On the Multivariate Gamma-Gamma (ΓΓ) Distribution with Arbitrary Correlation and Applications in Wireless Communications

The statistical properties of the multivariate GammaGamma (ΓΓ) distribution with arbitrary correlation have remained unknown. In this paper, we provide analytical expressions for the joint probability density function (PDF), cumulative distribution function (CDF) and moment generation function of the multivariate ΓΓ distribution with arbitrary correlation. Furthermore, we present novel approximating expressions for the PDF and CDF of the su m of ΓΓ random variables with arbitrary correlation. Based on this statistical analysis, we investigate the performance of radio frequency and optical wireless communication systems. It is noteworthy that the presented expressions include several previous results in the literature as special cases.

Epidermolysis bullosa:evidence for linkage to genetic markers on chromosome 1 in a family with the autosomal dominant simplex form

DNA from members of a three-generation pedigree of Irish origin, displaying an autosomal dominant simplex form of epidermolysis bullosa of the epidermolytic, simplex, or Koebner variety (EBS2), was analyzed for linkage with a set of markers derived from the long arm of chromosome 1. Two-point analysis revealed positive lod scores for five of these markers, AT3 (Z = 2.107, theta = 0), APOA2 (Z = 1.939, theta = 0.15), D1S66 (Z = 1.204, theta = 0), D1S13 (Z = 1.026, theta = 0.15), and D1S65 (Z = 0.329, theta = 0.15). Multilocus analysis, incorporating the markers D1S19, D1S16, D1S13, APOA2, D1S66, AT3, and D1S65, resulted in a lod score of 3 maximizing at AT3. These data strongly support previous tentative indications of linkage between EBS2 and genetic markers on the long arm of chromosome 1.

Compositional Data Analysis in Forensic Geoscience

Statistics are regularly used to make some form of comparison between trace evidence or deploy the exclusionary principle (Morgan and Bull, 2007) in forensic investigations. Trace evidence are routinely the results of particle size, chemical or modal analyses and as such constitute compositional data. The issue is that compositional data including percentages, parts per million etc. only carry relative information. This may be problematic where a comparison of percentages and other constraint/closed data is deemed a statistically valid and appropriate way to present trace evidence in a court of law. Notwithstanding an awareness of the existence of the constant sum problem since the seminal works of Pearson (1896) and Chayes (1960) and the introduction of the application of log-ratio techniques (Aitchison, 1986; Pawlowsky-Glahn and Egozcue, 2001; Pawlowsky-Glahn and Buccianti, 2011; Tolosana-Delgado and van den Boogaart, 2013) the problem that a constant sum destroys the potential independence of variances and covariances required for correlation regression analysis and empirical multivariate methods (principal component analysis, cluster analysis, discriminant analysis, canonical correlation) is all too often not acknowledged in the statistical treatment of trace evidence. Yet the need for a robust treatment of forensic trace evidence analyses is obvious. This research examines the issues and potential pitfalls for forensic investigators if the constant sum constraint is ignored in the analysis and presentation of forensic trace evidence. Forensic case studies involving particle size and mineral analyses as trace evidence are used to demonstrate the use of a compositional data approach using a centred log-ratio (clr) transformation and multivariate statistical analyses.

Geostatistical Fisher discriminant analysis

A geostatistical version of the classical Fisher rule (linear discriminant analysis) is presented.This method is applicable when a large dataset of multivariate observations is available within a domain split in several known subdomains, and it assumes that the variograms (or covariance functions) are comparable between subdomains, which only differ in the mean values of the available variables. The method consists on finding the eigen-decomposition of the matrix W-1B, where W is the matrix of sills of all direct- and cross-variograms, and B is the covariance matrix of the vectors of weighted means within each subdomain, obtained by generalized least squares. The method is used to map peat blanket occurrence in Northern Ireland, with data from the Tellus
survey, which requires a minimal change to the general recipe: to use compositionally-compliant variogram tools and models, and work with log-ratio transformed data.

