Bayesian inference for the multinomial probit model, using the Gibbs sampler with data augmentation, has been recently considered by some authors. The present paper introduces a modification of the sampling technique,...
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Bayesian inference for the multinomial probit model, using the Gibbs sampler with data augmentation, has been recently considered by some authors. The present paper introduces a modification of the sampling technique, by defining a hybrid Markov chain in which, after each Gibbs sampling cycle, a metropolis step is carried out along a direction of constant likelihood. Examples with simulated data sets motivate and illustrate the new technique. A proof of the ergodicity of the hybrid Markov chain is also given.
This paper deals with the analysis of multivariate survival data from a Bayesian perspective using Markov-chain Monte Carlo methods. The metropolis along with the Gibbs algorithm is used to calculate same of the margi...
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This paper deals with the analysis of multivariate survival data from a Bayesian perspective using Markov-chain Monte Carlo methods. The metropolis along with the Gibbs algorithm is used to calculate same of the marginal posterior distributions. A multivariate survival model is proposed, since survival times within the same group are correlated as a consequence of a frailty random block effect. The conditional proportional-hazards model of Clayton and Cuzick is used with a martingale structured prior process (Arjas and Gasbarra) for the discretized baseline hazard. Besides the calculation of the marginal posterior distributions of the parameters of interest, this paper presents some Bayesian EDA diagnostic techniques to detect model adequacy. The methodology is exemplified with kidney infection data where the times to infections within the same patients are expected to be correlated.
metropolis algorithms along with Gibbs steps are proposed to perform a Bayesian analysis for the Block and Basu (ACBVE) bivariate exponential distribution. We also consider the use of Gibbs sampling to develop Bayesia...
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metropolis algorithms along with Gibbs steps are proposed to perform a Bayesian analysis for the Block and Basu (ACBVE) bivariate exponential distribution. We also consider the use of Gibbs sampling to develop Bayesian inference for accelerated life tests assuming a power rule model and the ACBVE distribution. The methodology developed in this paper is exemplified with two examples.
The threshold autoregressive (TAR) model is generalized which results in more flexibility in applications. We construct a Bayesian framework to show that Markov chain Monte Carlo method can be applied to estimating pa...
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The threshold autoregressive (TAR) model is generalized which results in more flexibility in applications. We construct a Bayesian framework to show that Markov chain Monte Carlo method can be applied to estimating parameters with success. (C) 1998 Elsevier Science B.V. All rights reserved.
We study the problem of simulating a class of Gibbs random field models, called morphologically constrained Gibbs random fields, using Markov chain Monte Carlo sampling techniques. Traditional single site updating Mar...
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ISBN:
(纸本)0819429147
We study the problem of simulating a class of Gibbs random field models, called morphologically constrained Gibbs random fields, using Markov chain Monte Carlo sampling techniques. Traditional single site updating Markov chain Monte Carlo sampling algorithms, like the metropolis algorithm, tend to converge extremely slowly when used to simulate these models, particularly at low temperatures and for constraints involving large geometrical shapes. Moreover, the morphologically constrained Gibbs random fields are not, in general, Markov. Hence, a Markov chain Monte Carlo sampling algorithm based on the Gibbs sampler is not possible. We propose a variant of the metropolis algorithm that, at each iteration, allows multi-site updating and converges substantially faster than the traditional single-site updating algorithm. The set of sites that are updated at a particular iteration is specified in terms of a shape parameter and a size parameter. Computation of the acceptance probability involves a "test ratio," which requires computation of the ratio of the probabilities of the current and new realizations. Because of the special structure of our energy function, this computation can be done by means of a simple local iterative procedure. Therefore, lack of Markovianity does not impose any additional computational burden for model simulation. The proposed algorithm has been used to simulate a number of image texture models, both synthetic and natural.
Here I propose a convergence diagnostic for Markov chain Monte Carlo (MCMC) algorithms based on couplings of a Markov chain with an auxiliary chain that is periodically restarted from a fixed parameter value. The diag...
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Here I propose a convergence diagnostic for Markov chain Monte Carlo (MCMC) algorithms based on couplings of a Markov chain with an auxiliary chain that is periodically restarted from a fixed parameter value. The diagnostic provides a mechanism for estimating the specific constants governing the rate of convergence of geometrically and uniformly ergodic chains, and provides a lower bound on the effective sample size of a MCMC run. It also provides a simple procedure for obtaining what is, with high probability, an independent sample from the stationary distribution.
This article proposes a Bayesian procedure for simultaneous identification of the Kronecker indices and model parameters of a multivariate linear system. The model parameters include the starting values and innovation...
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This article proposes a Bayesian procedure for simultaneous identification of the Kronecker indices and model parameters of a multivariate linear system. The model parameters include the starting values and innovations of the system so that the series considered may be co-integrated or non-invertible. The procedure uses some recent developments in stochastic search variable selection in linear regression analysis and Markov chain Monte Carlo methods in statistical computing. It also takes into consideration the row structure of a vector model implied by the Kronecker indices. Comparison with other existing methods is discussed. Simulated and real examples are used to illustrate the proposed procedure.
This paper considers the problem of scaling the proposal distribution of a multidimensional random walk metropolis algorithm in order to maximize the efficiency of the algorithm. The main result is a weak convergence ...
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This paper considers the problem of scaling the proposal distribution of a multidimensional random walk metropolis algorithm in order to maximize the efficiency of the algorithm. The main result is a weak convergence result as the dimension of a sequence of target densities, n, converges to infinity. When the proposal variance is appropriately scaled according to n, the sequence of stochastic processes formed by the first component of each Markov chain converges to the appropriate limiting Langevin diffusion process. The limiting diffusion approximation admits a straightforward efficiency maximization problem, and the resulting asymptotically optimal policy is related to the asymptotic acceptance rate of proposed moves for the algorithm. The asymptotically optimal acceptance rate is 0.234 under quite general conditions. The main result is proved in the case where the target density has a symmetric product form. Extensions of the result are discussed.
In this paper, we propose a general model-determination strategy based on Bayesian methods for nonlinear mixed effects models. Adopting an exploratory data analysis viewpoint, we develop diagnostic tools based on cond...
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In this paper, we propose a general model-determination strategy based on Bayesian methods for nonlinear mixed effects models. Adopting an exploratory data analysis viewpoint, we develop diagnostic tools based on conditional predictive ordinates that conveniently get tied in with Markov chain Monte Carlo fitting of models. Sampling-based methods are used to carry out these diagnostics. Two examples are presented to illustrate the effectiveness of these criteria. The first one is the famous Langmuir equation, commonly used in pharmacokinetic models, whereas the second model is used in the growth curve model for longitudinal data.
this article we adopt Baddeley's delta metric as a loss function in Bayesian image restoration and classification. We develop a new algorithm that allows us to approximate the corresponding optimal Bayesian estima...
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this article we adopt Baddeley's delta metric as a loss function in Bayesian image restoration and classification. We develop a new algorithm that allows us to approximate the corresponding optimal Bayesian estimator. With this algorithm good practical estimates can be obtained at approximately the same computational cost as traditional estimators like the marginal posterior mode (MPM). A comparison of our proposed classification with MPM shows significant advantages, especially with respect to fine structures.
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