摘要:

A scheme is presented for modeling and local computation of exact probabilities, means, and variances for mixed qualitative and quantitative variables. The models assume that the conditional distribution of the quantitative variables, given the qualitative, is multivariate Gaussian. The computational architecture is set up by forming a tree of belief universes, and the calculations are then performed by local message passing between universes. The asymmetry between the quantitative and qualitative variables sets some additional limitations for the specification and propagation structure. Approximate methods when these are not appropriately fulfilled are sketched. It has earlier been shown how to exploit the local structure in the specification of a discrete probability model for fast and efficient computation, thereby paving the way for exploiting probability-based models as parts of realistic systems for planning and decision support. The purpose of this article is to extend this computational scheme to networks, where some vertices represent entities that are measured on a quantitative and some on a qualitative scale. An extension has the advantage of unifying several known techniques, but allows more flexible and faithful modeling and speeds computation as well. To handle this more general case, the properties of (CG) conditional Gaussian distributions are exploited. A fictitious but simple example is used for illustration throughout the paper, concerned with monitoring emissions from a waste incinerator. From optical measurements of the darkness of the smoke, the concentration of CO2—which are both on a continuous scale—and possible knowledge about qualitative characteristics such as the type of waste burned, one wants to infer about the state of the incinerator and the current emission of heavy metals.

ISSN:0162-1459    

DOI:10.1080/01621459.1992.10476265

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

A Bayes network is a directed acyclic graph in which the links are quantified by fixed conditional probabilities and the nodes represent random variables. The primary use of the network is to provide an efficient method for updating conditional probabilities in the graph. We consider the consequences of using the network as the computational device for updating parameter estimates in the dynamic linear model, a discrete time Bayesian model. We show that using the network characterizes the dynamic linear model and its computations in a unified way. The generality of the network permits nonsequential data collection and thereby provides a straightforward method of incorporating delayed data. An on-line diagnostic is offered to complement the conventional forecast error and an approximation to the posterior distribution is proposed. Algorithms for data propagation in multivariate Gaussian causal trees are presented.

ISSN:0162-1459    

DOI:10.1080/01621459.1992.10476266

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

Beginning with a finite population of units and the judgment of exchangeability for units with respect to lifetime, we argue that measures of similarity lead to the appropriate probabilistic models for aging. This in turn implies that Schur-concavity of the joint probability function (or, more generally, the joint survival distribution) provides the correct probabilistic description of aging. Following this argument and using the principle of indifference, we argue that the appropriate probability models for life distributions conditional onaverage lifeare in a family of distributions that we call thegeneralized gamma distributions. If, on the other hand, we are interested in probabilistic models for aging conditional on averagelifetime maintenance cost, it follows from our development thatgeneralized Weibulldistributions are appropriate.

ISSN:0162-1459    

DOI:10.1080/01621459.1992.10476267

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

Consider a natural exponential family parameterized byθ. It is well known that the standard conjugate prior onθis characterized by a condition of posterior linearity for the expectation of the model mean parameterμ. Often, however, this family is not parameterized in terms ofθbut rather in terms of a more usual parameter, such at the meanμ. The main question we address is: Under what conditions does astandard conjugate prior on μinduce a linear posterior expectation onμitself? We prove that essentially this happens iff the exponential family has quadratic variance function. A consequence of this result is that the standard conjugate onμcoincides with the prior onμinduced by the standard conjugate onθiff the variance function is quadratic. The rest of the article covers more specific issues related to conjugate priors for exponential families. In particular, we analyze the monotonicity of the expected posterior variance forμwith respect to the sample size and the hyperparameter “prior sample size” that appears in the conjugate distribution. Finally, we consider a situation in which a class of priors onθ, say Γ, is specified by some moment conditions. We revisit and extend previous results relating conjugate priors to Γ-least favorable distributions and Γ-minimax estimators.

ISSN:0162-1459    

DOI:10.1080/01621459.1992.10476268

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

Choosing the largest of several means can be a demanding problem, especially in the presence of a covariate. A hierarchical Bayesian approach to ranking and selection, as well as estimation of related means in the presence of a covariate, is considered. For the multiple slopes model we compute, in addition to the posterior means and standard deviations of the parameters, the posterior probabilities that each mean, at a given value of the covariate, is the largest. The vector of posterior probabilities thus obtained provides an easily understandable answer to the selection problem. Although calculation of the posterior probabilities may involve four-dimensional numerical integration in the difficult unbalanced design and unknown variance case, an efficient Monte Carlo method of evaluation has been developed and is given in the article. By reanalyzing a well-known data set on the breaking strength and thickness of starch films, we illustrate how our Bayesian approach produces meaningful conclusions, some of which would perhaps be difficult to obtain otherwise. For the starch film example, we found that it took only 1.4 seconds to compute the quantities of interest using an IBM 3090–600S machine. Because the computation time is quite small, it is apparent that the Bayesian procedure can be implemented for everyday use.

