Null Cases Research Articles

Constructing belief networks from realistic data

In this paper, we report our investigation on the behavior of some Bayesian belief network learning methods, when applied to realistic case data that do not accurately reflect the probability distribution of the underlying domain. The investigation focuses on two types of such data of practical interest, namely data excluding null or normal cases and data contaminated by noise, and their effects on the performance of two learning methods: the K2 algorithm, a representative method of Bayesian approach, and the extended Hebbian learning (EHL) method, representing those of neural network approach. Both analytical and experimental results show that when null cases are removed from the case database, the EHL method is able to accurately construct the underlying causal structure; whereas K2 algorithm may fail to properly handle root nodes. On the other hand, the EHL method is noise sensitive while K2 has certain inherent noise-resistance capability. Suggestions to extend both K2 and EHL to better cope with these problems are also made, and their effectiveness tested through a systematic computer simulation experiment.

ASYMPTOTIC DISTRIBUTION OF LIKELIHOOD RATIO STATISTIC FOR TESTING SPHERICITY IN GROWTH CURVE MODELS

In this paper, asymptotic expansions of the distribution of the likelihood ratio statistic for testing sphericity in a crowth curve model have been derived in the null and nonnull cases when the alternatives are close to the null hypothesis. These expansions are given in series form of beta distributions.

Population-based study of glutathione S-transferase mu gene deletion in adult glioma cases and controls.

Gene deletion at the glutathione S-transferase mu locus (GSTM1) has previously been associated with increased risk for environmentally-induced cancers (e.g. smoking-related lung cancer). In the present study we examined the hypothesis that GSTM1 deletion is a risk factor for malignant brain tumors in adults. We compared the prevalence of the GSTM1 homozygous deletion polymorphism in 158 Caucasian adults with gliomas with 157 controls. Cases and controls were drawn from a large population-based case-control study of brain cancers in six San Francisco Bay area counties. Overall, the prevalence of the GSTM1 deletion was similar in cases (83/158; 53%) and controls (78/157; 50%). Among brain tumor cases, analysis of variance modeling indicated a significant interaction of GSTM1 genotype and gender associated with age at diagnosis (P = 0.02). This effect was due to the fact that women with GSTM1 deletion were younger on average at diagnosis than women who were GSTM1 positive (43.9 years versus 52.4 years, respectively). Age at diagnosis among men was similar for those who were GSTM1 deleted and GSTM1 positive (49.4 years and 47.2 years, respectively). The younger age at diagnosis of GSTM1 null female cases compared with GSTM1 positive cases was observed in astrocytoma as well as the higher grade tumors (e.g. glioblastoma multiforme). There was no association of GSTM1 deletion with age or gender in controls. These studies suggest that among female cases, GSTM1 deletion may be associated with earlier age at onset. Confirmation of these findings could provide important clues to gene-environment interactions in the etiology of malignant brain tumors.

A unified description of null and non-null shear-free congruences

A simple tensor equation is given that is satisfied by null vectors if and only if they are proportional to shear-free geodesics. Non-null vectors satisfy this equation if and only if they can be normalized to shear-free unit vectors. Thus this equation unifies the treatment of the null and non-null cases. Conformal properties of the shear-free condition and this tensor equation are discussed.

Kinematic, Thermodynamic, and Visual Structure of Low-Reflectivity Microbursts

Abstract On 9 July 1987, a series of low-reflectivity microbursts were studied over Colorado using dual-Doppler analyses, cloud photogrammetry, and in situ measurements collected by aircraft. These types of wind-shear events are particularly hazardous to the aviation community since the parent cloud and pendant virga shafts appear innocuous. The microburst downdrafts are shown to develop at the location where the virga shafts are, visually, the lowest and opaque. As the downdraft intensifies, sublimation and evaporation (to a smaller extent) rapidly deplete the hydrometeors and result in a shift of the axis of maximum negative vertical velocities into a relatively low reflectivity and transparent region of the virga shafts. Comparisons with weak downdrafts or null null cases reveal that the maximum radar reflectivities within the parent clouds for the two cases are comparable; however, the microburst storm consistently exhibits a larger horizontal area encompassed by the 10-dBZ contour at midlevels prior ...

