We present a complete Bayesian treatment of autoregressive model estimation incorporating choice of autoregressive order, enforcement of stationarity, treatment of outliers, and allowance for missing values and multip...
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We present a complete Bayesian treatment of autoregressive model estimation incorporating choice of autoregressive order, enforcement of stationarity, treatment of outliers, and allowance for missing values and multiplicative seasonality. The paper makes three distinct contributions. First, we enforce the stationarity conditions using a very efficient metropolis-within-Gibbs algorithm to generate the partial autocorrelations. Second we show how to carry out the Gibbs sampler when the autoregressive order is unknown. Third, we show how to combine the various aspects of fitting an autoregressive model giving a more comprehensive and efficient treatment than previous work. We illustrate our methodology with a real example.
This paper addresses the problem of locating two straight and parallel road edges in images that are acquired from a stationary millimeter-wave radar platform positioned near ground-level. A fast, robust, and complete...
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This paper addresses the problem of locating two straight and parallel road edges in images that are acquired from a stationary millimeter-wave radar platform positioned near ground-level. A fast, robust, and completely data-driven Bayesian solution to this problem is developed, and it has applications in automotive vision enhancement. The method employed in this paper makes use of a deformable template model of the expected road edges, a two-parameter lognormal model of the ground-level millimeter-wave (GLEM) radar imaging process, a maximum a posteriori (MAP) formulation of the straight edge detection problem, and a Monte Carlo algorithm to maximize the posterior density. Experimental results are presented by applying the method on GLEM radar images of actual roads. The performance of the method is assessed against ground truth for a variety of road scenes.
We examine a number of models that generate random fractals. The models are studied using the tools of computational complexity theory from the perspective of parallel computation. Diffusion-limited aggregation and se...
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We examine a number of models that generate random fractals. The models are studied using the tools of computational complexity theory from the perspective of parallel computation. Diffusion-limited aggregation and several widely used algorithms for equilibrating the Ising model are shown to be highly sequential;it is unlikely they can be simulated efficiently in parallel. This is in contrast to Mandelbrot percolation, which can be simulated in constant parallel time. Our research helps shed light on the intrinsic complexity of these models relative to each other and to different growth processes that have been recently studied using complexity theory. In addition, the results may serve as a guide to simulation physics.
Geman and Reynolds [7] present an approach to linear image restoration which provides for recovery of horizontal and vertical gray-level discontinuities from blurred and noisy observations. We extend their model and p...
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Geman and Reynolds [7] present an approach to linear image restoration which provides for recovery of horizontal and vertical gray-level discontinuities from blurred and noisy observations. We extend their model and parameter selection method to include diagonal discontinuities. A hazard of this modeling approach is identified and addressed. We also comment on the truncated Gibbs sampler suggested in the paper [7].
Consider the exchangeable Bayesian hierarchical model where observations y(i) are independently distributed from sampling densities with unknown means, the means mu(i) are a random sample from a distribution g, and th...
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Consider the exchangeable Bayesian hierarchical model where observations y(i) are independently distributed from sampling densities with unknown means, the means mu(i) are a random sample from a distribution g, and the parameters of g are assigned a known distribution h. A simple algorithm is presented for summarizing the posterior distribution based on Gibbs sampling and the metropolis algorithm. The software program Matlab is used to implement the algorithm and provide a graphical output analysis. An binomial example is used to illustrate the flexibility of modeling possible using this algorithm. Methods of model checking and extensions to hierarchical regression modeling are discussed.
In this paper we obtain bounds on the spectral gap of the transition probability matrix of Markov chains associated with the metropolis algorithm and with the Gibbs sampler. In both cases we prove that, for small valu...
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In this paper we obtain bounds on the spectral gap of the transition probability matrix of Markov chains associated with the metropolis algorithm and with the Gibbs sampler. In both cases we prove that, for small values of T, the spectral gap is equal to 1 A2, where A2 is the second largest eigenvalue of P. In the case of the metropolis algorithm we give also two examples in which the spectral gap is equal to 1 Amm, where Amu., is the smallest eigenvalue of P. Furthermore we prove that random updating dynamics on sites based on the metropolis algorithm and on the Gibbs sampler have the same rate of convergence at low temperatures. The obtained bounds are discussed and compared with those obtained with a different approach.
