A bayesian approach to prediction in the presence of spurious observations for several models

The problem of spuriousity has been dealt with from a Bayesian perspective by, among others, Box and Taio (1968) and in several papers by Guttman with various co-authors, beginning with Guttman (1973), The main objective of these papers has been to obtain posterior distributions of parameters, and to base inference on these distributions. In the current paper, the Bayesian argument is carried one step further by deriving predictive distributions of future observations. Inferences are then based on these distributions. We will obtain predictive results for several models, First, we consider the univariate normal case with one spurious observation, This is then generalized to several spurious observations. The multivariate normal situation is studied next. Finally, we consider the general linear model with normal errors.     

A bayesian wls approach to generalized linear models

We use a Bayesian approach to fitting a linear regression model to transformations of the natural parameter for the exponential class of distributions. The usual Bayesian approach is to assume that a linear model exactly describes the relationship among the natural parameters. We assume only that a linear model is approximately in force. We approximate the theta-links by using a linear model obtained by minimizing the posterior expectation of a loss function.While some posterior results can be obtained analytically considerable generality follows from an exact Monte Carlo method for obtaining random samples of parameter values or functions of parameter values from their respective posterior distributions. The approach that is presented is justified for small samples, requires only one-dimensional numerical integrations, and allows for the use of regression matrices with less than full column rank. Two numerical examples are provided.     

A bayesian analysis of the multinomial model for a dichotomous response with nonrespondents

This paper studies the mu1tinomial model 2x2 contingency table data with some cell counts missing .Various hypotheses of interest including row-column independence are tested by using Bayes factors which represent the ratio of the posterior odds to the prior odds for the null hypothesis. The Dirichlet-Beta family of prior distributions is considered for the multinomial parameters cond itional on the complement of the null hypothesis. The Bayes factor for the incomplete data is a mixture of the Bayes factors for different possibilities for the full data.     

Bayesian analysis of reliability in multicomponent stress-strength models

This paper provides a Bayesian treatment of the problem of inference about the reliability of a multicomponent stress-strength system which functions if s or more of k identical components simultaneously operate. All stresses and strengths are assumed to be independent, exponentially distributed random variables. Exact and approximate asymptotic posterior distributions for the reliability are derived, and the results are illustrated by a numerical example.     

A recursive approach for lot sentencing problem in the presence of inspection errors

In this paper, a new sequential acceptance sampling plans in the presence of inspection errors is developed. A suitable profit objective function is employed for optimizing the lot sentencing problem. A backward recursive approach is applied for obtaining the profit of different decisions in each stage of sampling. Required probabilities are obtained using Bayesian rule. A case study is solved for illustrating the application of proposed models and sensitivity analysis are carried out on the parameters of the proposed methodologies and the behaviour of models by changing the parameters are investigated.     

Some essentially complete classes for bayesian multistage sampling inspection

Bayesian multistage inspection plans are often used in inadequate cost models. By means of essentially complete classes this point is made, as well as that of fixed and truncated plans.     

Modified chain sampling plans for lot inspection by variables and attributes

The purpose of acceptance sampling is to develop decision rules to accept or reject production lots based on sample data. When testing is destructive or expensive, dependent sampling procedures cumulate results from several preceding lots. This chaining of past lot results reduces the required size of the samples. A large part of these procedures only chain past lot results when defects are found in the current sample. However, such selective use of past lot results only achieves a limited reduction of sample sizes. In this article, a modified approach for chaining past lot results is proposed that is less selective in its use of quality history and, as a result, requires a smaller sample size than the one required for commonly used dependent sampling procedures, such as multiple dependent sampling plans and chain sampling plans of Dodge. The proposed plans are applicable for inspection by attributes and inspection by variables. Several properties of their operating characteristic-curves are derived, and search procedures are given to select such modified chain sampling plans by using the two-point method.     

A bayesian analysis of autoregressive models with random normal coefficients

In this paper we consider a Bayesian analysis for an autoregressive model with random normal coefficients (RCA). For the proposed procedure we use conjugate priors for some parameters and improper vague priors for others. The inference for the parameters is made via Gibbs sampler and the convergence is assessed with multiple chains and Gelman and Rubin criterium. Forecasts are based on the predictive density of future observations. Some remarks are also made regarding order determination and stationarity. Applications to simulated and real series are given.     

A bayesian analysis of multivariate survival data from multi-stage cluster sampling

Large scale sample surveys often collect survival times that are clustered at a number of hierarchical levels. Only the case where three levels are nested is considered here: that is, individual response times (level- i) are grouped into larger units (level-2) which in turn are grouped into much larger units (level-3). It is assumed that individuals in a unit share a common, unobservable and specific random frailty which induces an association between survival times in the unit. A Bayesian hierarchical analysis of the data is examined by modelling the survival time (level-1) using a semipanmietric Cox proportional hazards and specific level-2 and level-3 random frailty effects are assumed independent and modelled as gamma distributions. The complete posterior distribution of all the model parameters is estimated using the Gibbs sampler, a Monte Carlo method.     

