorithms. We then present a new and efficient algorithm, which is specially tailored for determining sensitivity functions in HMMs.     

A fitting algorithm for Markov-modulated poisson processes having two arrival rates

Point processes with fluctuating arrival rates arise in many current applications of queueing theory, notably in communications modeling. Markov-modulated Poisson processes (MMPP) have been used to describe such processes because they incorporate a mechanism to account for the temporal inhomogeneity of the arrival rates, yet yield analytically tractable queueing results. An iterative statistical procedure is developed for fitting MMPP having two arrival rates to observational data. The procedure is largely numerical-experimental and is motivated by maximum likelihood estimation.     

The Alive Particle Filter and Its Use in Particle Markov Chain Monte Carlo

In the following article, we investigate a particle filter for approximating Feynman–Kac models with indicator potentials and we use this algorithm within Markov chain Monte Carlo (MCMC) to learn static parameters of the model. Examples of such models include approximate Bayesian computation (ABC) posteriors associated with hidden Markov models (HMMs) or rare-event problems. Such models require the use of advanced particle filter or MCMC algorithms to perform estimation. One of the drawbacks of existing particle filters is that they may “collapse,” in that the algorithm may terminate early, due to the indicator potentials. In this article, using a newly developed special case of the locally adaptive particle filter, we use an algorithm that can deal with this latter problem, while introducing a random cost per-time step. In particular, we show how this algorithm can be used within MCMC, using particle MCMC. It is established that, when not taking into account computational time, when the new MCMC algorithm is applied to a simplified model it has a lower asymptotic variance in comparison to a standard particle MCMC algorithm. Numerical examples are presented for ABC approximations of HMMs.     

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.     

sppmix: Poisson point process modeling using normal mixture models

This paper describes the package sppmix for the statistical environment R. The sppmix package implements classes and methods for modeling spatial point patterns using inhomogeneous Poisson point processes, where the intensity surface is assumed to be a multiple of a finite additive mixture of normal components and the number of components is a finite, fixed or random integer. Extensions to the marked inhomogeneous Poisson point processes case are also presented. We provide an extensive suite of R functions that can be used to simulate, visualize and model point patterns, estimate the parameters of the models, assess convergence of the algorithms and perform model selection and checking in the proposed modeling context. In addition, several approaches have been implemented in order to handle the standard label switching issue which arises in any modeling approach involving mixture models. We adapt a hierarchical Bayesian framework in order to model the intensity surfaces and have implemented two major algorithms in order to estimate the parameters of the mixture models involved: the data augmentation and the birth–death Markov chain Monte Carlo (DAMCMC and BDMCMC). We used C++ (via the Rcpp package) in order to implement the most computationally intensive algorithms.     

Modeling Dependencies in Operational Risk with Hybrid Bayesian Networks

This paper addresses the problem of quantifying and modeling financial institutions’ operational risk in accordance with the Advanced Measurement Approach put forth in the Basel II Accord. We argue that standard approaches focusing on modeling stochastic dependencies are not sufficient to adequately assess operational risk. In addition to stochastic dependencies, causal topological dependencies between the risk classes are typically encountered. These dependencies arise when risk units have common information- and/or work-flows and when failure of upstream processes imply risk for downstream processes. In this paper, we present a modeling strategy that explicitly captures both topological and stochastic dependencies between risk classes. We represent the operational-risk taxonomy in the framework of a hybrid Bayesian network (BN) and provide an intuitively compelling approach for handling causal relationships and external influences. We demonstrate the use of hybrid BNs as a tool for mapping causal dependencies between frequencies and severities of risk events and for modeling common shocks. Monte-Carlo simulations illustrate that the impact of topological dependencies on triggering overall system breakdowns can be substantial.     

Modeling financial asset returns with shot noise processes

We introduce a new class of continuous time processes for modeling the rate of returns of financial assets. The statistical characterization is based on the so-called shot noise processes. The probabilistic structure of the shot noise process provides a very realistic framework for asset returns modeling of the stock price processes. Our class of processes exhibits the natural phenomena well known in empirical financial studies:

1. (a) fat-tail distribution function for the asset returns,

2. (b) dependence of the returns,

3. (c) nonstationarity in time.

Financial asset returns in new emerging markets such as those of Eastern European countries exhibit a highly volatile behavior. Statistical investigations of the unconditional distribution of returns of stocks, commodities, exchange rates, etc., show extremely heavy tails and steep peaks around the expectation. We use a class of shot noise processes with Poissonian times and Brownian magnitudes for modeling this phenomenon.     

Discrete time modeling of mean-reverting stochastic processes for real option valuation

In this paper the recombining binomial lattice approach for modeling real options and valuing managerial flexibility is generalized to address a common issue in many practical applications, underlying stochastic processes that are mean-reverting. Binomial lattices were first introduced to approximate stochastic processes for valuation of financial options, and they provide a convenient framework for numerical analysis. Unfortunately, the standard approach to constructing binomial lattices can result in invalid probabilities of up and down moves in the lattice when a mean-reverting stochastic process is to be approximated. There have been several alternative methods introduced for modeling mean-reverting processes, including simulation-based approaches and trinomial trees, however they unfortunately complicate the numerical analysis of valuation problems. The approach developed in this paper utilizes a more general binomial approximation methodology from the existing literature to model simple homoskedastic mean-reverting stochastic processes as recombining lattices. This approach is then extended to model dual correlated one-factor mean-reverting processes. These models facilitate the evaluation of options with early-exercise characteristics, as well as multiple concurrent options.     

Cross-entropic learning of a machine for the decision in a partially observable universe

In this paper, we are interested in optimal decisions in a partially observable universe. Our approach is to directly approximate an optimal strategic tree depending on the observation. This approximation is made by means of a parameterized probabilistic law. A particular family of Hidden Markov Models (HMM), with input and output, is considered as a model of policy. A method for optimizing the parameters of these HMMs is proposed and applied. This optimization is based on the cross-entropic (CE) principle for rare events simulation developed by Rubinstein.