On a resampling approach for tests on the number of clusters with mixture model-based clustering of tissue samples

We consider the problem of assessing the number of clusters in a limited number of tissue samples containing gene expressions for possibly several thousands of genes. It is proposed to use a normal mixture model-based approach to the clustering of the tissue samples. One advantage of this approach is that the question on the number of clusters in the data can be formulated in terms of a test on the smallest number of components in the mixture model compatible with the data. This test can be carried out on the basis of the likelihood ratio test statistic, using resampling to assess its null distribution. The effectiveness of this approach is demonstrated on simulated data and on some microarray datasets, as considered previously in the bioinformatics literature. (C) 2004 Elsevier Inc. All rights reserved.

Price discovery and volatility spillovers in index futures markets: Some evidence from Mexico

This paper investigates the hypotheses that the recently established Mexican stock index futures market effectively serves the price discovery function, and that the introduction of futures trading has provoked volatility in the underlying spot market. We test both hypotheses simultaneously with daily data from Mexico in the context of a modified EGARCH model that also incorporates possible cointegration between the futures and spot markets. The evidence supports both hypotheses, suggesting that the futures market in Mexico is a useful price discovery vehicle, although futures trading has also been a source of instability for the spot market. Several managerial implications are derived and discussed. (C) 2004 Elsevier B.V. All rights reserved.

Clustering of related individuals in a population of the Australian lizard, Egernia frerei

Stable social aggregations are rarely recorded in lizards, but have now been reported from several species in the Australian scincid genus Egernia. Most of those examples come from species using rock crevice refuges that are relatively easy to observe. But for many other Egernia species that occupy different habitats and are more secretive, it is hard to gather the observational data needed to deduce their social structure. Therefore, we used genotypes at six polymorphic microsatellite DNA loci of 229 individuals of Egernia frerei, trapped in 22 sampling sites over 3500 ha of eucalypt forest on Fraser Island, Australia. Each sampling site contained 15 trap locations in a 100 x 50 m grid. We estimated relatedness among pairs of individuals and found that relatedness was higher within than between sites. Relatedness of females within sites was higher than relatedness of males, and was higher than relatedness between males and females. Within sites we found that juvenile lizards were highly related to other juveniles and to adults trapped at the same location, or at adjacent locations, but relatedness decreased with increasing trap separation. We interpreted the results as suggesting high natal philopatry among juvenile lizards and adult females. This result is consistent with stable family group structure previously reported in rock dwelling Egernia species, and suggests that social behaviour in this genus is not habitat driven.

Canonical valuation of options in the presence of stochastic volatility

Proposed by M. Stutzer (1996), canonical valuation is a new method for valuing derivative securities under the risk-neutral framework. It is non-parametric, simple to apply, and, unlike many alternative approaches, does not require any option data. Although canonical valuation has great potential, its applicability in realistic scenarios has not yet been widely tested. This article documents the ability of canonical valuation to price derivatives in a number of settings. In a constant-volatility world, canonical estimates of option prices struggle to match a Black-Scholes estimate based on historical volatility. However, in a more realistic stochastic-volatility setting, canonical valuation outperforms the Black-Scholes model. As the volatility generating process becomes further removed from the constant-volatility world, the relative performance edge of canonical valuation is more evident. In general, the results are encouraging that canonical valuation is a useful technique for valuing derivatives. (C) 2005 Wiley Periodicals, Inc.

Socioeconomic position, cognitive function, and clustering of cardiovascular risk factors in adolescence: Findings from the Mater University Study of Pregnancy and its outcomes

Objectives: The objectives of this study were to examine the extent of clustering of smoking, high levels of television watching, overweight, and high blood pressure among adolescents and whether this clustering varies by socioeconomic position and Cognitive function. Methods: This study was a cross-sectional analysis of 3613 (1742 females) participants of an Australian birth cohort who were examined at age 14. Results: Three hundred fifty-three (9.8%) of the participants had co-occurrence of three or four risk factors. Risk factors clustered in these adolescents with a greater number of participants than would be predicted by assumptions of independence having no risk factors and three or four risk factors. The extent of clustering tended to be greater in those from lower-income families and among those with lower cognitive function. The age-adjusted ratio of observed to expected cooccurrence of three or four risk factors was 2.70 (95% confidence interval [Cl], 1.80-4.06) among those from low-income families and 1.70 (95% Cl, 1.34-2.16) among those from more affluent families. The ratio among those with low Raven's scores (nonverbal reasoning) was 2.36 (95% Cl, 1.69-3.30) and among those with higher scores was 1.51 (95% Cl, 1.19-1.92); similar results for the WRAT 3 score (reading ability) were 2.69 (95% Cl, 1.85-3.94) and 1.68 (95% Cl, 1.34-2.11). Clustering did not differ by sex. Conclusion: Among adolescents, coronary heart disease risk factors cluster, and there is some evidence that this clustering is greater among those from families with low income and those who have lower cognitive function.

