An analysis of implied volatility jump dynamics: Novel functional data representation in crude oil markets

The predominant fear in capital markets is that of a price spike. Commodity markets differ in that there is a fear of both upward and down jumps, this results in implied volatility curves displaying distinct shapes when compared to equity markets. The use of a novel functional data analysis (FDA) approach, provides a framework to produce and interpret functional objects that characterise the underlying dynamics of oil future options. We use the FDA framework to examine implied volatility, jump risk, and pricing dynamics within crude oil markets. Examining a WTI crude oil sample for the 2007–2013 period, which includes the global financial crisis and the Arab Spring, strong evidence is found of converse jump dynamics during periods of demand and supply side weakness. This is used as a basis for an FDA-derived Merton (1976) jump diffusion optimised delta hedging strategy, which exhibits superior portfolio management results over traditional methods.

ENHANCING MULTISCALE FRACTAL DESCRIPTORS USING FUNCTIONAL DATA ANALYSIS

This work presents a novel approach in order to increase the recognition power of Multiscale Fractal Dimension (MFD) techniques, when applied to image classification. The proposal uses Functional Data Analysis (FDA) with the aim of enhancing the MFD technique precision achieving a more representative descriptors vector, capable of recognizing and characterizing more precisely objects in an image. FDA is applied to signatures extracted by using the Bouligand-Minkowsky MFD technique in the generation of a descriptors vector from them. For the evaluation of the obtained improvement, an experiment using two datasets of objects was carried out. A dataset was used of characters shapes (26 characters of the Latin alphabet) carrying different levels of controlled noise and a dataset of fish images contours. A comparison with the use of the well-known methods of Fourier and wavelets descriptors was performed with the aim of verifying the performance of FDA method. The descriptor vectors were submitted to Linear Discriminant Analysis (LDA) classification method and we compared the correctness rate in the classification process among the descriptors methods. The results demonstrate that FDA overcomes the literature methods (Fourier and wavelets) in the processing of information extracted from the MFD signature. In this way, the proposed method can be considered as an interesting choice for pattern recognition and image classification using fractal analysis.

MODELING FUNCTIONAL DATA WITH SPATIALLY HETEROGENEOUS SHAPE CHARACTERISTICS

We propose a novel class of models for functional data exhibiting skewness or other shape characteristics that vary with spatial or temporal location. We use copulas so that the marginal distributions and the dependence structure can be modeled independently. Dependence is modeled with a Gaussian or t-copula, so that there is an underlying latent Gaussian process. We model the marginal distributions using the skew t family. The mean, variance, and shape parameters are modeled nonparametrically as functions of location. A computationally tractable inferential framework for estimating heterogeneous asymmetric or heavy-tailed marginal distributions is introduced. This framework provides a new set of tools for increasingly complex data collected in medical and public health studies. Our methods were motivated by and are illustrated with a state-of-the-art study of neuronal tracts in multiple sclerosis patients and healthy controls. Using the tools we have developed, we were able to find those locations along the tract most affected by the disease. However, our methods are general and highly relevant to many functional data sets. In addition to the application to one-dimensional tract profiles illustrated here, higher-dimensional extensions of the methodology could have direct applications to other biological data including functional and structural MRI.

Functional data analysis approaches for genotype-phenotype association studies from next-generation sequencing

Next-generation DNA sequencing platforms can effectively detect the entire spectrum of genomic variation and is emerging to be a major tool for systematic exploration of the universe of variants and interactions in the entire genome. However, the data produced by next-generation sequencing technologies will suffer from three basic problems: sequence errors, assembly errors, and missing data. Current statistical methods for genetic analysis are well suited for detecting the association of common variants, but are less suitable to rare variants. This raises great challenge for sequence-based genetic studies of complex diseases.^ This research dissertation utilized genome continuum model as a general principle, and stochastic calculus and functional data analysis as tools for developing novel and powerful statistical methods for next generation of association studies of both qualitative and quantitative traits in the context of sequencing data, which finally lead to shifting the paradigm of association analysis from the current locus-by-locus analysis to collectively analyzing genome regions.^ In this project, the functional principal component (FPC) methods coupled with high-dimensional data reduction techniques will be used to develop novel and powerful methods for testing the associations of the entire spectrum of genetic variation within a segment of genome or a gene regardless of whether the variants are common or rare.^ The classical quantitative genetics suffer from high type I error rates and low power for rare variants. To overcome these limitations for resequencing data, this project used functional linear models with scalar response to develop statistics for identifying quantitative trait loci (QTLs) for both common and rare variants. To illustrate their applications, the functional linear models were applied to five quantitative traits in Framingham heart studies. ^ This project proposed a novel concept of gene-gene co-association in which a gene or a genomic region is taken as a unit of association analysis and used stochastic calculus to develop a unified framework for testing the association of multiple genes or genomic regions for both common and rare alleles. The proposed methods were applied to gene-gene co-association analysis of psoriasis in two independent GWAS datasets which led to discovery of networks significantly associated with psoriasis.^