Small-sample power of uncorrected and satterthwaite corrected t tests for comparing binomial proportions

When testing the equality of proportions from two independent binomial populations, one may reject the arguments for conditioning all testing and inference on the observed data and choose to employ the exact unconditional test (Suissa and Shuster, 1985), or the t test approximation (D'agostino, Chase, and Belanger, 1988). The achieved size of the t test with a pooled variance has been investigated previously for small sample sizes, but the power has not. Exact calculations, computed via enumeration, of the power of the t test with pooled variance and with Satterthwaite's variance approximation are reported here. The pooled variance approach was superior in both null and nonnull cases. For very small sample sizes, the tests achieved a power of at least .8 only when differences between proportions were at least .45. The calculations allowed demonstrating the accuracy of noncentral F integrals as approximations of empirical power, at least when power is acceptably high. The pooled variance approach provides ...

On the asymptotic distribution of likelihood ratio statistic for testing multisample spherically in the complex case

In this paper, asymptotic expansions of the distribution of the likelihood ratio statistic for testing multisample spherically in the complex case have been derived in the null and nonnull cases when the alternative are close to the null hypothesis. These expansions are obtained in the form of series of beta distributions.

Distributions of Lawley-Hotelling'sT02and Related Statistics: A Review

SYNOPTIC ABSTRACTIn this review article on the distributions of Lawley–Hotelling's T02 and related statistics, the following topics are reviewed and discussed: (1) exact distributions, (2) system of partial differential equations related to T02, (3) asymptotic expansions for the distribution of T02 by several methods, (4) percentage points and tables, and (5) miscellanea (including the distributions of two T02 statistics and their ratio and the maximum of ordinary T2's). T02 in this paper is the test statistic for noncentrality due to population mean vectors, i.e. the MANOVA test statistic. However the discussion for the central case is valid for the null cases of equality of two population covariance matrices and the independence of two sets of variates.

Non-T, non-B acute lymphocytic leukemias: cellular origin based on molecular analyses of immunoglobulin and T-cell alpha- and beta-chain receptor gene rearrangements.

Fifteen non-T, non-B acute lymphocytic leukemia (ALL) cases were investigated for determining cellular origin based on molecular (immunoglobulin and T-cell alpha-receptor (TcR alpha) and T-cell beta-receptor (TcR beta) genes) and immunophenotypical analyses. As defined by monoclonal antibodies, they were classified into 2 groups; 12 cases as common ALL antigen (CALLA)-positive ALL and 3 cases as CALLA-negative ALL. Southern blot analysis revealed that 11 CALLA-positive ALL cases contained rearranged JH gene and 2 of them contained rearranged Jx genes, similar to recent views that most CALLA-positive leukemic cells are neoplastic B-cell precursors. One CALLA-positive ALL case, whose leukemic cells were also Leu-1 positive, showed no rearrangement of JH and TcR beta genes. On the other hand, non-T, non-B CALLA-negative ALL, so called null ALL, consisted of heterogenous groups with regard to lymphocyte differentiation and lineage; one out of 3 null ALL cases may be truely undifferentiated as shown neither JH nor TcR beta gene rearrangement, but other 2 cases showed either JH or TcR beta gene rearrangement. Dual rearrangements of Ig and TcR beta genes occur frequently in 3 out of 15 non-T, non-B ALL cases, but all cases of bigenotype showed no doubly marked profile and retained a completely fidelous immunophenotypic pattern. We further investigated the possibility that analysis of TcR alpha gene may be useful for determining cellular origin of non-T, non-B ALL leukemic cells.

The relaxation time of two queueing systems in series

This paper deals with the time-dependent behaviour of two queueing systems in series, with a Posson arrival stream and exponential service times. The Laplace transform of the probability p0(t) that the tandem system is empty at time t given that it was empty at time 0 is obtained by reducing the functional equation for the generating function of the joint queue length distribution to a Riemann-Hilbert boundary value problem. From this Laplace transform the relaxation time of p 0(t) is determined for all parameter values, and the first term of the asymptotic expansion of p 0(t)-p 0(∞) as t →∞ is found in the ergodic and in the null recurrent cases.

