Testing the Equality of the Intra‐Subject Treatment Covariance Matrices in a Crossover Study

In a 2 × 2 crossover bioavailability study, the sets of estimates of the pharmacokinetic parameters quite often have a symmetric covariance structure between the two treatments. For testing the equality of the intra‐subject covariance matrices for the two treatments in such studies, we suggest in this paper some statistical tests. When the response vectors are bivariate, we propose an exact test. Since the statistical procedures depend on the assumption of a symmetric covariance structure between the two treatments, we put forth some statistical tests for this assumption. We then apply the discussed tests to real data from a crossover bioavailability trial.     

Exponentiated Exponential Family: An Alternative to Gamma and Weibull Distributions

In this article we study some properties of a new family of distributions, namely Exponentiated Exponential distribution, discussed in Gupta , Gupta , and Gupta (1998). The Exponentiated Exponential family has two parameters (scale and shape) similar to a Weibull or a gamma family. It is observed that many properties of this new family are quite similar to those of a Weibull or a gamma family, therefore this distribution can be used as a possible alternative to a Weibull or a gamma distribution. We present two real life data sets, where it is observed that in one data set exponentiated exponential distribution has a better fit compared to Weibull or gamma distribution and in the other data set Weibull has a better fit than exponentiated exponential or gamma distribution. Some numerical experiments are performed to see how the maximum likelihood estimators and their asymptotic results work for finite sample sizes.     

Confidence Intervals of the Simple Difference between the Proportions of a Primary Infection and a Secondary Infection,Given the Primary Infection

This paper discusses interval estimation of the simple difference (SD) between the proportions of the primary infection and the secondary infection, given the primary infection, by developing three asymptotic interval estimators using Wald's test statistic, the likelihood‐ratio test, and the basic principle of Fieller's theorem. This paper further evaluates and compares the performance of these interval estimators with respect to the coverage probability and the expected length of the resulting confidence intervals. This paper finds that the asymptotic confidence interval using the likelihood ratio test consistently performs well in all situations considered here. When the underlying SD is within 0.10 and the total number of subjects is not large (say, 50), this paper further finds that the interval estimators using Fieller's theorem would be preferable to the estimator using the Wald's test statistic if the primary infection probability were moderate (say, 0.30), but the latter is preferable to the former if this probability were large (say, 0.80). When the total number of subjects is large (say, ≥200), all the three interval estimators perform well in almost all situations considered in this paper. In these cases, for simplicity, we may apply either of the two interval estimators using Wald's test statistic or Fieller's theorem without losing much accuracy and efficiency as compared with the interval estimator using the asymptotic likelihood ratio test.     

A Likelihood Ratio Test for the Nonparametric Behrens‐Fisher Problem

The nonparametric Behrens‐Fisher hypothesis is the most appropriate null hypothesis for the two‐sample comparison when one does not wish to make restrictive assumptions about possible distributions. In this paper, a numerical approach is described by which the likelihood ratio test can be calculated for the nonparametric Behrens‐Fisher problem. The approach taken here effectively reduces the number of parameters in the score equations to one by using a recursive formula for the remaining parameters. The resulting single dimensional problem can be solved numerically. The power of the likelihood ratio test is compared by simulation to that of a generalized Wilcoxon test of Brunner and Munzel. The tests have similar power for all alternatives considered when a simulated null distribution is used to generate cutoff values for the tests. The methods are illustrated on data on shoulder pain from a clinical trial.     

正态总体均值与标准差比在半序约束下的最大似然估计

考虑两个正态总体X_i～N(μ_i,σ_i~2) i=1,2,均值μ_i和方差σ_i~2>0是未知参数,它们的比在半序约束μ_1/σ_1≤μ_2/σ_2下的最大似然估计(MLE)问题,给出了计算MLE的方法,对三个正态总体的情况,给出了相关的结果,这些方法在生物遗传和药物检验等方面都有广泛应用。     

分子进化生物学中序列分析方法的新进展

简要介绍了分子进化生物学中序列分析方法的最新进展,特别强调了似然比检验和贝叶斯推论在分子进化和系统发育假说检验中的重要性,并介绍了新方法的一些成功应用,同时还给出了一些重要的信息资源。     

Techniques for temporal detection of neural sensitivity to external stimulation

We propose a simple measure of neural sensitivity for characterizing stimulus coding. Sensitivity is defined as the fraction of neurons that show positive responses to n stimuli out of a total of N. To determine a positive response, we propose two methods: Fisherian statistical testing and a data-driven Bayesian approach to determine the response probability of a neuron. The latter is non-parametric, data-driven, and captures a lower bound for the probability of neural responses to sensory stimulation. Both methods are compared with a standard test that assumes normal probability distributions. We applied the sensitivity estimation based on the proposed method to experimental data recorded from the mushroom body (MB) of locusts. We show that there is a broad range of sensitivity that the MB response sweeps during odor stimulation. The neurons are initially tuned to specific odors, but tend to demonstrate a generalist behavior towards the end of the stimulus period, meaning that the emphasis shifts from discrimination to feature learning.     

Stochastic modelling of prey depletion processes

The modelling of prey-predator interactions is of major importance for the understanding of population dynamics. Classically, these interactions are modelled using ordinary differential equations, but this approach has the drawbacks of assuming continuous population variables and of being deterministic. We propose a general approach to stochastic modelling based on the concept of functional response for a prey depletion process with a constant number of predators. Our model could involve any kind of functional response, and permits a likelihood-based approach to statistical modelling and stable computation using matrix exponentials. To illustrate the method we use the Holling-Juliano functional response and compare the outcomes of our model with a deterministic counterpart considered by Schenk and Bacher [2002. Functional response of a generalist insect predator to one of its prey species in the field. Journal of Animal Ecology 71 (3), 524-531], who observed the depletion of Cassida rubiginosa due to its exclusive predator, Polistes dominulus. The predation was found to be Holling type III, reflecting the ability of the predator to regulate its prey. Our approach corroborates this result, but suggests that the prey depletion census should have been performed more often, and that predation features were significantly different between the two years for which data are available.     

Importance sampling for Lambda-coalescents in the infinitely many sites model

We present and discuss new importance sampling schemes for the approximate computation of the sample probability of observed genetic types in the infinitely many sites model from population genetics. More specifically, we extend the ‘classical framework’, where genealogies are assumed to be governed by Kingman’s coalescent, to the more general class of Lambda-coalescents and develop further Hobolth et al.’s (2008) idea of deriving importance sampling schemes based on ‘compressed genetrees’. The resulting schemes extend earlier work by Griffiths and Tavaré (1994), Stephens and Donnelly (2000), Birkner and Blath (2008) and Hobolth et al. (2008). We conclude with a performance comparison of classical and new schemes for Beta- and Kingman coalescents.