GALANT: a Cytoscape plugin for visualizing data as functional landscapes projected onto biological networks

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Statistical methods for electromyography data and associated problems

This thesis proposes three novel models which extend the statistical methodology for motor unit number estimation, a clinical neurology technique. Motor unit number estimation is important in the treatment of degenerative muscular diseases and, potentially, spinal injury. Additionally, a recent and untested statistic to enable statistical model choice is found to be a practical alternative for larger datasets. The existing methods for dose finding in dual-agent clinical trials are found to be suitable only for designs of modest dimensions. The model choice case-study is the first of its kind containing interesting results using so-called unit information prior distributions.

Genetic, functional, and histopathological evaluation of two C-terminal BRCA1 missense variants

Background: The vast majority of BRCA1 missense sequence variants remain uncharacterised for their possible effect on protein expression and function, and therefore are unclassified in terms of their pathogenicity. BRCA1 plays diverse cellular roles and it is unlikely that any single functional assay will accurately reflect the total cellular implications of missense mutations in this gene. Objective: To elucidate the effect of two BRCA1 variants, 5236G>C (G1706A) and 5242C>A (A1708E) on BRCA1 function, and to survey the relative usefulness of several assays to direct the characterisation of other unclassified variants in BRCA genes. Methods and Results: Data from a range of bioinformatic, genetic, and histopathological analyses, and in vitro functional assays indicated that the 1708E variant was associated with the disruption of different cellular functions of BRCA1. In transient transfection experiments in T47D and 293T cells, the 1708E product was mislocalised to the cytoplasm and induced centrosome amplification in 293T cells. The 1708E variant also failed to transactivate transcription of reporter constructs in mammalian transcriptional transactivation assays. In contrast, the 1706A variant displayed a phenotype comparable to wildtype BRCA1 in these assays. Consistent with functional data, tumours from 1708E carriers showed typical BRCA1 pathology, while tumour material from 1706A carriers displayed few histopathological features associated with BRCA1 related tumours. Conclusions: A comprehensive range of genetic, bioinformatic, and functional analyses have been combined for the characterisation of BRCA1 unclassified sequence variants. Consistent with the functional analyses, the combined odds of causality calculated for the 1706A variant after multifactorial likelihood analysis (1:142) indicates a definitive classification of this variant as "benign". In contrast, functional assays of the 1708E variant indicate that it is pathogenic, possibly through subcellular mislocalisation. However, the combined odds of 262:1 in favour of causality of this variant does not meet the minimal ratio of 1000:1 for classification as pathogenic, and A1708E remains formally designated as unclassified. Our findings highlight the importance of comprehensive genetic information, together with detailed functional analysis for the definitive categorisation of unclassified sequence variants. This combination of analyses may have direct application to the characterisation of other unclassified variants in BRCA1 and BRCA2.

Functional annotation signatures of disease susceptibility loci improve SNP association analysis.

BACKGROUND: Genetic association studies are conducted to discover genetic loci that contribute to an inherited trait, identify the variants behind these associations and ascertain their functional role in determining the phenotype. To date, functional annotations of the genetic variants have rarely played more than an indirect role in assessing evidence for association. Here, we demonstrate how these data can be systematically integrated into an association study's analysis plan. RESULTS: We developed a Bayesian statistical model for the prior probability of phenotype-genotype association that incorporates data from past association studies and publicly available functional annotation data regarding the susceptibility variants under study. The model takes the form of a binary regression of association status on a set of annotation variables whose coefficients were estimated through an analysis of associated SNPs in the GWAS Catalog (GC). The functional predictors examined included measures that have been demonstrated to correlate with the association status of SNPs in the GC and some whose utility in this regard is speculative: summaries of the UCSC Human Genome Browser ENCODE super-track data, dbSNP function class, sequence conservation summaries, proximity to genomic variants in the Database of Genomic Variants and known regulatory elements in the Open Regulatory Annotation database, PolyPhen-2 probabilities and RegulomeDB categories. Because we expected that only a fraction of the annotations would contribute to predicting association, we employed a penalized likelihood method to reduce the impact of non-informative predictors and evaluated the model's ability to predict GC SNPs not used to construct the model. We show that the functional data alone are predictive of a SNP's presence in the GC. Further, using data from a genome-wide study of ovarian cancer, we demonstrate that their use as prior data when testing for association is practical at the genome-wide scale and improves power to detect associations. CONCLUSIONS: We show how diverse functional annotations can be efficiently combined to create 'functional signatures' that predict the a priori odds of a variant's association to a trait and how these signatures can be integrated into a standard genome-wide-scale association analysis, resulting in improved power to detect truly associated variants.