Asymptotic distributions of the likelihood ratio test statistics for covariance structures of the complex multivariate normal distributions

In this paper, the authors derived asymptotic expressions for the null distributions of the likelihood ratio test statistics for multiple independence and multiple homogeneity of the covariance matrices when the underlying distributions are complex multivariate normal. Also, asymptotic expressions are obtained in the non-null cases for the likelihood ratio test statistics for independence of two sets of variables and the equality of two covariance matrices. The expressions obtained in this paper are in terms of beta series. In the null cases, the accuracy of the first terms alone is sufficient for many practical purposes.

Invariant scale matrix hypothesis tests under elliptical symmetry

The usual assumption in multivariate hypothesis testing is that the sample consists of n independent, identically distributed Gaussian m-vectors. In this paper this assumption is weakened by considering a class of distributions for which the vector observations are not necessarily either Gaussian or independent. This class contains the elliptically symmetric laws with densities of the form f( X( n × m)) = ψ[tr( X − M)′ ( X − M)Σ −1]. For testing the equality of k scale matrices and for the sphericity hypothesis it is shown, by using the structure of the underlying distribution rather than any specific form of the density, that the usual invariant normal-theory tests are exactly robust, for both the null and non-null cases, under this wider class.

The analysis of several 2× 2 contingency tables

SUMMARY Consider data arranged into k 2 x 2 contingency tables. The principal result is the derivation of a statistical test for making an inference on whether each of the k contingency tables has the same relative risk. The test is based on a conditional reference set and can be regarded as an extension of the Fisher-Irwin treatment of a single 2 x 2 contingency table. Both exact and asymptotic procedures are presented. The analysis of k 2 x 2 contingency tables is required in several contexts. The two principal ones are (i) the comparison of binary response random variables, i.e. random variables taking on the values zero or one, for two treatments, over a spectrum of different conditions or populations; and (ii) the comparison of the degree of association among two binary random variables over k different populations. Cochran (1954) has investigated this problem with respect to testing if the success probability for each of two treatments is the same for every contingency table. Cochran's recommendation is that the equality of the two success probabilities should be tested using the total number, summed over all tables, of successes for one of the treatments. Cochran considers the asymptotic distribution of the total number of successes, for one of the treatments, conditional on all marginals being fixed in every table. He recommends this technique whenever the difference between the two populations on a logistic or probit scale is nearly constant for each contingency table. The constant logistic difference is equivalent to the relative risk being equal for each table. Mantel & Haenlszel (1959), in an important paper discussing retrospective studies, have also proposed an asymptotic method for analysing several 2 x 2 contingency tables. Their worlk on this problem was evidently done independently of Cochran, for their method is exactly the same as Cochran's except for a modification dealing with the correction factor associated with a finite population. Birch (1964) and Cox (1966) clarified the problem by showing, that under the assumption of constant logistic differences for each table, same relative risk, the conditional distribution of the total number of successes, for one of the treatments, leads to a uniformly most powerful unbiased test. Birch and Cox also derived the exact probability distribution of this conditional random variable under the given model. In this paper, we investigate the more general situation where the difference between the logits in each table is not necessarily constant. Procedures are derived for making an inference with regard to the hypothesis of constant logistic differences. Both the exact and asymptotic distributions are derived for the null and nonnull cases. This problem has been discussed by several investigators. A constant logistic difference corresponds to no interaction between the treatments and the k populations. The case k = 2 corresponds to one in which Bartlett (1935) has derived both an exact and an asymptotic procedure. Norton (1945)

A Proposed Two-Sample Rank Test: The Psi Test and its Properties

Summary Since the power of the Psi test proposed by Gibbons (1964) compares favourably with that of other one-sided, two-sample rank tests on the equality of two distribution functions, its properties merit further investigation. This paper is devoted to such a study. A table of exact critical values for the test statistic is given for selected small sample sizes, and compared with critical values for the approximate distribution which is a function of Student's t. The agreement is good even for small samples. Using the results of Chernoff and Savage (1958), the asymptotic distribution is found to be normal in both the null and alternative cases. The null mean and variance are 0 and rπ 2l(3mN) respectively. Expressions are given for the alternative moments. The relation of the Psi test to other test statistics, specifically Terry's c 1 test, the Wilcoxon or Mann-Whitney test, and Savage's DN statistic, is investigated in terms of correlation coefficients in the null case. The test is most similar to Terry's c 1 statistic.