epsilon-Contaminated priors in contingency tables

An r x s table is used for different approaches to statistical inference. We develop a Bayesian procedure to test simple null hypotheses versus bilateral alternatives in contingency tables. We consider testing equality of proportions of independent multinomial distributions when the common proportions are known. A lower bound of the posterior probabilities of the null hypothesis is calculated with respect to a mixture of a point prior on the null and an epsilon-contaminated prior on the proportions under the alternative. The resulting Bayes tests are compared numerically to Pearson's chi(2) in a number of examples. For the examined examples the lower bound and the p-value can be made close. The obtained results are generalized when the common proportions vector under the null is unknown or has a known functional form

Tunneling times in a taut string

The mathematical analogy of classical and matter waves can help to teach the elusive subject of tunneling times in undergraduate physics courses. The tunneling of mechanical energy through a taut string is revisited in this paper in order to study tunneling times for this classical system. General properties of the group delay, the dwell time and the interference time are described. Moreover, we explain how to build string arrays with piecewise constitutive parameters that behave like quantum mechanical heterostructures with alternating well and barrier layers. The paradoxical Hartman effect is also analyzed