Compositonal Analysis of Potentially harmful Elements in Soils: Implications for Epidemiology and Kidney Disease

A substantial proportion of aetiological risks for many cancers and chronic diseases remain unexplained. Using geochemical soil and stream water samples collected as part of the Tellus Project studies, current research is investigating naturally occurring background levels of potentially toxic elements (PTEs) in soils and stream sediments and their possible relationship with progressive chronic kidney disease (CKD). The Tellus geological mapping project, Geological Survey Northern Ireland, collected soil sediment and stream water samples on a grid of one sample site every 2 km2 across the rural areas of Northern Ireland resulting in an excess of 6800 soil sampling locations and more than 5800 locations for stream water sampling. Accumulation of several PTEs including arsenic, cadmium, chromium, lead and mercury have been linked with human health and implicated in renal function decline. The hypothesis is that long-term exposure will result in cumulative exposure to PTEs and act as risk factor(s) for cancer and diabetes related CKD and its progression. The ‘bioavailable’ fraction of total PTE soil concentration depends on the ‘bioaccessible’ proportion through an exposure pathway. Recent work has explored this bioaccessible fraction for a range of PTEs across Northern Ireland. In this study the compositional nature of the multivariate geochemical PTE variables and bioaccessible data is explored to augment the investigation into the potential relationship between PTEs, bioaccessibility and disease data.

Analysis of multirate behavior in electronic systems

Esta tese insere-se na área da simulação de circuitos de RF e microondas, e visa o estudo de ferramentas computacionais inovadoras que consigam simular, de forma eficiente, circuitos não lineares e muito heterogéneos, contendo uma estrutura combinada de blocos analógicos de RF e de banda base e blocos digitais, a operar em múltiplas escalas de tempo. Os métodos numéricos propostos nesta tese baseiam-se em estratégias multi-dimensionais, as quais usam múltiplas variáveis temporais definidas em domínios de tempo deformados e não deformados, para lidar, de forma eficaz, com as disparidades existentes entre as diversas escalas de tempo. De modo a poder tirar proveito dos diferentes ritmos de evolução temporal existentes entre correntes e tensões com variação muito rápida (variáveis de estado activas) e correntes e tensões com variação lenta (variáveis de estado latentes), são utilizadas algumas técnicas numéricas avançadas para operar dentro dos espaços multi-dimensionais, como, por exemplo, os algoritmos multi-ritmo de Runge-Kutta, ou o método das linhas. São também apresentadas algumas estratégias de partição dos circuitos, as quais permitem dividir um circuito em sub-circuitos de uma forma completamente automática, em função dos ritmos de evolução das suas variáveis de estado. Para problemas acentuadamente não lineares, são propostos vários métodos inovadores de simulação a operar estritamente no domínio do tempo. Para problemas com não linearidades moderadas é proposto um novo método híbrido frequência-tempo, baseado numa combinação entre a integração passo a passo unidimensional e o método seguidor de envolvente com balanço harmónico. O desempenho dos métodos é testado na simulação de alguns exemplos ilustrativos, com resultados bastante promissores. Uma análise comparativa entre os métodos agora propostos e os métodos actualmente existentes para simulação RF, revela ganhos consideráveis em termos de rapidez de computação.

Analysis of the organic matter associated to sea salt : definition of potential molecular markers based on the volatile composition and presence of glycosidic derivatives and polysaccharides

