摘要:

Autoregressive (AR) models of orderkare often used for forecasting and control of time series, as well as for the estimation of functionals such as the spectrum. Here we propose a method that consists of calculating the posterior probabilities of the competing AR(k) models in a way that is robust to outliers, and then obtaining the predictive distributions of quantities of interest, such as future observations and the spectrum, as a weighted average of the predictive distributions conditional on each model. This method is based on the idea ofrobust Bayes factors, calculated by replacing the likelihood for the nominal model by arobust likelihood. It draws on and synthesizes several recent research advances, namely robust filtering and the Laplace method for integrals, modified to take account of the finite range of the parameters. The method performs well in simulation experiments and on real and artificial data. Software is available from StatLib.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476669

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

We consider adaptive importance sampling techniques that use kernel density estimates at each iteration as importance sampling functions. These can provide more nearly constant importance weights and more precise estimates of quantities of interest than the sampling importance resampling algorithm when the initial importance sampling function is diffuse relative to the target. We propose a new method that adapts to the varying local structure of the target. When the target has unusual structure, such as strong nonlinear relationships between variables, this method provides estimates with smaller mean squared error than alternative methods.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476670

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

We propose a regression model for binary response data that places no structural restrictions on the link function except monotonicity and known location and scale. Predictors enter linearly. We demonstrate Bayesian inference calculations in this model. By modifying the Dirichlet process, we obtain a natural prior measure over this semiparametric model, and we use Polya sequence theory to formulate this measure in terms of a finite number of unobserved variables. We design a Markov chain Monte Carlo algorithm for posterior simulation and apply the methodology to data on radiotherapy treatments for cancer.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476671

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

I describe a simple procedure for investigating the convergence properties of Markov chain Monte Carlo sampling schemes. The procedure uses coupled chains from the same sampler, obtained by using the same sequence of random deviates for each run. By examining the distribution of the iteration at which all sample paths couple, convergence properties for the system can be established. The procedure also provides a simple diagnostic for detecting modes in multimodal posteriors. Several examples of the procedure are provided. In Ising models, the relation between the correlation parameter and the convergence rate of rudimentary Gibbs samplers is investigated. In another example, the effects of multiple modes on the convergence of coupled paths are explored using mixtures of bivariate normal distributions. The technique is also used to evaluate the convergence properties of a Gibbs sampling scheme applied to a model for rat growth rates.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476672

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

Algorithms for deriving isotonic regression estimators in order-restricted linear models and more generally restricted maximum likelihood estimators are usually quite dependent on the particular problem considered. We propose here an optimization method based on a sequence of formal Bayes estimates whose variances converge to zero. This method, akin to simulated annealing, can be applied “universally”; that is, as long as these Bayes estimators can be derived by exact computation or Markov chain Monte Carlo sampling approximation. We then give an illustration of our method for two real-life examples.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476673

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

Here we use posterior densities based on relative entropy reference priors for two purposes. The first purpose is to identify data implicit in the use of informative priors. We represent an informative prior as the posterior from an experiment with a known likelihood and a reference prior. Minimizing the relative entropy distance between this posterior and the informative prior over choices of data results in a data set that can be regarded as representative of the information in the informative prior. The second implication from reference priors is obtained by replacing the informative prior with a class of densities from which one might wish to make inferences. For each density in this class, one can obtain a data set that minimizes a relative entropy. The maximum of these sample sizes as the inferential density varies over its class can be used as a guess as to how much data is required for the desired inferences. We bound this sample size above and below by other techniques that permit it to be approximated.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476674

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

The problem of designing an optimal experiment for the purpose of performing one or more hypothesis tests is considered. The Bayesian decision theoretic approach is used to arrive at several new optimality criteria for this purpose. For a single hypothesis test, the resulting optimal designs are the well-known φ-optimal designs that minimize the posterior variance of the parameter being tested. For multiple tests, an experimental design must perform well under several competing criteria. Different approaches to achieving this goal are explored, including constrained optimization and an additive weighted loss. The resulting optimality criteria are sensitive not only to the posterior variances of the parameters under test but also to their prior means.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476675

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

Using both frequentist and Bayesian techniques, predicting densities are derived for future observations from a multivariate linear model with matrix normal error terms. All the candidates belong to a general location-scale family of predicting densities. An analytic comparison is undertaken, using a Kullback—Leibler loss, by citing an optimal member of a subclass including most of these predicting densities as members. The subclass is based on an invariant Student-trandom matrix, and the optimal member is the Bayesian predictive density corresponding to a Jeffreys noninformative prior. Information-based numerical comparisons illustrate the nature of the dominance.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476676

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

A flexible method is introduced to model the structure of a covariance matrixCand study the dependence of the covariances on explanatory variables by observing that for any real symmetric matrixA, the matrix exponential transformation,C= exp (A), is a positive definite matrix. Because there is no constraint on the possible values of the upper triangular elements onA, any possible structure of interest can be imposed on them. The method presented here is not intended to replace the existing special models available for a covariance matrix, but rather to provide a broad range of further structures that supplements existing methodology. Maximum likelihood estimation procedures are used to estimate the parameters, and the large-sample asymptotic properties are obtained. A simulation study and two real-life examples are given to illustrate the method introduced.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476677

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

This article presents a new inequality for the multivariate-tdistribution, which implies a new method for multiple comparisons whose foundation rests on a recent inequality due to Naiman. The new method is promising in view of the fact that it utilizes information (estimator intercorrelations) ignored by the most widely used multiple comparison methods yet is not computationally prohibitive, requiring only the numerical evaluation of a single one-dimensional integral. In this article the validity of the new method in the normal-theoretic general linear model is established, and efficiency studies relative to the methods of Scheffé, Bonferroni, Šidák, and Hunter-Worsley are presented. The new method is shown to always improve on Scheffé's method. The new method is also shown to perform well; that is, to lead to a smaller critical point than its competitors, with low degrees of freedom. But the method is not as efficient as the Hunter-Worsley method for high degrees of freedom. In addition, the method appears to increase in relative efficiency as the number of comparisons increases relative to the rank of the correlation matrix of the estimators.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476678

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor