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混合卡尔曼滤波器AI 解读

Summary In treating dynamic systems, sequential Monte Carlo methods use discrete samples to represent a complicated probability distribution and use rejection sampling, importance sampling and weighted resampling to complete the on-line ‘filtering’ task. We propose a special sequential Monte Carlo method, the mixture Kalman filter, which uses a random mixture of the Gaussian distributions to approximate a target distribution. It is designed for on-line estimation and…

Metropolis 抽样中的多重尝试方法与局部优化AI 解读

This article describes a new Metropolis-like transition rule, the multiple-try Metropolis, for Markov chain Monte Carlo (MCMC) simulations. By using this transition rule together with adaptive direction sampling, we propose a novel method for incorporating local optimization steps into a MCMC sampler in continuous state-space. Numerical studies show that the new method performs significantly better than the traditional Metropolis-Hastings (M-H) sampler. With minor tailoring…

数据增广的参数扩展AI 解读

Viewing the observed data of a statistical model as incomplete and augmenting its missing parts are useful for clarifying concepts and central to the invention of two well-known statistical algorithms: expectation-maximization (EM) and data augmentation. Recently, Liu, Rubin, and Wu demonstrated that expanding the parameter space along with augmenting the missing data is useful for accelerating iterative computation in an EM algorithm. The main purpose of this article is to…

生物序列比对中的马尔可夫结构AI 解读

The alignment of multiple homologous biopolymer sequences is crucial in research on protein modeling and engineering, molecular evolution, and prediction in terms of both gene function and gene product structure. In this article we provide a coherent view of the two recent models used for multiple sequence alignment—the hidden Markov model (HMM) and the block-based motif model—to develop a set of new algorithms that have both the sensitivity of the block-based model and the…

动态系统的序贯蒙特卡洛方法AI 解读

We provide a general framework for using Monte Carlo methods in dynamic systems and discuss its wide applications. Under this framework, several currently available techniques are studied and generalized to accommodate more complex features. All of these methods are partial combinations of three ingredients: importance sampling and resampling, rejection sampling, and Markov chain iterations. We provide guidelines on how they should be used and under what circumstance each…

拒绝控制与序贯重要性抽样AI 解读

We discuss ways of combining rejection sampling and importance sampling methods in Monte Carlo computations and demonstrate their usefulness in updating dynamic systems. Specifically, we propose the rejection controlled sequential importance sampling (RC-SIS) algorithm, which is designed to simultaneously reduce Monte Carlo variation and retain independent samples in sequential importance sampling. The proposed method is demonstrated by three examples taken from…

预测更新方法及其在贝叶斯分类中的应用AI 解读

SUMMARY We propose algorithms based on random draws from predictive distributions of unknown quantities (missing values, for instance). This procedure can either be iterative, which is a special variation of the Gibbs sampler, or be sequential, which is a variation of sequential imputation. In the latter case one can update the posterior distribution with new observations easily. The methods proposed have intuitive statistical implications and can be generalized to…

通过序贯插补实现非参数分层贝叶斯估计AI 解读

We consider the empirical Bayes estimation of a distribution using binary data via the Dirichlet process. Let $\mathscr{D}(\alpha)$ denote a Dirichlet process with $\alpha$ being a finite measure on Instead of having direct samples from an unknown random distribution F from $\mathscr{D}(\alpha)$, we assume that only indirect binomial data are observable. This paper presents a new interpretation of Lo's formula, and thereby relates the predictive density of the observations…

多重局部序列比对的贝叶斯模型与 Gibbs 抽样策略AI 解读

A wealth of data concerning life's basic molecules, proteins and nucleic acids, has emerged from the biotechnology revolution. The human genome project has accelerated the growth of these data. Multiple observations of homologous protein or nucleic acid sequences from different organisms are often available. But because mutations and sequence errors misalign these data, multiple sequence alignment has become an essential and valuable tool for understanding structures and…