Functional effect of the C242T polymorphism in the NAD(P)H oxidase p22phox gene on vascular superoxide production in atherosclerosis.

BACKGROUND:

Increased superoxide anion production increases oxidative stress and reduces nitric oxide bioactivity in vascular disease states. NAD(P)H oxidase is an important source of superoxide in human blood vessels, and some studies suggest a possible association between polymorphisms in the NAD(P)H oxidase CYBA gene and atherosclerosis; however, no functional data address this hypothesis. We examined the relationships between the CYBA C242T polymorphism and direct measurements of superoxide production in human blood vessels.

METHODS AND RESULTS:

Vascular NAD(P)H oxidase activity was determined in human saphenous veins obtained from 110 patients with coronary artery disease and identified risk factors. Immunoblotting, reverse-transcription polymerase chain reaction, and DNA sequencing showed that p22phox protein, mRNA, and 242C/T allelic variants are expressed in human blood vessels. Vascular superoxide production, both basal and NADH-stimulated, was highly variable between patients, but the presence of the CYBA 242T allele was associated with significantly reduced vascular NAD(P)H oxidase activity, independent of other clinical risk factors for atherosclerosis.

CONCLUSIONS:

Association of the CYBA 242T allele with reduced NAD(P)H oxidase activity in human blood vessels suggests that genetic variation in NAD(P)H oxidase components may play a significant role in modulating superoxide production in human atherosclerosis.

Evolution, gene regulation and functional analysis of BMP2 in fish

Bone morphogenetic proteins (BMPs) are multifunctional growth factors belonging to the transforming growth factor β (TGFβ) superfamily with a central role in bone formation and mineralization. BMP2, a founding member of this family, has demonstrated remarkable osteogenic properties and is clinically used to promote bone repair and fracture healing. Lack of basic data on factors regulating BMP2 expression and activity have hampered a better understanding of its role in bone formation and bone-related diseases. The objective of this work was to collect new functional data and determine spatiotemporal expression patterns in a fish system aiming towards a better understanding of BMP2 function and regulation. Transcriptional and post-transcriptional regulation of gilthead seabream BMP2 gene was inferred from luciferase reporter systems. Several bone- and cartilage-related transcription factors (e.g. RUNX3, MEF2c, SOX9 and ETS1) were found to regulate BMP2 transcription, while microRNA 20a was shown to affect stability of the BMP2 transcript and thus the mineralogenic capacity of fish bone-derived host cells. The regulation of BMP2 activity through an interaction with the matrix Gla protein (MGP) was investigated in vitro using BMP responsive elements (BRE) coupled to luciferase reporter gene. Although we demonstrated the functionality of the experimental system in a fish cell line and the activation of BMP signaling pathway by seabream BMP2, no conclusive evidence could be collected on a possible interaction beween MGP and BMP2. The evolutionary relationship among the members of BMP2/4/16 subfamily was inferred from taxonomic and phylogenetic analyses. BMP16 diverged prior to BMP2 and BMP4 and should be the result of an ancient genome duplication that occurred early in vertebrate evolution. Structural and functional data suggested that all three proteins are effectors of the BMP signaling pathway, but expression data revealed different spatiotemporal patterns in teleost fish suggesting distinct mechanisms of regulation. In this work, through the collection of novel data, we provide additional insight into the regulation, the structure and the phylogenetic relationship of BMP2 and its closely related family members.

Molecular structure and functional analysis of runx3 in zebrafish

Tese de doutoramento, Ciências Biomédicas, Universidade do Algarve, Departamento de Ciências Biomédicas e Medicina, 2014

Anatomo-functional magnetic resonance imaging of the spinal cord and its application to the characterization of spinal lesions in cats

