The genetic polymorphism maintained by host-pathogen coevolution is analyzed in a multilocus model. The model assumes gene-for-gene interactions of the type commonly observed between host plants and their fungal pathogens. Unstable (epidemic) systems maintain more resistance genes, fewer virulence genes, and less overall genetic diversity than stable (endemic) diseases. The stability of the sys...

Received: September 4, 2005, Revised:February 2, 2008 – c © Springer-Verlag 2008 Abstract. Most epidemic models assume equal mixing among members of a population. An alternative approach is to model a population as a random network in which individuals may have heterogeneous connectivity. This paper builds on previous research by describing the exact dynamical behavior of epidemics as they occu...

Data heterogeneity appears when the sample comes from at least two different populations. We analyze three types of situations. In the first and simplest case the majority of the data come from a central model and a few isolated observations come from a contaminating distribution. The data from the contaminating distribution are called outliers and they have been studied in depth in the statist...

Hierarchies of discrete probability measures are remarkably popular as nonparametric priors in applications, arguably due to two key properties: (i) they naturally represent multiple heterogeneous populations; (ii) they produce ties across populations, resulting in a shrinkage property often described as “sharing of information”. In this paper we establish a distribution theory for hierarchical...

The age distribution of the crust is a fundamental parameter in modeling continental evolution and the rate of crustal accretion through Earth’s history, but this is usually estimated from surface exposures. The exposed Yangtze craton in eastern China consists mainly of Proterozoic rocks with rare Archean outcrops. However, the U-Pb ages and Hf isotope systematics of xenocrystic zircons brought...

The one-sample paired t-test may be used to test whether the mean difference of two populations is greater than, less than, or not equal to a specific value. Because the t distribution is used to calculate critical values for the test, this test is often called the paired t-test. If the standard deviation of the differences is known, the normal distribution is used instead of the t distribution...

Fiber lengths were analyzed for random samples of medium-density fiberboard (MDF) fibers and wood particles taken from eleven different populations. For six of the samples, the lognormal distribution fit the data, while the Weibull distribution did not. For three of the samples, the Weibull fit the data, while the lognormal did not. For two of the samples, both the lognormal and Weibull fit the...

A nonparametric upper tolerance limit (UTL) bounds a specified percentage of the population distribution with specified confidence. The most common UTL is based on the largest order statistic (the maximum) where the number of samples required for a given confidence and coverage is easily derived for an infinitely large population. However, for other order statistics such as the second largest, ...

Consider s + 1 univariate normal populations with common variance σ2 and means μi, i = 0, 1, . . . , s, constrained by the tree-order restrictions μ0 ≤ μi, i = 1, 2, . . . , s. For certain sequences μ0, μ1, . . . the maximum likelihood-based estimator (MLBE) of μ0 diverges to −∞ as s → ∞ and its bias is unbounded. By contrast, the bias of an alternative estimator of μ0 proposed by Cohen and Sac...