Using extreme value theory to measure value-at-risk for daily electricity spot prices

The recent deregulation in electricity markets worldwide has heightened the importance of risk management in energy markets. Assessing Value-at-Risk (VaR) in electricity markets is arguably more difficult than in traditional financial markets because the distinctive features of the former result in a highly unusual distribution of returns-electricity returns are highly volatile, display seasonalities in both their mean and volatility, exhibit leverage effects and clustering in volatility, and feature extreme levels of skewness and kurtosis. With electricity applications in mind, this paper proposes a model that accommodates autoregression and weekly seasonals in both the conditional mean and conditional volatility of returns, as well as leverage effects via an EGARCH specification. In addition, extreme value theory (EVT) is adopted to explicitly model the tails of the return distribution. Compared to a number of other parametric models and simple historical simulation based approaches, the proposed EVT-based model performs well in forecasting out-of-sample VaR. In addition, statistical tests show that the proposed model provides appropriate interval coverage in both unconditional and, more importantly, conditional contexts. Overall, the results are encouraging in suggesting that the proposed EVT-based model is a useful technique in forecasting VaR in electricity markets. (c) 2005 International Institute of Forecasters. Published by Elsevier B.V. All rights reserved.

A Mixture model with random-effects components for clustering correlated gene-expression profiles

Motivation: The clustering of gene profiles across some experimental conditions of interest contributes significantly to the elucidation of unknown gene function, the validation of gene discoveries and the interpretation of biological processes. However, this clustering problem is not straightforward as the profiles of the genes are not all independently distributed and the expression levels may have been obtained from an experimental design involving replicated arrays. Ignoring the dependence between the gene profiles and the structure of the replicated data can result in important sources of variability in the experiments being overlooked in the analysis, with the consequent possibility of misleading inferences being made. We propose a random-effects model that provides a unified approach to the clustering of genes with correlated expression levels measured in a wide variety of experimental situations. Our model is an extension of the normal mixture model to account for the correlations between the gene profiles and to enable covariate information to be incorporated into the clustering process. Hence the model is applicable to longitudinal studies with or without replication, for example, time-course experiments by using time as a covariate, and to cross-sectional experiments by using categorical covariates to represent the different experimental classes. Results: We show that our random-effects model can be fitted by maximum likelihood via the EM algorithm for which the E(expectation) and M(maximization) steps can be implemented in closed form. Hence our model can be fitted deterministically without the need for time-consuming Monte Carlo approximations. The effectiveness of our model-based procedure for the clustering of correlated gene profiles is demonstrated on three real datasets, representing typical microarray experimental designs, covering time-course, repeated-measurement and cross-sectional data. In these examples, relevant clusters of the genes are obtained, which are supported by existing gene-function annotation. A synthetic dataset is considered too.

On the statistical analysis of the GS-NS0 cell proteome: Imputation, clustering and variability testing

We have undertaken two-dimensional gel electrophoresis proteomic profiling on a series of cell lines with different recombinant antibody production rates. Due to the nature of gel-based experiments not all protein spots are detected across all samples in an experiment, and hence datasets are invariably incomplete. New approaches are therefore required for the analysis of such graduated datasets. We approached this problem in two ways. Firstly, we applied a missing value imputation technique to calculate missing data points. Secondly, we combined a singular value decomposition based hierarchical clustering with the expression variability test to identify protein spots whose expression correlates with increased antibody production. The results have shown that while imputation of missing data was a useful method to improve the statistical analysis of such data sets, this was of limited use in differentiating between the samples investigated, and highlighted a small number of candidate proteins for further investigation. (c) 2006 Elsevier B.V. All rights reserved.

Symptom prevalence and clustering of symptoms in people living with chronic hepatitis C infection

Quality of life has been shown to be poor among people living with chronic hepatitis C However, it is not clear how this relates to the presence of symptoms and their severity. The aim of this study was to describe the typology of a broad array of symptoms that were attributed to hepatitis C virus (HCV) infection. Phase I used qualitative methods to identify symptoms. In Phase 2, 188 treatment-naive people living with HCV participated in a quantitative survey. The most prevalent symptom was physical tiredness (86%) followed by irritability (75%), depression (70%), mental tiredness (70%), and abdominal pain (68%). Temporal clustering of symptoms was reported in 62% of participants. Principal components analysis identified four symptom clusters: neuropsychiatric (mental tiredness, poor concentration, forgetfulness, depression, irritability, physical tiredness, and sleep problems); gastrointestinal (day sweats, nausea, food intolerance, night sweats, abdominal pain, poor appetite, and diarrhea); algesic (joint pain, muscle pain, and general body pain); and dysesthetic (noise sensitivity, light sensitivity, skin. problems, and headaches). These data demonstrate that symptoms are prevalent in treatment-naive people with HCV and support the hypothesis that symptom clustering occurs.

Efficient spatial clustering algorithm using binary tree

In this paper we present an efficient k-Means clustering algorithm for two dimensional data. The proposed algorithm re-organizes dataset into a form of nested binary tree*. Data items are compared at each node with only two nearest means with respect to each dimension and assigned to the one that has the closer mean. The main intuition of our research is as follows: We build the nested binary tree. Then we scan the data in raster order by in-order traversal of the tree. Lastly we compare data item at each node to the only two nearest means to assign the value to the intendant cluster. In this way we are able to save the computational cost significantly by reducing the number of comparisons with means and also by the least use to Euclidian distance formula. Our results showed that our method can perform clustering operation much faster than the classical ones. © Springer-Verlag Berlin Heidelberg 2005