通过序贯插补进行盲反卷积AI 解读

The sequential imputation procedure is applied to adaptively and sequentially reconstruct discrete input signals that are blurred by an unknown linear moving average channel and contaminated by additive Gaussian noises, a problem known as blind deconvolution in digital communication. A rejuvenation procedure for improving the efficiency of sequential imputation is introduced and theoretically justified. The proposed method does not require the channel to be nonminimum phase…

非线性自回归的可加性检验AI 解读

Additivity is commonly used in the statistical literature to simplify data analysis, especially in analysis of variance and in multivariate smoothing. In this paper, we propose three procedures for testing additivity in nonlinear time series analysis. The first procedure combines some smoothing techniques with analysis of variance, the second is a Lagrange multiplier test using nonparametric estimation, and the third is a permutation test which uses smoothing techniques to…

不同扫描方式下 Gibbs 采样器的协方差结构与收敛速率AI 解读

SUMMARY This paper presents results on covariance structure and convergence for the Gibbs sampler with both systematic and random scans. It is shown that, under conditions that guarantee the compactness of the Markov forward operator and irreducibility of the corresponding chain, the Gibbs sampling scheme converges geometrically in terms of Pearson χ 2-distance. In particular, for the random scan, the autocovariance can be expressed as variances of iterative conditional…

非线性自回归的可加性检验AI 解读

Additivity is commonly used in the statistical literature to simplify data analysis, especially in analysis of variance and in multivariate smoothing. In this paper, we propose three procedures for testing additivity in nonlinear time series analysis. The first procedure combines some smoothing techniques with analysis of variance, the second is a Lagrange multiplier test using nonparametric estimation, and the third is a permutation test which uses smoothing techniques to…

贝叶斯计算中的折叠 Gibbs 抽样及基因调控应用AI 解读

This article describes a method of “grouping” and “collapsing” in using the Gibbs sampler and proves from an operator theory viewpoint that the method is in general beneficial. The norms of the forward operators associated with the corresponding nonreversible Markov chains are used to discriminate among different simulation schemes. When applied to Bayesian missing data problems, the idea of collapsing suggests skipping the steps of sampling parameter(s) values in standard…

Attention is drawn to a method of sampling a finite population of N units with unequal probabilities and without replacement. The method was originally proposed by Stern & Cover (1989) as a model for lotteries. The method can be characterized as maximizing entropy given coverage probabilities πi, or equivalently as having the probability of a selected sample proportional to the product of a set of ‘weights’ wi. We show the essential uniqueness of the wi given the πi. We…

序贯插补与贝叶斯缺失数据问题AI 解读

For missing data problems, Tanner and Wong have described a data augmentation procedure that approximates the actual posterior distribution of the parameter vector by a mixture of complete data posteriors. Their method of constructing the complete data sets is closely related to the Gibbs sampler. Both required iterations, and, similar to the EM algorithm, convergence can be slow. We introduce in this article an alternative procedure that involves imputing the missing data…

Gibbs 抽样的协方差结构：估计量与数据增广方案的比较AI 解读

We study the covariance structure of a Markov chain generated by the Gibbs sampler, with emphasis on data augmentation. When applied to a Bayesian missing data problem, the Gibbs sampler produces two natural approximations for the posterior distribution of the parameter vector: the empirical distribution based on the sampled values of the parameter vector, and a mixture of complete data posteriors. We prove that Rao-Blackwellization causes a one-lag delay for the…

最大化熵的有限总体加权抽样AI 解读

Attention is drawn to a method of sampling a finite population of N units with unequal probabilities and without replacement. The method was originally proposed by Stern & Cover (1989) as a model for lotteries. The method can be characterized as maximizing entropy given coverage probabilities πi, or equivalently as having the probability of a selected sample proportional to the product of a set of ‘weights’ wi. We show the essential uniqueness of the wi given the πi. We…