摘要:

General methods are provided for analyzing the convergence of discrete-time, general state-space Markov chains, such as those used in stochastic simulation algorithms including the Gibbs sampler. The methods provide rigorous, a priori bounds on how long these simulations should be run to give satisfactory results. Results are applied to two models of the Gibbs sampler: a bivariate normal model, and a hierarchical Poisson model (with gamma conditionals). The methods use the notion ofminorization conditionsfor Markov chains.

ISSN:0162-1459    

DOI:10.1080/01621459.1995.10476548

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

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 asblind deconvolutionin 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 and can be used in real time signal restoration. Two simulated systems are studied to illustrate the proposed method. Our result shows that the ideas of multiple imputations and flexible simulation techniques are as powerful in engineering as in survey sampling.

ISSN:0162-1459    

DOI:10.1080/01621459.1995.10476549

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

We describe and illustrate Bayesian inference in models for density estimation using mixtures of Dirichlet processes. These models provide natural settings for density estimation and are exemplified by special cases where data are modeled as a sample from mixtures of normal distributions. Efficient simulation methods are used to approximate various prior, posterior, and predictive distributions. This allows for direct inference on a variety of practical issues, including problems of local versus global smoothing, uncertainty about density estimates, assessment of modality, and the inference on the numbers of components. Also, convergence results are established for a general class of normal mixture models.

ISSN:0162-1459    

DOI:10.1080/01621459.1995.10476550

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

Two reference priors for the product of means ofnnormal distributions with common known variance are developed. One of them induces an improper posterior distribution and therefore is not of much interest. The other is a generalized form of then= 2 case derived by Berger and Bernardo. The latter is compared with the uniform prior (the Jeffreys prior) in posterior inference and the optimal frequentist coverage criterion. The reference prior is shown to be better than the uniform prior in the sense of correct frequentist coverage probability of the posterior quantile, by numerical computation. The computation was performed by Gibbs sampling forn= 3 andn= 10. Furthermore, it is shown that the reference prior is among the asymptotic optimal frequentist coverage probability priors under a transformation of the parameter space such that the parameter of interest and the nuisance parameters are orthogonal. In an example, the Bayesian credible interval for the product of normal means using the reference prior is compared to the confidence interval using the method of Yfantis and Flatman.

ISSN:0162-1459    

DOI:10.1080/01621459.1995.10476551

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

Expert opinion is often sought with regard to unknowns in a decision-making setting. For a univariate unknown, θ, our presumption is that such opinion is elicited as a partial probabilistic specification in the form of either probability assignments regarding the chance of θ falling in a fixed set of disjoint exhaustive intervals or selected quantiles for θ. Treating such specification as “data,” our focus is on the development of suitable probability densities for these data given the true θ. In particular, we advocate a rich class of densities created by transformation of random mixtures of beta distributions. These densities become likelihoods when viewed as a function of θ given the data. We presume that a decision-maker (here a so-called supra Bayesian) presides over the opinion collection, offering his or her assessment as well. All of this opinion is synthesized using Bayes's theorem, resulting in the posterior distribution as the pooling mechanism. The models are applied to opinion collected regarding points per game for participants in the 1991 National Basketball Association championship basketball series.

ISSN:0162-1459    

DOI:10.1080/01621459.1995.10476552

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

Very little work on stable distribution parameter estimation and inference appears in the literature due to the nonexistence of the probability density function. This has led in particular to a dearth of Bayesian work in this area. But Bayesian computation via Markov chain Monte Carlo allows us to sample from the distribution of the parameters of the stable distributions, by exploiting a particular mathematical representation involving the stable density.

ISSN:0162-1459    

DOI:10.1080/01621459.1995.10476553

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

We present a simple method for computing Bayes factors. The method derives from observing that in general, a Bayes factor can be written as the product of a quantity called the Savage-Dickey density ratio and a correction factor; both terms are easily estimated from posterior simulation. In some cases it is possible to do these computations without ever evaluating the likelihood.

ISSN:0162-1459    

DOI:10.1080/01621459.1995.10476554

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

Variable selection is ubiquitous in statistical practice. Forward selection, backwards elimination, or a combination thereof are among the most popular techniques. Statistical texts teach direct interpretation of coefficients after variable selection. For scientific purposes, the desired interpretation is unconditional on the variable selection. In this article an influence analysis of variable selection is performed from a Bayesian viewpoint. Variable selection is shown to be surprisingly influential. A new statistic is recommended for routine examination during variable selection.

ISSN:0162-1459    

DOI:10.1080/01621459.1995.10476555

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

In the usual, countably additive definition of probability, it is not possible to have a distribution giving equal probabilities to every one of the natural numbers. Yet such a distribution would be interesting and potentially useful. This article considers an approach to this problem based on finitely additive probability. We give a necessary and sufficient condition for when specifications of the probabilities of an arbitrary collection of subsets of a space Ω can be extended to define a finitely additive probability on all the subsets of Ω. This is applied to probability statements modeling the uniform distribution on the natural numbers, using relative frequencies and residue classes to make precise notions of uniformity. Tight bounds are given on the possible values of the probability of an arbitrary set under both interpretations. These bounds are applied to several sets of interest.

ISSN:0162-1459    

DOI:10.1080/01621459.1995.10476556

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

We propose modified exact inferential methods for contingency tables. Ordinary “exact” inference is conservative, because of the discreteness. For estimating a common odds ratio in several 2 × 2 tables, two modifications of the ordinary “exact” confidence interval maintain at least a fixed confidence level but tend to be much narrower. One approach inverts results of a test with a modifiedPvalue utilizing the test statistic and table probabilities. The second approach inverts one two-sided test rather than two one-sided tests. This approach is much less conservative when the true odds ratio is relatively small or large. We also generalize results of Cohen and Sackrowitz and relate modifiedPvalues to construction of exact, unbiased, and admissible tests for an ordinal alternative to conditional independence.

ISSN:0162-1459    

DOI:10.1080/01621459.1995.10476557

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor