In the context of survival analysis it is possible that increasing the value of a covariate "X" has a beneficial effect on a failure time, but this effect is reversed when conditioning on any possible value of another covariate "Y". When studying causal effects and influence of covariates on a...

Unlike the usual stochastic order, total positivity order is closed under conditioning. Here we provide a general formulation of the preservation properties of the order under conditioning; we study certain properties of the order including translation properties and the implications of having...

In the context of survival analysis, we define a covariate X as protective (detrimental) for the failure time T if the conditional distribution of [T | X = x] is stochastically increasing (decreasing) as a function of x. In the presence of another covariate Y, there exist situations where [T | X...

We compare estimators of the (essential) supremum and the integral of a function f defined on a measurable space when f may be observed at a sample of points in its domain, possibly with error. The estimators compared vary in their levels of stratification of the domain, with the result that...

Based on a model introduced by Kaminsky, Luks, and Nelson (1984), we consider a zero-sum allocation game called the Gladiator Game, where two teams of gladiators engage in a sequence of one-to-one fights in which the probability of winning is a function of the gladiators' strengths. Each team's...

A problem of optimally allocating partially effective ammunition x to be used on randomly arriving enemies in order to maximize an aircraft's probability of surviving for time t, known as the Bomber Problem, was first posed by Klinger and Brown (1968). They conjectured a set of apparently...

This note revisits the problem of selection bias, using a simple binomial example. It focuses on selection that is introduced by observing the data and making decisions prior to formal statistical analysis. Decision rules and interpretation of confidence measure and results must then be taken...