ISSN:0162-1459    

DOI:10.1080/01621459.1992.10476269

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

Three multivariate “one-sided” testing problems are studied. All problems concern A: independent normal populations with unknown means and common unknown variance. For the first problem the null hypothesis is that all means are zero while the alternative is that each mean is nonnegative and at least one is positive. For the second problem the null hypothesis is that all means are equal and the alternative is that all of the first (k-1) means are greater than or equal to the mean of the last population (with strict inequality for at least one). The alternative for the second problem is called the “tree-top” alternative. For the third problem the null hypothesis is that all means are equal while the alternative is that the means are ordered, say nonincreasing. This latter alternative is called the “simple order” alternative. All three of these problems are discussed extensively in the book by Robertson, Wright, and Dykstra. We will assume that random samples of sizenare drawn from each population although our results will hold if unequal sample sizes are drawn. For the first problem we will prove that tests of every size (with one exception) based on the maximum modulus statistic (properly normalized by the usual estimate of the standard deviation) are inadmissible. For the second problem we prove that all contrast type tests (normalized by the usual estimate of the standard deviation) are inadmissible for all sizes but one. For the third problem we prove that the one sided range test as well as others recommended in the literature are inadmissible. In all three problems better tests are offered and the amount of improvement is studied.

ISSN:0162-1459    

DOI:10.1080/01621459.1992.10476270

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

Goodness-of-fit tests for independent multinomials with parameters to be estimated are usually based on Pearson'sX2or the likelihood ratioG2. Both are included in the family of power-divergence statisticsSDλ. For increasing sample sizes eachSDλhas an asymptoticX2distribution, provided that the number of cells remains fixed. We are dealing with an increasing-cells approach, where the numberJof independent multinomials increases while the number of classes for each multinomial and the number of parameters remain fixed. Extending results onX2andG2, the asymptotic normality of anySDλis obtained for increasing cells. The corresponding normal goodness-of-fit tests discussed here apply for models with large degrees of freedom with no restrictions imposed on the sizesNjof each multinomial, allowing large as well as small expectations (sparse data) within each cell. The asymptotic expectation and variance ofSDλare easy to compute for Pearson'sX2and simplify considerably for general λ if the harmonic or arithmetic mean of the multinomial sizesNjare large. Applications to quantal response models for binomial data are treated in more detail. It turns out that the asymptotic expectation and variance ofX2andG2agree to first order with the conditional moments given the estimated parameters. And for binary data (withNj= 1 for allj), the goodness-of-fit tests appear as score tests with respect to an enlarged model. Our presentation focuses on general aspects of the tests and its applications rather than on formal proofs for the underlying limit results, which are only outlined here.

ISSN:0162-1459    

DOI:10.1080/01621459.1992.10476271

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

When the choice of estimator for the coefficients in a linear regression model is determined by the outcome of a prior test of the validity of restrictions on the model, it is well known that a minimax (risk) regret criterion leads to the simple rule that the optimal critical value for the preliminary test is approximately two in value, regardless of the degrees of freedom. We show that this result no longer holds in the (likely) event that relevant regressors are excluded from the model at the outset.

ISSN:0162-1459    

DOI:10.1080/01621459.1992.10476272

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

A class of multidimensional designs is presented for factorial experiments with two treatment factors and two or more orthogonal blocking factors. We assume that interactions between all factors, except for the two treatment factors, are negligible. A table of efficient three-dimensional designs is given together with tables of component designs that can be used to construct two-, three-, or higher-dimensional designs. All the multidimensional designs considered in this article haved> 2 crossed orthogonal blocking factors and exactly one treatment combination observed at each combination of levels of the blocking factors. They are constructed by amalgamating one-dimensional generalized cyclic designs with known properties. The purpose of this article is to increase the availability of multidimensional designs, three-dimensional designs in particular. Our main objective is to achieve efficient estimation of the factorial effects via least squares estimators that are uncorrelated after adjustment for fixed-block effects; that is, we require designs withorthogonal factorial structure. This property is guaranteed for thed-dimensional designs considered in this article. Several tables of designs are given. The first lists a selection of efficient three-dimensional designs together with their generalized cyclic components and their efficiency factors. The remaining tables list generalized cyclic block designs that can be used either as (one-dimensional) block designs or chosen for amalgamation into a multidimensional design. The multidimensional designs can be constructed so that they possess the property ofadjusted orthogonalityof the block effects after adjusting for the treatment effects. This property allows its factorial efficiency factors to be calculated simply from the factorial efficiency factors of its component designs.

ISSN:0162-1459    

DOI:10.1080/01621459.1992.10476273

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

Predictive regression estimators using functions of the probability of selectionπi, as covariates are studied as an alternative to classicalp-weighting estimators for the finite population mean in complex sample surveys. Variance estimators are developed based on the relationship var(yi|πi), wherey, is the response andπiis the probability of selection. Extensions to cluster sample designs are outlined, and an example is given from the National Educational Longitudinal Survey of 1988.

ISSN:0162-1459    

DOI:10.1080/01621459.1992.10476274

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor