We analyze the convergence to stationarity of a simple nonreversible Markov chain that serves as a model for several nonreversible Markov chain sampling methods that are used in practice. Our theoretical and numerical...
详细信息
We analyze the convergence to stationarity of a simple nonreversible Markov chain that serves as a model for several nonreversible Markov chain sampling methods that are used in practice. Our theoretical and numerical results show that nonreversibility can indeed lead to improvements over the diffusive behavior of simple Markov chain sampling schemes. The analysis uses both probabilistic techniques and an explicit diagonalization.
We describe a Bayesian method based on Markov chain simulation to study the phylogenetic relationship in a group of DNA sequences. Under simple models of mutational events, our method produces a Markov chain whose sta...
详细信息
We describe a Bayesian method based on Markov chain simulation to study the phylogenetic relationship in a group of DNA sequences. Under simple models of mutational events, our method produces a Markov chain whose stationary distribution is the conditional distribution of the phylogeny given the observed sequences. Our algorithm strikes a reasonable balance between the desire to move globally through the space of phylogenies and the need to make computationally feasible moves in areas of high probability. Because phylogenetic information is described by a tree, we have created new diagnostics to handle this type of data structure. An important byproduct of the Markov chain Monte Carlo phylogeny building technique is that it provides estimates and corresponding measures of variability foranyaspect of the phylogeny under study.
In this paper, we describe Bayesian modeling of dependent multivariate survival data using positive stable frailty distributions. A flexible baseline hazard formulation using a piecewise exponential model with a corre...
详细信息
In this paper, we describe Bayesian modeling of dependent multivariate survival data using positive stable frailty distributions. A flexible baseline hazard formulation using a piecewise exponential model with a correlated prior process is used. The estimation of the stable law parameter together with the parameters of the (conditional) proportional hazards model is facilitated by a modified Gibbs sampling procedure. The methodology is illustrated on kidney infection data (McGilchrist and Aisbett, 1991).
Bayesian inference for the superposition of nonhomogeneous Poisson processes is studied. A Markov-chain Monte Carlo method with data augmentation is developed to compute the features of the posterior distribution. For...
详细信息
Bayesian inference for the superposition of nonhomogeneous Poisson processes is studied. A Markov-chain Monte Carlo method with data augmentation is developed to compute the features of the posterior distribution. For each observed failure epoch, a latent variable is introduced that indicates which component of the superposition model gives rise to the failure. This data-augmentation approach facilitates specification of the transitional kernel in the Markov chain. Moreover, new Bayesian tests are developed for the full superposition model against simpler submodels. Model determination by a predictive likelihood approach is studied. A numerical example based on a real data set is given.
A new class of Gibbs random fields (GRFs) is proposed capable of modeling geometrical constraints in images by means of mathematical morphology. The proposed models, known as morphologically constrained GRFs, model im...
详细信息
A new class of Gibbs random fields (GRFs) is proposed capable of modeling geometrical constraints in images by means of mathematical morphology. The proposed models, known as morphologically constrained GRFs, model images by means of their size density. Since the size density is a multiresolution statistical summary morphologically constrained GRFs explicitly incorporate multiresolution information into image modeling. Important properties are studied and their implication to texture synthesis and analysis is discussed. For morphologically constrained GRFs to be useful in practice, it is important that an efficient technique is available for fitting these models to real data. It is shown that, at low enough temperatures and under a natural condition, the maximum-likelihood estimator of the morphologically constrained GRF parameters can be approximated by means of an important tool of mathematical morphology known as the pattern spectrum. Therefore, statistical inference can he easily implemented by means of mathematical morphology. This allows the design of a, computationally simple morphological Bayes classifier which produces excellent results in classifying natural textures.
Electrostatic interactions have important effects on the physical properties of macromolecules such as DNA. DNA modeled as simple polyelectrolyte contain monomers with the same charge which can effectively attract eac...
详细信息
Electrostatic interactions have important effects on the physical properties of macromolecules such as DNA. DNA modeled as simple polyelectrolyte contain monomers with the same charge which can effectively attract each other due to electrostatic ion-ion correlations. This explains the phenomenon known as DNA condensation. The condensation of DNA in vitro can be induced by a number of small polyvalent ions and by lowering the dielectric constant.
This paper presents a method for Bayesian inference for the regression parameters in a linear model with independent and identically distributed errors that does not require the specification of a parametric family of...
详细信息
This paper presents a method for Bayesian inference for the regression parameters in a linear model with independent and identically distributed errors that does not require the specification of a parametric family of densities for the error distribution. This method first selects a nonparametric kernel density estimate of the error distribution which is unimodal and based on the least-squares residuals. Once the error distribution is selected, the. metropolis algorithm is used to obtain the marginal posterior distribution of the regression parameters. The methodology is illustrated with data sets, and its performance relative to standard Bayesian techniques is evaluated using simulation results.
Maximum pseudo-likelihood estimation has hitherto been viewed as a practical but flawed alternative to maximum likelihood estimation, necessary because the maximum likelihood estimator is too hard to compute, but flaw...
详细信息
Maximum pseudo-likelihood estimation has hitherto been viewed as a practical but flawed alternative to maximum likelihood estimation, necessary because the maximum likelihood estimator is too hard to compute, but flawed because of its inefficiency when the spatial interactions are strong. We demonstrate that a single Newton-Raphson step starting from the maximum pseudo-likelihood estimator produces an estimator which is close to the maximum likelihood estimator in terms of its actual value, attained likelihood, and efficiency, even in the presence of strong interactions. This hybrid technique greatly increases the practical applicability of pseudo-likelihood-based estimation. Additionally, in the case of the spatial point processes, we propose a proper maximum pseudo-likelihood estimator which is different from the conventional one. The proper maximum pseudo-likelihood estimator clearly shows better performance than the conventional one does when the spatial interactions are strong.
We propose an unobserved-component time series model of gross domestic product that includes Markov switching as an unobserved component. In addition to a trend component, the model has two time-varying drift componen...
详细信息
We propose an unobserved-component time series model of gross domestic product that includes Markov switching as an unobserved component. In addition to a trend component, the model has two time-varying drift components. One drift represents the expected rate of growth during recession;the other drift represents the expected rate during expansion. Estimates indicate a substantial decline in the latter annual rate for the United States from 6.4% in 1950 to 3.6% by 1990. We have employed weak priors based on prewar data. The estimation makes use of the Gibbs sampler and the metropolis algorithm.
This paper analyzes the performance of importance sampling distributions for computing expectations with respect to a whole family of probability laws in the context of Markov chain Monte Carlo simulation methods. Mot...
详细信息
This paper analyzes the performance of importance sampling distributions for computing expectations with respect to a whole family of probability laws in the context of Markov chain Monte Carlo simulation methods. Motivations for such a study arise in statistics as well as in statistical physics. Two choices of importance sampling distributions are considered in detail: mixtures of the distributions of interest and distributions that are "uniform over energy levels" (motivated by physical applications). We analyze two examples, a "witch's hat" distribution and the mean field Ising model, to illustrate the advantages that such simulation procedures are expected to offer in a greater generality. The connection with the recently proposed simulated tempering method is also examined.
暂无评论