Sea salt is a natural product obtained from the evaporation of seawater in saltpans due to the combined effect of wind and sunlight. Nowadays, there is a growing interest for protection and re-valorisation of saltpans intrinsically associated to the quality of sea salt that can be evaluated by its physico-chemical properties. These man-made systems can be located in different geographical areas presenting different environmental surroundings. During the crystallization process, organic compounds coming from these surroundings can be incorporated into sea salt crystals, influencing their final composition. The organic matter associated to sea salt arises from three main sources: algae, surrounding bacterial community, and anthropogenic activity. Based on the hypothesis that sea salt contains associated organic compounds that can be used as markers of the product, including saltpans surrounding environment, the aim of this PhD thesis was to identify these compounds. With this purpose, this work comprised: 1) a deep characterisation of the volatile composition of sea salt by headspace solid phase microextraction combined with comprehensive two-dimensional gas chromatography time-of-flight mass spectrometry (HS-SPME/GCGC–ToFMS) methodology, in search of potential sea salt volatile markers; 2) the development of a methodology to isolate the polymeric material potentially present in sea salt, in amounts that allow its characterisation in terms of polysaccharides and protein; and 3) to explore the possible presence of triacylglycerides. The high chromatographic resolution and sensitivity of GC×GC–ToFMS enabled the separation and identification of a higher number of volatile compounds from sea salt, about three folds, compared to unidimentional chromatography (GC–qMS). The chromatographic contour plots obtained revealed the complexity of marine salt volatile composition and confirmed the relevance of GC×GC–ToFMS for this type of analysis. The structured bidimentional chromatographic profile arising from 1D volatility and 2D polarity was demonstrated, allowing more reliable identifications. Results obtained for analysis of salt from two locations in Aveiro and harvested over three years suggest the loss of volatile compounds along the time of storage of the salt. From Atlantic Ocean salts of seven different geographical origins, all produced in 2007, it was possible to identify a sub-set of ten compounds present in all salts, namely 6-methyl-5-hepten-2-one, 2,2,6-trimethylcyclohexanone, isophorone, ketoisophorone, β-ionone-5,6-epoxide, dihydroactinidiolide, 6,10,14-trimethyl-2-pentadecanone, 3-hydroxy-2,4,4-trimethylpentyl 2-methylpropanoate, 2,4,4-trimethylpentane-1,3-diyl bis(2-methylpropanoate), and 2-ethyl-1-hexanol. These ten compounds were considered potential volatile markers of sea salt. Seven of these compounds are carotenoid-derived compounds, and the other three may result from the integration of compounds from anthropogenic activity as metabolites of marine organisms. The present PhD work also allowed the isolation and characterisation, for the first time, of polymeric material from sea salt, using 16 Atlantic Ocean salts. A dialysis-based methodology was developed to isolate the polymeric material from sea salt in amounts that allowed its characterisation. The median content of polymeric material isolated from the 16 salts was 144 mg per kg of salt, e.g. 0.014% (w/w). Mid-infrared spectroscopy and thermogravimetry revealed the main occurrence of sulfated polysaccharides, as well as the presence of protein in the polymeric material from sea salt. Sea salt polysaccharides were found to be rich in uronic acid residues (21 mol%), glucose (18), galactose (16), and fucose (13). Sulfate content represented a median of 45 mol%, being the median content of sulfated polysaccharides 461 mg/g of polymeric material, which accounted for 66 mg/kg of dry salt. Glycosidic linkage composition indicates that the main sugar residues that could carry one or more sulfate groups were identified as fucose and galactose. This fact allowed to infer that the polysaccharides from sea salt arise mainly from algae, due to their abundance and composition. The amino acid profile of the polymeric material from the 16 Atlantic Ocean salts showed as main residues, as medians, alanine (25 mol%), leucine (14), and valine (14), which are hydrophobic, being the median protein content 35 mg/g, i.e. 4,9 mg per kg of dry salt. Beside the occurrence of hydrophobic volatile compounds in sea salt, hydrophobic non-volatile compounds were also detected. Triacylglycerides were obtained from sea salt by soxhlet extraction with n-hexane. Fatty acid composition revealed palmitic acid as the major residue (43 mol%), followed by stearic (13), linolenic (13), oleic (12), and linoleic (9). Sea salt triacylglycerides median content was 1.5 mg per kg of dry salt. Both protein and triacylglycerides seem to arise from macro and microalgae, phytoplankton and cyanobacteria, due to their abundance and composition. Despite the variability resulting from saltpans surrounding environment, this PhD thesis allowed the identification of a sea salt characteristic organic compounds profile based on volatile compounds, polysaccharides, protein, and triacylglycerides.

Electronic Journal of Applied Multivariate Statistics

The ecological sciences have experienced immense growth over the course of this century, and chances are that they will continue to grow well on into the next millennium. There are some good reasons for this – ecology encompasses some of the most pressing concerns facing humanity. With recent advances in data collection technology and ambitious field research, ecologists are increasingly calling upon multivariate statistics to explore and test for patterns in their data. The goal of FISH 560 (Applied Multivariate Statistics for Ecologists) at the University of Washington is to introduce graduate students to the multivariate statistical techniques necessary to carry out sophisticated analyses and to critically evaluate scientific papers using these approaches. It is a practical, hands-on course emphasizing the analysis and interpretation of multivariate analysis, and covers the majority of approaches in common use by ecologists. To celebrate the hard work of past students, I am pleased to announce the creation of the Electronic Journal of Applied Multivariate Statistics (EJAMS). Each year, students in FISH 560 are required to write a final paper consisting of a statistical analysis of their own multivariate data set. These papers are submitted to EJAMS at the end of quarter and are peer reviewed by two other class members. A decision on publication is based on the reviewers’ recommendations and my own reading the paper. In closing, there is a need for the rapid dissemination of ecological research using multivariate statistics at the University of Washington. EJAMS is committed to this challenge.

