Efficient heterogeneous sampling for stochastic simulation with an illustration in health care applications

In modeling disease transmission, contacts are assumed to have different infection rates. A proper simulation must model the heterogeneity in the transmission rates. In this article, we present a computationally efficient algorithm that can be applied to a population with heterogeneous transmission rates. We conducted a simulation study to show that the algorithm is more efficient than other algorithms for sampling the disease transmission in a subset of the heterogeneous population. We use a valid stochastic model of pandemic influenza to illustrate the algorithm and to estimate the overall infection attack rates of influenza A (H1N1) in a Canadian city.     

Permutation tests of scale using deviances

Robust tests for comparing scale parameters, based on deviances—absolute deviations from the median—are examined. Higgins (2004) proposed a permutation test for comparing two treatments based on the ratio of deviances, but the performance of this procedure has not been investigated. A simulation study examines the performance of Higgins’ test relative to other tests of scale utilizing deviances that have been shown in the literature to have good properties. An extension of Higgins’ procedure to three or more treatments is proposed, and a second simulation study compares its performance to other omnibus tests for comparing scale. While no procedure emerged as a preferred choice in every scenario, Higgins’ tests are found to perform well overall with respect to Type I error rate and power.     

On the mathematics of the Jeffreys–Lindley paradox

This paper is concerned with the well known Jeffreys–Lindley paradox. In a Bayesian set up, the so-called paradox arises when a point null hypothesis is tested and an objective prior is sought for the alternative hypothesis. In particular, the posterior for the null hypothesis tends to one when the uncertainty, i.e., the variance, for the parameter value goes to infinity. We argue that the appropriate way to deal with the paradox is to use simple mathematics, and that any philosophical argument is to be regarded as irrelevant.     

Jensen's Inequality for General Location Parameter

A wide class of location parameters is shown to satisfy Jensen's inequality. When the expectation EX exists and l is a convex function, Jensen's inequality states that El(x) ≥ l(EX). It is shown that for μ, a properly defined location parameter, μ(l(x)) μ l(μ(x)).