EVVMA and cusum control charts in the presence of correlation

The statistical properties of control charts are usually evaluated under the assumption that the observations from the process are independent. For many processes however, observations which are closely spaced in time will be correlated. This paper considers EWMA and CUSUM control charts for the process mean when the observations are from an AR(1) process with additional random error. This simple model may be a reasonable model for many processes encountered in practice. The ARL and steady state ARL of the EWMA and CUSUM charts are evaluated numerically using an integral equation approach and a Markov chain approach. The numerical results show that correlation can have a significant effect on the properties of these charts. Tables are given to aid in the design of these charts when the observations follow the assumed model.     

Conditional interval estimation of the mean following rejection of a two sided test

The effect of rejecting a two-sided preliminary test of significance for the mean of a normal distribution upon subsequent interval estimation of the mean is examined. For the case where the variance is known, conditional confidence intervals may be shorter than unconditional intervals, in contrast to the one-sided preliminary test case examined by Meeks and D’Agostino (1983, The American Statistician, 7, 134-136) . For the case where the variance is unknown and must be estimated by the sample variance, it is shown that customary intervals do not offer uniformly greater or lesser coverage than the nominal level.     

Inference in hybrid Bayesian networks using dynamic discretization

We consider approximate inference in hybrid Bayesian Networks (BNs) and present a new iterative algorithm that efficiently combines dynamic discretization with robust propagation algorithms on junction trees. Our approach offers a significant extension to Bayesian Network theory and practice by offering a flexible way of modeling continuous nodes in BNs conditioned on complex configurations of evidence and intermixed with discrete nodes as both parents and children of continuous nodes. Our algorithm is implemented in a commercial Bayesian Network software package, AgenaRisk, which allows model construction and testing to be carried out easily. The results from the empirical trials clearly show how our software can deal effectively with different type of hybrid models containing elements of expert judgment as well as statistical inference. In particular, we show how the rapid convergence of the algorithm towards zones of high probability density, make robust inference analysis possible even in situations where, due to the lack of information in both prior and data, robust sampling becomes unfeasible.     

Multi-phase sampling under cost constraints

Multi-phase sampling (M-PhS) scheme is useful when the interest is in the estimation of the population mean of an expensive variable strictly connected with other cheaper (auxiliary) variables. The MSE is an accuracy measure of an estimator. Usually it decreases as the sample size increases. In practice the sample size cannot become arbitrarily large for possible cost constraints. From a practical point of view it would be useful to know the sample sizes which guarantee the best accuracy of the estimates for fixed costs. These “optimum” sample sizes can be, in some cases, computable but not admissible. In other cases, they can be neither admissible nor computable. The main goal of this paper is to propose a solution for both these situations. It will be clear that in both situations the solution is to consider a M-PhS scheme with one or more phases less.     

H-likelihood: problems and solutions

In recent issues of this journal it has been asserted in two papers that the use of h-likelihood is wrong, in the sense of giving unsatisfactory estimates of some parameters for binary data (Kuk and Cheng, 1999; Waddington and Thompson, 2004) or theoretically unsound (Kuk and Cheng, 1999). We wish to refute both these assertions.     

A direct derivation of the REML likelihood function

The original derivation of the widely cited form of the REML likelihood function for mixed linear models is difficult and indirect. This paper derives it directly using familiar operations with matrices and determinants.     

Nonconglomerative coherent conditional probabilities in statistical inference

Noteworthy connections among conglomerability, countable additivity and coherence are discussed in detail, reaching the conclusion that nonconglomerable conditional probabilities must not be doomed and play a significant role in statistical inference. Extended and updated version of a contributed paper presented at the International Conference on “Information Processing and Management of Uncertainty in knowledge-based systems”, IPMU 2004, Perugia, Italy.     

Data skeletons: simultaneous estimation of multiple quantiles for massive streaming datasets with applications to density estimation

We consider the problem of density estimation when the data is in the form of a continuous stream with no fixed length. In this setting, implementations of the usual methods of density estimation such as kernel density estimation are problematic. We propose a method of density estimation for massive datasets that is based upon taking the derivative of a smooth curve that has been fit through a set of quantile estimates. To achieve this, a low-storage, single-pass, sequential method is proposed for simultaneous estimation of multiple quantiles for massive datasets that form the basis of this method of density estimation. For comparison, we also consider a sequential kernel density estimator. The proposed methods are shown through simulation study to perform well and to have several distinct advantages over existing methods.     

A multivariate version of Gini's rank association coefficient

In this paper, we introduce a multivariate generalization of the population version of Gini's rank association coefficient, giving a response to this open question posed in [4]. We also study some properties of this version, present the corresponding results for the sample statistic, and provide several examples.     

Acceleration of the Multiple-Try Metropolis algorithm using antithetic and stratified sampling

The Multiple-Try Metropolis is a recent extension of the Metropolis algorithm in which the next state of the chain is selected among a set of proposals. We propose a modification of the Multiple-Try Metropolis algorithm which allows for the use of correlated proposals, particularly antithetic and stratified proposals. The method is particularly useful for random walk Metropolis in high dimensional spaces and can be used easily when the proposal distribution is Gaussian. We explore the use of quasi Monte Carlo (QMC) methods to generate highly stratified samples. A series of examples is presented to evaluate the potential of the method.