论模糊数学在假设检验中的应用

文章通过对隶属函数的集中度系数确定的探讨,将模糊数学应用于贝叶斯统计学,从而形成了一种新的假设检验方法.     

假设的哲学——用假设和集合论研究哲学的方法

思维和存在的关系问题或是哲学的一个部分呢?还是全部?在逻辑的基础上,运用假设和集合论是研究哲学的一种方法,正如数学是建立在假设和逻辑之上的一样。假设1:一切论都建立在假设之上。假设2:任何概念都有论域。运用假设和集合论的方法,应该可以得到下面的一些概念:(1)任何两个概念仅在一定的条件下相同。(2)任何命题仅在一定的条件下为真。(3)运用假设2可以在概念上解决悖论,悖论是由于论域不清造成的。     

Approximation of power in multivariate analysis

We consider the calculation of power functions in classical multivariate analysis. In this context, power can be expressed in terms of tail probabilities of certain noncentral distributions. The necessary noncentral distribution theory was developed between the 1940s and 1970s by a number of authors. However, tractable methods for calculating the relevant probabilities have been lacking. In this paper we present simple yet extremely accurate saddlepoint approximations to power functions associated with the following classical test statistics: the likelihood ratio statistic for testing the general linear hypothesis in MANOVA; the likelihood ratio statistic for testing block independence; and Bartlett's modified likelihood ratio statistic for testing equality of covariance matrices.     

怀疑主义直觉的实验研究

主流知识论者认为,怀疑主义论证诉诸“我们不知道,甚至无法知道,怀疑主义假设是错误的”这种怀疑主义直觉。诉诸怀疑主义直觉是怀疑主义论证的普遍形式。然而,实验哲学对斑马案例直觉和缸中之脑假设直觉的研究表明,怀疑主义直觉受文化背景、社会经济地位、教育背景和性别的影响,具有多样性。怀疑主义直觉的多样性不仅对怀疑主义直觉的可靠性提出了质疑,而且对怀疑主义问题在西方哲学中的核心地位提出了挑战。对于这些质疑与挑战,我们提出了尝试性的回应。     

亲属立法的人性基础

人性本身无所谓善恶,其涵盖“人的动物性”和“人的社会性”.前者涵盖性冲动和生存欲两种自然欲求,后者涵盖性结合方式和群体性生活方式两种社会要求.亲属立法并不直接以人性为基础,从人性界分到亲属立法,中间需要有婚姻家庭伦理的介入.婚姻家庭伦理是对“人的动物性”和“人的社会性”进行道德评价的结果.婚姻伦理通过性禁忌、贞操观念分别对性冲动、性结合方式进行规制,家庭伦理通过不伤害原则、“同居共财”伦理/物权平等伦理分别对生存欲、群体性生活方式进行规制,而立法对婚姻家庭伦理的吸纳采歉抑路径.人性善恶假设是影响中西方亲属立法价值取向的关键原因.中国立法应以个体主义为基础,兼顾家庭本位的整体主义.     

An Improved Test for Continuous Local Martingales

We present a new test for the “continuous martingale hypothesis”. That is, a test for the hypothesis that observed data are from a process which is a continuous local martingale. The basis of the test is an embedded random walk at first passage times, obtained from the well-known representation of a continuous local martingale as a continuous time-change of Brownian motion. With a variety of simulated diffusion processes our new test shows higher power than existing tests using either the crossing tree or the quadratic variation, including the situation where non-negligible drift is present. The power of the test in the presence of jumps is also explored with a variety of simulated jump diffusion processes. The test is also applied to two sequences of high-frequency foreign exchange trade-by-trade data. In both cases the continuous martingale hypothesis is rejected at times less than hourly and we identify significant dependence in price movements at these small scales.     

Sequential procedures in identification

In this paper we study the problem of identifying a popula-tion with one of the two populations, with an aim to control both types of errors. We assume that the populations are normal with unknown means, but with unit variance. We have cited examples from anthropological studies where our formulation of the problem fits in quite nicely. We observe that SPRT’s based on the maximal invariant may not terminate with probability one. Simulation studies reported here show a substantial saving in the average number of samples compared to the best invariant fixed sample test.     

Practical bayesian approaches to the analystcs of a 2×2 contingency table with incompletely categorized data

To assess the efficacy of a treatment, patients are administered a pre-test, the treatment, and a post-test (identical to the pre-test). These patients are then categorized according to their outcomes observed on both tests,e.g., (S,S), (S,F), etc. Also, we observe "incomplete" information on the pre-tests' outcomes for some patients and the results of only the post-test being known for thers, A Bayesian framework is fit to the problem and Bayes factors, posterior odds ratios, and utility functions are given to evaluate th e treatment, A method of assessing the prior distribution is specified and a numerical example is worked.     

Estimation of the parameters of a regression model with a multivariate t error variable

This paper deals with a regression model for several vari¬ables under the assumption that the errors have a multivariate t-distribution. The parameters of the model, the regression parameters, as well as the scale parameters and the degress of freedom of the error variable are estimated and the estimation procedure is illustrated by a numerical example, Also, the prop¬erties of the estimators and tests for the regression parameters are discussed.