Computation of the percentage points and the power for the two-sided Kolmogorov-Smirnov one sample test

Two recursive schemes are presented for the calculation of the probabilityP(g(x)≤S _n (x)≤h(x) for allx∈®), whereS _n is the empirical distribution function of a sample from a continuous distribution andh, g are continuous and isotone functions. The results are specialized for the calculation of the distribution and the corresponding percentage points of the test statistic of the two-sided Kolmogorov-Smirnov one sample test. The schemes allow the calculation of the power of the test too. Finally an extensive tabulation of percentage points for the Kolmogorov-Smirnov test is given.     

Iterated full partitions

Algebraic calculations that depend upon a full partition can be automated through the use of an operator P for the derivation of such a partition. Calculations that require the repeated use of P are automated by simply iterating the operator. The resulting output is general and contains sufficient structure to identify the result of a calculation for a variety of settings.     

Characterizations based on Rényi entropy of order statistics and record values

Two different distributions may have equal Rényi entropy; thus a distribution cannot be identified by its Rényi entropy. In this paper, we explore properties of the Rényi entropy of order statistics. Several characterizations are established based on the Rényi entropy of order statistics and record values. These include characterizations of a distribution on the basis of the differences between Rényi entropies of sequences of order statistics and the parent distribution.     

A modified Kolmogorov-Smirnov test for a rectangular distribution with unknown parameters: Computation of the distribution of the test statistic

A recursive scheme for the calculation of the distribution of the test statistic of a modified Kolmogorov-Smirnov-test for a rectangular distribution with unknown parameters is given.     

Computation of the central and noncentral f distributions

Recursion relations suitable for rapid computation are derived for the cumulative distribution of F′ = (X/m)/(Y/n) where X is χ²(λ, m) and Y is independently χ²(n). When n is even no complicated function evaluations are needed. For n odd, a special doubly noncentral t distribution is needed to start the computation. Series representations for this t distribution are given with rigorous bounds on truncation errors. Proper recursion techniques for numerical evaluation of the special functions are given.     

PERT时间参数的算法及工期费用的优化

建立了PERT时间参数计算的数学模型,即工期-费用优化的精确模型,给出了数值计算的实例.在PERT技术中运用对偶理论,为敏度分析创造了必要条件.     

An alternative to the analysis of covariance for comparing randomized treatments

The problem of comparing mean responses for several treatments applied to a common population is considered. The analysis of co-variance ‘ANCOVA’ is frequently used to take advantage of covariate information in this setting, but in many cases ANCOVA's assumption of parallel regression functions precludes the use of ANCOVA. In this paper, an alternative method is developed which does not make this assumption     

Bayes linear analysis for graphical models: The geometric approach to local computation and interpretive graphics

This paper concerns the geometric treatment of graphical models using Bayes linear methods. We introduce Bayes linear separation as a second order generalised conditional independence relation, and Bayes linear graphical models are constructed using this property. A system of interpretive and diagnostic shadings are given, which summarise the analysis over the associated moral graph. Principles of local computation are outlined for the graphical models, and an algorithm for implementing such computation over the junction tree is described. The approach is illustrated with two examples. The first concerns sales forecasting using a multivariate dynamic linear model. The second concerns inference for the error variance matrices of the model for sales, and illustrates the generality of our geometric approach by treating the matrices directly as random objects. The examples are implemented using a freely available set of object-oriented programming tools for Bayes linear local computation and graphical diagnostic display.     

计算主义思辩

本文从毕达哥拉斯的万物皆数的思想到图灵的可计算理论,再到智能计算,论述了计算主义认知观的形成和发展的全过程。从哲学、复杂性科学和生物学、计算机科学三个方面对计算主义进行了反思,倡导认知是算法不可完全的认知观。     

Approximating probability density functions in hybrid Bayesian networks with mixtures of truncated exponentials

Mixtures of truncated exponentials (MTE) potentials are an alternative to discretization and Monte Carlo methods for solving hybrid Bayesian networks. Any probability density function (PDF) can be approximated by an MTE potential, which can always be marginalized in closed form. This allows propagation to be done exactly using the Shenoy-Shafer architecture for computing marginals, with no restrictions on the construction of a join tree. This paper presents MTE potentials that approximate standard PDF’s and applications of these potentials for solving inference problems in hybrid Bayesian networks. These approximations will extend the types of inference problems that can be modelled with Bayesian networks, as demonstrated using three examples.