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There is a little-known but very simple generalization of the standard result that for uncorrelated random variables with common mean [mu] and variance [sigma][superscript 2], the expected value of the sample variance is [sigma][superscript 2]. The generalization justifies the use of the usual standard error of the sample mean in possibly heteroscedastic situations, and motivates elementary estimators in even unbalanced linear random effects models. The latter both provides nontrivial examples and exercises concerning method-of-moments estimation, and also helps "demystify" the whole matter of variance component estimation. This is illustrated in general for the simple one-way context and for a specific unbalanced two-factor hierarchical data structure. (Contains 1 figure.)

Several potential development test programs for one-shot systems that are destroyed during testing or first normal use are considered. One of the most promising development test programs is based on a two-state reliability approach. The results of the two-state reliability test program can analyzed to generate optimal R and D decisions in a research environment characterized by a limited amount of resources.

We propose tractable symmetric exponential families of distributions for multivariate vectors of 0's and 1's in p dimensions, or what are referred to in this paper as binary vectors, that allow for nontrivial amounts of variation around some central value μ∈{0,1}p. We note that more or less standard asymptotics provides likelihood‐based inference in the one‐sample problem. We then consider mixture models where component distributions are of this form. Bayes analysis based on Dirichlet processes and Jeffreys priors for the exponential family parameters prove tractable and informative in problems where relevant distributions for a vector of binary variables are clearly not symmetric. We also extend our proposed Bayesian mixture model analysis to datasets with missing entries. Performance is illustrated through simulation studies and application to real datasets. [ABSTRACT FROM AUTHOR]

A probability model exhibits instability if small changes in a data outcome result in large and, often unanticipated, changes in probability. This instability is a property of the probability model, given by a distributional form and a given configuration of parameters. For correlated data structures found in several application areas, there is increasing interest in identifying such sensitivity in model probability structure. We consider the problem of quantifying instability for general probability models defined on sequences of observations, where each sequence of length |$N$| has a finite number of possible values that can be taken at each point. A sequence of probability models, indexed by |$N$|⁠ , and an associated parameter sequence result to accommodate data of expanding dimension. Model instability is formally shown to occur when a certain log probability ratio under such models grows faster than |$N$|⁠. In this case, a one component change in the data sequence can shift probability by orders of magnitude. Also, as instability becomes more extreme, the resulting probability models are shown to tend to degeneracy, placing all their probability on potentially small portions of the sample space. These results on instability apply to large classes of models commonly used in random graphs, network analysis and machine learning contexts. [ABSTRACT FROM AUTHOR]