James D. Stamey

Bayesian sample-size determination for one and two Poisson rate parameters with applications to quality control

Abstract We formulate Bayesian approaches to the problems of determining the required sample size for Bayesian interval estimators of a predetermined length for a single Poisson rate, for the difference between two Poisson rates, and for the ratio of two Poisson rates. We demonstrate the efficacy of our Bayesian-based sample-size determination method with two real-data quality-control examples and compare the results to frequentist sample-size determination methods.

Parameter subset selection and multiple comparisons of Poisson rate parameters with misclassification

Abstract We develop a fully Bayesian model for estimating a Poisson rate parameter subject to the presence of both false-positive and false-negative misclassification of the counts for a multiple sample scheme. We also propose a decision-theoretic-based parameter subset selection and multiple comparisons method for comparing Poisson rate parameters where counts are subject to misclassification. We apply our new data analysis methodologies to real-data examples. Probabilities used in these methods are approximated via Gibbs samplers.

Bayesian Sample Size Determination for Estimating a Poisson Rate with Underreported Data

Abstract We consider the problem of estimating the required sample size to achieve a credible set of specified length for the Poisson model with underreporting using an average coverage criterion. The actual posterior is found to be computationally taxing; thus we approximate via two approaches. The first method approximates the marginal and posterior densities with more tractable densities. The second is a Monte Carlo approach. We provide a limited study of the effect of the prior information and the magnitude of the reporting probability.

Bayesian subset selection approach to ranking normal means

In this, article we consider a Bayesian approach to the problem of ranking the means of normal distributed populations, which is a common problem in the biological sciences. We use a decision-theoretic approach with a straightforward loss function to determine a set of candidate rankings. This loss function allows the researcher to balance the risk of not including the correct ranking with the risk of increasing the number of rankings selected. We apply our new procedure to an example regarding the effect of zinc on the diversity of diatom species.

A note on tests for interaction in quantal response data

There are few distribution-free methods for detecting interaction in fixed-dose trials involving quantal response data, despite the fact that such trials are common. We present three new tests to address this issue, including a simple bootstrap procedure. We examine the power of the likelihood ratio test and our new bootstrap test statistic using an innovative linear extrapolation power-estimation technique described in Boos, D. D. and Zhang, J. (2000) in Monte Carlo evaluation of resampling-based hypothesis tests. Journal of the American Statistical Association, 95, 486–492.

A Note on Inference on Multiple Generalized Poisson Populations

SYNOPTIC ABSTRACT We consider a fully Bayesian approach to estimation of parameters for generalized Poisson data in a multiple population context. The hierarchical model we consider here extends previous single population models. This hierarchical model has applications in industrial, biological and sociological disciplines. We also extend two recently developed subset selection criteria to the generalized Poisson hierarchical model we propose. The procedures are used to analyze two real data sets. Probabilities are approximated via Markov Chain Monte Carlo.