Approximations to Bayesian Sequential Tests of Composite Hypotheses

Bayesian tests for composite alternative hypotheses in cross-tabulated data

Composite Hypotheses and Generalized Likelihood Ratio Tests

In many real world problems, it is difficult to precisely specify probability distributions. Our models for data may involve unknown parameters or other characteristics. Here are a few motivating examples. Example: Unknown amplitudes/delays in wireless communications. We don't always know how many relays a signal will go through, how strong the signal will be at each receiver, the distance betw...

Analysis of Robustness for Sequential Tests of Composite Hypotheses under Functional Distortion of Priors and Likelihoods

Composite hypotheses are tested sequentially in many applications, especially in medicine and quality control (see Lai (2001)). Although some optimal properties of sequential tests are valid (see, for example, Malyutov et al. (2000)) in frames of hypothetical models, the observed data do not follow these models exactly, the hypothetical models are distorted (see Huber (2004) and Hampel et al. (...

Robustness Evaluation in Sequential Testing of Composite Hypotheses

The problem of sequential testing of composite hypotheses is considered. Asymptotic expansions are constructed for the conditional error probabilities and expected sample sizes under “contamination” of the probability distribution of observations. To obtain these results a new approach based on approximation of the generalized likelihood ratio statistic by a specially constructed Markov chain i...

Unified Conditional Frequentist and Bayesian Testing of Composite Hypotheses

Testing of a composite null hypothesis versus a composite alternative is considered when both have a related invariance structure. The goal is to develop conditional frequentist tests that allow the reporting of data-dependent error probabilities, error probabilities that have a strict frequentist interpretation and that reflect the actual amount of evidence in the data. The resulting tests are...