A new family of lifetime models

We introduce a new family of distributions by adding a parameter to the Marshall–Olkin family of distributions. Some properties of the new family of distributions are derived. A particular case of the family, a three-parameter generalization of the exponential distribution, is given special attention. The shape properties, moments, distributions of the order statistics, entropies and estimation procedures are derived. An application to a real data set is discussed.     

A new class of multivariate skew distributions with applications to bayesian regression models

Abstract: The authors develop a new class of distributions by introducing skewness in multivariate elliptically symmetric distributions. The class, which is obtained by using transformation and conditioning, contains many standard families including the multivariate skew‐normal and t distributions. The authors obtain analytical forms of the densities and study distributional properties. They give practical applications in Bayesian regression models and results on the existence of the posterior distributions and moments under improper priors for the regression coefficients. They illustrate their methods using practical examples.     

A bayesian predictive approach to sequential search for an optimal dose: Parametric and nonparametric models

Summary This paper looks at a new approach to the problem of finding the maximal tolerated dose (or optimal dose, Eichhorn and Zacks, 1973) of certain drugs which in addition to their therapeutic effects have secondary harmful effects. The problem is investigated in a sequential setting from a Bayesian predictive approach. Search procedures are proposed for parametric and nonparametric models.     

Sample size choice for reliability verification in strength-stress models

This paper discusses the choice of sample size for experiments concerned with inference on R = P(Y < X), where X and Y are normal variates, in an acceptance-sampling-theory framework. A conservative approach is derived, and the properties of this solution examined by simulation.     

A bayesian analysis for less smooth departures from polynomial regression models

Observations y_i are made at points t_i according to the model _i=θ(t_i)+e_i where the e_i are independent normals with constant variance. It is conjec tured that the function θ lies in a set G of functions spanned by the basis functions φ₁,φ₂,…,φ_p. A prior distribution is developed whereby the proba bility assigned to a function θ is a decreasing function of a particular measure of the distance of θ from the set G. Bayes' theorem is used to construct an estimateθ. A marginal likelihood is derived which is used to estimate the parameter of the prior and also for testing the null hypothesis H_o θ ? G. The new methodology is tested in a Monte Carlo study and applied to a set of data representing the average weight to height ratio of a group of boys recorded at one month intervals.     

Incomplete categorical data analysis: a bayesian perspective

In this paper the Bayesian analysis of incomplete categorical data under informative general censoring proposed by Paulino and Pereira (1995) is revisited. That analysis is based on Dirichlet priors and can be applied to any missing data pattern. However, the known properties of the posterior distributions are scarce and therefore severe limitations to the posterior computations remain. Here is shown how a Monte Carlo simulation approach based on an alternative parameterisation can be used to overcome the former computational difficulties. The proposed simulation approach makes available the approximate estimation of general parametric functions and can be implemented in a very straightforward way.     

Semiparametric hierarchical selection models for bayesian meta analysis

Meta-analysis refers to quantitative methods for combining results from independent studies in order to draw overall conclusions. Hierarchical models including selection models are introduced and shown to be useful in such Bayesian meta-analysis. Semiparametric hierarchical models are proposed using the Dirichlet process prior. These rich class of models combine the information of independent studies, allowing investigation of variability both between and within studies, and weight function. Here we investigate sensitivity of results to unobserved studies by considering a hierarchical selection model with including unknown weight function and use Markov chain Monte Carlo methods to develop inference for the parameters of interest. Using Bayesian method, this model is used on a meta-analysis of twelve studies comparing the effectiveness of two different types of flouride, in preventing cavities. Clinical informative prior is assumed. Summaries and plots of model parameters are analyzed to address questions of interest.     

Use of bayesian analysis to design of clinical trials with one treatment

Assuming a Weibull distribution, the posterior distribution for the median survival time is derived in the presence of arbitrary right censorship. In the design of clinical triaLs, suppose k follow-up periods have been completed and it is desired to plan the follow-up period k+1. In this context, criteria are presented that can be employed in determining the number of new patients to be enrolled in the follow-up period k+1.     

A bayesian approach to dynamic tobit models

This paper develops a posterior simulation method for a dynamic Tobit model. The major obstacle rooted in such a problem lies in high dimensional integrals, induced by dependence among censored observations, in the likelihood function. The primary contribution of this study is to develop a practical and efficient sampling scheme for the conditional posterior distributions of the censored (i.e., unobserved) data, so that the Gibbs sampler with the data augmentation algorithm is successfully applied. The substantial differences between this approach and some existing methods are highlighted. The proposed simulation method is investigated by means of a Monte Carlo study and applied to a regression model of Japanese exports of passenger cars to the U.S. subject to a non-tariff trade barrier.     

A bayesian approach to dynamic tobit models

This paper develops a posterior simulation method for a dynamic Tobit model. The major obstacle rooted in such a problem lies in high dimensional integrals, induced by dependence among censored observations, in the likelihood function. The primary contribution of this study is to develop a practical and efficient sampling scheme for the conditional posterior distributions of the censored (i.e., unobserved) data, so that the Gibbs sampler with the data augmentation algorithm is successfully applied. The substantial differences between this approach and some existing methods are highlighted. The proposed simulation method is investigated by means of a Monte Carlo study and applied to a regression model of Japanese exports of passenger cars to the U.S. subject to a non-tariff trade barrier.