作者：
Lim, HABioinformatics
HYSEQ Inc. 670 Almanor Avenue Sunnyvale California 94086 USA
Mathematical and numerical models for studying the electrophoresis of topologically nontrivial molecules in two and three dimensions are presented. The molecules are modeled as polygons residing on a square lattice an...
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Mathematical and numerical models for studying the electrophoresis of topologically nontrivial molecules in two and three dimensions are presented. The molecules are modeled as polygons residing on a square lattice and a cubic lattice whereas the electrophoretic media of obstacle network are simulated by removing vertices from the lattices at random. The dynamics of the polymeric molecules are modeled by configurational readjustments of segments of the polygons. Configurational readjustments arise from thermal fluctuations and they correspond to piecewise reptation in the simulations. A metropolis algorithm is introduced to simulate these dynamics, and the algorithms are proven to be reversible and ergodic. Monte Carlo simulations of steady field random obstacle electrophoresis are performed and the results are presented.
Gibbs sampling is a powerful technique for statistical inference. It involves little more than sampling from full conditional distributions, which can be both complex and computationally expensive to evaluate. Gilks a...
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Gibbs sampling is a powerful technique for statistical inference. It involves little more than sampling from full conditional distributions, which can be both complex and computationally expensive to evaluate. Gilks and Wild have shown that in practice full conditionals are often log-concave, and they proposed a method of adaptive rejection sampling for efficiently sampling from univariate log-concave distributions. In this paper, to deal with non-log-concave full conditional distributions, we generalize adaptive rejection sampling to include a Hastings-metropolis algorithm step. One important field of application in which statistical models may lead to non-log-concave full conditionals is population pharmacokinetics. Here, the relationship between drug dose and blood or plasma concentration in a group of patients typically is modelled by using non-linear mixed effects models. Often, the data used for analysis are routinely collected hospital measurements, which tend to be noisy and irregular. Consequently, a robust (t-distributed) error structure is appropriate to account for outlying observations and/or patients. We propose a robust non-linear full probability model for population pharmacokinetic data. We demonstrate that our method enables Bayesian inference for this model. through an analysis of antibiotic administration in new-born babies.
Markov chain Monte Carlo methods have been increasingly popular since their introduction by Gelfand and Smith. However, while the breadth and variety of Markov chain Monte Carlo applications are properly astounding, p...
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Markov chain Monte Carlo methods have been increasingly popular since their introduction by Gelfand and Smith. However, while the breadth and variety of Markov chain Monte Carlo applications are properly astounding, progress in the control of convergence for these algorithms has been slow, despite its relevance in practical implementations. We present here different approaches toward this goal based on functional and mixing theories, while paying particular attention to the central limit theorem and to the approximation of the limiting variance. Renewal theory in the spirit of Mykland, Tierney and Yu is presented as the most promising technique in this regard, and we illustrate its potential in several examples. In addition, we stress that many strong convergence properties can be derived from the study of simple subchains which are produced by Markov chain Monte Carlo algorithms, due to a duality principle obtained in Diebolt and Robert for mixture estimation. We show here the generality of this principle which applies, for instance, to most missing data models. A more empirical stopping rule for Markov chain Monte Carlo algorithms is related to the simultaneous convergence of different estimators of the quantity of interest. Besides the regular ergodic average,we propose the Rao-Blackwellized version as well as estimates based on importance sampling and trapezoidal approximations of the integrals.
Markov chain sampling has recently received considerable attention, in particular in the context of Bayesian computation and maximum likelihood estimation. This article discusses the use of Markov chain splitting, ori...
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Markov chain sampling has recently received considerable attention, in particular in the context of Bayesian computation and maximum likelihood estimation. This article discusses the use of Markov chain splitting, originally developed for the theoretical analysis of general state-space Markov chains, to introduce regeneration into Markov chain samplers. This allows the use of regenerative methods for analyzing the output of these samplers and can provide a useful diagnostic of sampler performance. The approach is applied to several samplers, including certain metropolis samplers that can be used on their own or in hybrid samplers, and is illustrated in several examples.
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