Analysis of stock market indices through multidimensional scaling

We propose a graphical method to visualize possible time-varying correlations between fifteen stock market values. The method is useful for observing stable or emerging clusters of stock markets with similar behaviour. The graphs, originated from applying multidimensional scaling techniques (MDS), may also guide the construction of multivariate econometric models.

Some reflections on acquisition, processing and analysis of statistical data in forest soils

Beyond the classical statistical approaches (determination of basic statistics, regression analysis, ANOVA, etc.) a new set of applications of different statistical techniques has increasingly gained relevance in the analysis, processing and interpretation of data concerning the characteristics of forest soils. This is possible to be seen in some of the recent publications in the context of Multivariate Statistics. These new methods require additional care that is not always included or refered in some approaches. In the particular case of geostatistical data applications it is necessary, besides to geo-reference all the data acquisition, to collect the samples in regular grids and in sufficient quantity so that the variograms can reflect the spatial distribution of soil properties in a representative manner. In the case of the great majority of Multivariate Statistics techniques (Principal Component Analysis, Correspondence Analysis, Cluster Analysis, etc.) despite the fact they do not require in most cases the assumption of normal distribution, they however need a proper and rigorous strategy for its utilization. In this work, some reflections about these methodologies and, in particular, about the main constraints that often occur during the information collecting process and about the various linking possibilities of these different techniques will be presented. At the end, illustrations of some particular cases of the applications of these statistical methods will also be presented.

Exploraty Multivariate Statistical Methods Applied to Pharmaceutical Industry CRM Data

Dissertação apresentada como requisito parcial para obtenção do grau de Mestre em Estatística e Gestão de Informação

Insertion dans les soins après une première hospitalisation dans un secteur pour psychose [Linkage to care after first hospitalisation for psychosis]

BACKGROUND: First hospitalisation for a psychotic episode causes intense distress to patients and families, but offers an opportunity to make a diagnosis and start treatment. However, linkage to outpatient psychiatric care remains a notoriously difficult step for young psychotic patients, who frequently interrupt treatment after hospitalisation. Persistence of symptoms, and untreated psychosis may therefore remain a problem despite hospitalisation and proper diagnosis. With persisting psychotic symptoms, numerous complications may arise: breakdown in relationships, loss of family and social support, loss of employment or study interruption, denial of disease, depression, suicide, substance abuse and violence. Understanding mechanisms that might promote linkage to outpatient psychiatric care is therefore a critical issue, especially in early intervention in psychotic disorders. OBJECTIVE: To study which factors hinder or promote linkage of young psychotic patients to outpatient psychiatric care after a first hospitalisation, in the absence of a vertically integrated program for early psychosis. Method. File audit study of all patients aged 18 to 30 who were admitted for the first time to the psychiatric University Hospital of Lausanne in the year 2000. For statistical analysis, chi2 tests were used for categorical variables and t-test for dimensional variables; p<0.05 was considered as statistically significant. RESULTS: 230 patients aged 18 to 30 were admitted to the Lausanne University psychiatric hospital for the first time during the year 2000, 52 of them with a diagnosis of psychosis (23%). Patients with psychosis were mostly male (83%) when compared with non-psychosis patients (49%). Furthermore, they had (1) 10 days longer mean duration of stay (24 vs 14 days), (2) a higher rate of compulsory admissions (53% vs 22%) and (3) were more often hospitalised by a psychiatrist rather than by a general practitioner (83% vs 53%). Other socio-demographic and clinical features at admission were similar in the two groups. Among the 52 psychotic patients, 10 did not stay in the catchment area for subsequent treatment. Among the 42 psychotic patients who remained in the catchment area after discharge, 20 (48%) did not attend the scheduled or rescheduled outpatient appointment. None of the socio demographic characteristics were associated with attendance to outpatient appointments. On the other hand, voluntary admission and suicidal ideation before admission were significantly related to attending the initial appointment. Moreover, some elements of treatment seemed to be associated with higher likelihood to attend outpatient treatment: (1) provision of information to the patient regarding diagnosis, (2) discussion about the treatment plan between in- and outpatient staff, (3) involvement of outpatient team during hospitalisation, and (4) elaboration of concrete strategies to face basic needs, organise daily activities or education and reach for help in case of need. CONCLUSION: As in other studies, half of the patients admitted for a first psychotic episode failed to link to outpatient psychiatric care. Our study suggests that treatment rather than patient's characteristics play a critical role in this phenomenon. Development of a partnership and involvement of patients in the decision process, provision of good information regarding the illness, clear definition of the treatment plan, development of concrete strategies to cope with the illness and its potential complications, and involvement of the outpatient treating team already during hospitalisation, all came out as critical strategies to facilitate adherence to outpatient care. While the current rate of disengagement after admission is highly concerning, our finding are encouraging since they constitute strategies that can easily be implemented. An open approach to psychosis, the development of partnership with patients and a better coordination between inpatient and outpatient teams should therefore be among the targets of early intervention programs. These observations might help setting up priorities when conceptualising new programs and facilitate the implementation of services that facilitate engagement of patients in treatment during the critical initial phase of psychotic disorders.

