Debugging software often involves a removal process: the process of detection and removal of faults from a program. This paper gives an e4cient procedure to detect all faults in a software item with high probability. The procedure is such that at any step the probability of leaving just one fault is equal to some speci6ed value: the probability of leaving more than one fault is much smaller. It is found that, after eliminating the risk of early stopping, the probability of incomplete detection is then only slightly greater than). The performance of the proposed procedure is demonstrated by simulation and by application to a real example.

点过程是一个应用广泛的统计模型，在医学，社会学，经济学，电子与通信科学以及软件与硬件可靠性等许多科学领域都能找到应用点过程的例子。在这些实际应用中，一般是根据问题的实际背景假定模型具有一定的参数形式，然后根据观测数据给出未知参数的极大似然估计值以推断事物发展的客观规律。我们知道，一种估计量是否收敛以及收敛速度的快慢，是决定这种估计量好坏的最为重要的标准。本文对于一般的点过程模型中向量参数极大似然估计（MLE）首先给出了一个保证其强相合的较为广泛的充分性条件，然后在进一步的条件下得到了重对数型的收敛速度。

给出了EM算法在统计一个新的应用领域-假设检验，EM算法通常是用来求胸脯模型参数极大似然估计的一种有效的迭代算法，这种算法利用数据扩张，将比较复杂的似然函数的最优化问题成一系列比较简单的函数的优化问题，而对于一个模型来说，假设检验往往极大似然估计更为得杂，所以有必要找到简单的方法解决检验中的较复杂的优化问题，所给出的方法不是建设立在大样本理论基础上，因此特别适合于中小样本情形。

Gene expression studies bridge the gap between DNA information and trait information by dissecting biochemical pathways into intermediate components between genotype and phenotype. These studies open new avenues for identifying complex disease genes and biomarkers for disease diagnosis and for assessing drug efficacy and toxicity. However, the majority of analytical methods applied to gene expression data are not efficient for biomarker identification and disease diagnosis. In this paper, we propose a general framework to incorporate feature (gene) selection into pattern recognition in the process to identify biomarkers. Using this framework, we develop three feature wrappers that search through the space of feature subsets using the classification error as measure of goodness for a particular feature subset being “wrapped around”: linear discriminant analysis, logistic regression, and support vector machines. To effectively carry out this computationally intensive search process, we employ sequential forward search and sequential forward floating search algorithms. To evaluate the performance of feature selection for biomarker identification we have applied the proposed methods to three data sets. The preliminary results demonstrate that very high classification accuracy can be attained by identified composite classifiers with several biomarkers.

We use the semiparametric additive hazards model to formulate the effects of individual covariates on the capture rates in the continuous-time capturerecapture experiment, and then construct a Horvitz-Thompson-type estimator for the unknown population size. The resulting estimator is consistent and asymptotically normal with an easily estimated variance. Simulation studies show that the asymptotic approximations are adequate for practical use when the average capture probabilities exceed.5. Ignoring covariates would underestimate the population size and the coverage probability is poor. A wildlife example is provided.