Les lésions de la moelle épinière ont un impact significatif sur la qualité de la vie car elles peuvent induire des déficits moteurs (paralysie) et sensoriels. Ces déficits évoluent dans le temps à mesure que le système nerveux central se réorganise, en impliquant des mécanismes physiologiques et neurochimiques encore mal connus. L'ampleur de ces déficits ainsi que le processus de réhabilitation dépendent fortement des voies anatomiques qui ont été altérées dans la moelle épinière. Il est donc crucial de pouvoir attester l'intégrité de la matière blanche après une lésion spinale et évaluer quantitativement l'état fonctionnel des neurones spinaux. Un grand intérêt de l'imagerie par résonance magnétique (IRM) est qu'elle permet d'imager de façon non invasive les propriétés fonctionnelles et anatomiques du système nerveux central. Le premier objectif de ce projet de thèse a été de développer l'IRM de diffusion afin d'évaluer l'intégrité des axones de la matière blanche après une lésion médullaire. Le deuxième objectif a été d'évaluer dans quelle mesure l'IRM fonctionnelle permet de mesurer l'activité des neurones de la moelle épinière. Bien que largement appliquées au cerveau, l'IRM de diffusion et l'IRM fonctionnelle de la moelle épinière sont plus problématiques. Les difficultés associées à l'IRM de la moelle épinière relèvent de sa fine géométrie (environ 1 cm de diamètre chez l'humain), de la présence de mouvements d'origine physiologique (cardiaques et respiratoires) et de la présence d'artefacts de susceptibilité magnétique induits par les inhomogénéités de champ, notamment au niveau des disques intervertébraux et des poumons. L'objectif principal de cette thèse a donc été de développer des méthodes permettant de contourner ces difficultés. Ce développement a notamment reposé sur l'optimisation des paramètres d'acquisition d'images anatomiques, d'images pondérées en diffusion et de données fonctionnelles chez le chat et chez l'humain sur un IRM à 3 Tesla. En outre, diverses stratégies ont été étudiées afin de corriger les distorsions d'images induites par les artefacts de susceptibilité magnétique, et une étude a été menée sur la sensibilité et la spécificité de l'IRM fonctionnelle de la moelle épinière. Les résultats de ces études démontrent la faisabilité d'acquérir des images pondérées en diffusion de haute qualité, et d'évaluer l'intégrité de voies spinales spécifiques après lésion complète et partielle. De plus, l'activité des neurones spinaux a pu être détectée par IRM fonctionnelle chez des chats anesthésiés. Bien qu'encourageants, ces résultats mettent en lumière la nécessité de développer davantage ces nouvelles techniques. L'existence d'un outil de neuroimagerie fiable et robuste, capable de confirmer les paramètres cliniques, permettrait d'améliorer le diagnostic et le pronostic chez les patients atteints de lésions médullaires. Un des enjeux majeurs serait de suivre et de valider l'effet de diverses stratégies thérapeutiques. De telles outils représentent un espoir immense pour nombre de personnes souffrant de traumatismes et de maladies neurodégénératives telles que les lésions de la moelle épinière, les tumeurs spinales, la sclérose en plaques et la sclérose latérale amyotrophique.

Clustering compositional data trajectories

Our essay aims at studying suitable statistical methods for the clustering of compositional data in situations where observations are constituted by trajectories of compositional data, that is, by sequences of composition measurements along a domain. Observed trajectories are known as “functional data” and several methods have been proposed for their analysis. In particular, methods for clustering functional data, known as Functional Cluster Analysis (FCA), have been applied by practitioners and scientists in many fields. To our knowledge, FCA techniques have not been extended to cope with the problem of clustering compositional data trajectories. In order to extend FCA techniques to the analysis of compositional data, FCA clustering techniques have to be adapted by using a suitable compositional algebra. The present work centres on the following question: given a sample of compositional data trajectories, how can we formulate a segmentation procedure giving homogeneous classes? To address this problem we follow the steps described below. First of all we adapt the well-known spline smoothing techniques in order to cope with the smoothing of compositional data trajectories. In fact, an observed curve can be thought of as the sum of a smooth part plus some noise due to measurement errors. Spline smoothing techniques are used to isolate the smooth part of the trajectory: clustering algorithms are then applied to these smooth curves. The second step consists in building suitable metrics for measuring the dissimilarity between trajectories: we propose a metric that accounts for difference in both shape and level, and a metric accounting for differences in shape only. A simulation study is performed in order to evaluate the proposed methodologies, using both hierarchical and partitional clustering algorithm. The quality of the obtained results is assessed by means of several indices

Comparing methods for dimensionality reduction when data are density functions

Functional Data Analysis (FDA) deals with samples where a whole function is observed for each individual. A particular case of FDA is when the observed functions are density functions, that are also an example of infinite dimensional compositional data. In this work we compare several methods for dimensionality reduction for this particular type of data: functional principal components analysis (PCA) with or without a previous data transformation and multidimensional scaling (MDS) for diferent inter-densities distances, one of them taking into account the compositional nature of density functions. The difeerent methods are applied to both artificial and real data (households income distributions)