Genome-wide linkage and association analyses to identify genes influencing adiponectin levels: the GEMS Study.

Adiponectin has a variety of metabolic effects on obesity, insulin sensitivity, and atherosclerosis. To identify genes influencing variation in plasma adiponectin levels, we performed genome-wide linkage and association scans of adiponectin in two cohorts of subjects recruited in the Genetic Epidemiology of Metabolic Syndrome Study. The genome-wide linkage scan was conducted in families of Turkish and southern European (TSE, n = 789) and Northern and Western European (NWE, N = 2,280) origin. A whole genome association (WGA) analysis (500K Affymetrix platform) was carried out in a set of unrelated NWE subjects consisting of approximately 1,000 subjects with dyslipidemia and 1,000 overweight subjects with normal lipids. Peak evidence for linkage occurred at chromosome 8p23 in NWE subjects (lod = 3.10) and at chromosome 3q28 near ADIPOQ, the adiponectin structural gene, in TSE subjects (lod = 1.70). In the WGA analysis, the single-nucleotide polymorphisms (SNPs) most strongly associated with adiponectin were rs3774261 and rs6773957 (P < 10(-7)). These two SNPs were in high linkage disequilibrium (r(2) = 0.98) and located within ADIPOQ. Interestingly, our fourth strongest region of association (P < 2 x 10(-5)) was to an SNP within CDH13, whose protein product is a newly identified receptor for high-molecular-weight species of adiponectin. Through WGA analysis, we confirmed previous studies showing SNPs within ADIPOQ to be strongly associated with variation in adiponectin levels and further observed these to have the strongest effects on adiponectin levels throughout the genome. We additionally identified a second gene (CDH13) possibly influencing variation in adiponectin levels. The impact of these SNPs on health and disease has yet to be determined.

Discovery and fine mapping of serum protein loci through transethnic meta-analysis.

Many disorders are associated with altered serum protein concentrations, including malnutrition, cancer, and cardiovascular, kidney, and inflammatory diseases. Although these protein concentrations are highly heritable, relatively little is known about their underlying genetic determinants. Through transethnic meta-analysis of European-ancestry and Japanese genome-wide association studies, we identified six loci at genome-wide significance (p < 5 × 10(-8)) for serum albumin (HPN-SCN1B, GCKR-FNDC4, SERPINF2-WDR81, TNFRSF11A-ZCCHC2, FRMD5-WDR76, and RPS11-FCGRT, in up to 53,190 European-ancestry and 9,380 Japanese individuals) and three loci for total protein (TNFRS13B, 6q21.3, and ELL2, in up to 25,539 European-ancestry and 10,168 Japanese individuals). We observed little evidence of heterogeneity in allelic effects at these loci between groups of European and Japanese ancestry but obtained substantial improvements in the resolution of fine mapping of potential causal variants by leveraging transethnic differences in the distribution of linkage disequilibrium. We demonstrated a functional role for the most strongly associated serum albumin locus, HPN, for which Hpn knockout mice manifest low plasma albumin concentrations. Other loci associated with serum albumin harbor genes related to ribosome function, protein translation, and proteasomal degradation, whereas those associated with serum total protein include genes related to immune function. Our results highlight the advantages of transethnic meta-analysis for the discovery and fine mapping of complex trait loci and have provided initial insights into the underlying genetic architecture of serum protein concentrations and their association with human disease.