Trajectorial Models based on Operational Assumptions
Monday, 30.10.17, 14:15-15:15, Raum 125, Eckerstr. 1
We illustrate by example the construction of\none-dimensional models for\noption pricing based on operational and observable features of a\nsingle class of investors and a\nrisky asset. Market models are defined based on a class of investors\ncharacterized by how they operate on financial data leading to\npotential portfolio re-balances.\nOnce observable variables are selected for modeling, necessary conditions\nconstraining these variables and resulting from the operational setup are\nderived. Future uncertainty is then reflected in the construction of\ncombinatorial trajectory spaces satisfying such constraints. In the absence\nof probability assumptions, a minmax methodology is available to price option\ncontracts; numerical results are presented based on worst case estimation of\nparameters.
Vorträge zum 30-jährigen Bestehen des FDM-Seminars
Friday, 3.11.17, 13:30-14:30, Raum 404, Eckerstraße 1, Freiburg i. Br.
Programm:\n\n13:30 Einführung mit Beiträgen von Rektor Prof. Dr. Hans-Jochen Schiewer und dem Mit-Gründer des FDM, Prof. Dr. Josef Honerkamp\n\n14:00 Prof. Dr. Leonhard Held (University of Zurich): Building a Statistical Model: The Endemic-Epidemic Modelling Framework\n\n15:00 Kaffee\n\n15:30 Prof. Dr. Rainer Dahlhaus (Heidelberg University): Cointegration and Phase Synchronization: Bridging Two Theories\n\n16:30 Prof. Dr. Josef Teichmann (ETH Zürich): Affine processes in mathematical Finance\n\n17:30 Schluss\n\n
On detecting changes in the jumps of arbitrary size of a time-continuous stochastic process
Friday, 24.11.17, 12:00-13:00, Raum 404, Eckerstr. 1
An Ito semimartingale is a superposition of a roughly fluctuating Brownian part and a pure jump process. Therefore, it is a very challenging task to disentangle the small jumps of the process from increments of the continuous part. We solve this problem by deriving a statistical procedure for inference on the general jump behaviour of an Ito semimartingale. Finally, we apply this technique to detect abrupt and gradual changes in the jumps of the underlying process using bootstrap tests, where we also allow for local alternatives.
Detection and Estimation of Local Signals
Tuesday, 28.11.17, 12:00-13:00, Raum 404, Eckerstr. 1
I will discuss a general framework for detection of local signals, primarily defined\nby change-points, in sequences of data. Changes can occur continuously, e.g., a\nchange in the slope of a regression line, or discontinuously, e.g., a jump in the\nlevel of a process. I will focus on the problem of segmentation of independent\nnormal observations according to changes in the mean. Results will be illustrated\nby simulations and applications to copy number changes and to historical weather\npatterns. Confidence regions for the change- points and some difficulties associated\nwith dependent observations will also be discussed. Aspects of this research involve\ncollaboration with Fang Xiao, Li Jian, Liu Yi, Nancy Zhang, Benjamin Yakir and\nLi (Charlie) Xia.
Understanding Biological Processes using Stochastic Modelling
Friday, 1.12.17, 12:00-13:00, Raum 404, Eckerstr. 1
The molecular biology of life seems inaccessibly complex, and gene expression is an essential part of it. It is subject to random variation and not exactly predictable. Still, mathematical models and statistical inference pave the way towards the identification of underlying gene regulatory processes. In contrast to deterministic models, stochastic processes capture the randomness of natural phenomena and result in more reliable predictions of cellular dynamics. Stochastic models and their parameter estimation have to take into account the nature of molecular-biological data, including experimental techniques and measurement error.\n \nThis talk presents according modelling and estimation techniques and their applications: the derivation of mRNA contents in single cells; the identification of differently regulated cells from heterogeneous populations using mixed models; and parameter estimation for stochastic differential equations using computer-intensive Markov chain Monte Carlo techniques.
Chronological Age Determination for Forensic Applications using Random Forest Regression and DNA Methylation Analysis
Friday, 19.1.18, 12:00-13:00, Raum 404, Eckerstr. 1
Over the last few years it became clear that additional information is hidden wi-\nthin epigenetic modifications of the DNA, and that especially DNA methylation\n(DNAm) could provide useful evidence to the criminal justice system. Within this\nproject, specific changes in DNAm levels upon age progression at selected loci were\nused to develop an objective scientific tool to determine the chronological age of\nan (unknown) individual. This information can be used to narrow down the list\nof suspects during criminal investigations or to determine the age of a person in\nother legal contexts such as human trafficking. A model for age prediction based\non whole blood samples, 13 selected age-dependent DNAm markers, and a ran-\ndom forest regression (RFR) approach was developed. The analysis of the DNAm\nwas performed using amplicon based massive parallel sequencing (MPS) and the\nRFR model created with the R package RandomForest. The performance of the\nmodel was evaluated using cross-validation for the training set and by indepen-\ndent analysis of an additional test set. Within the seminar, a short introduction\ninto the field of forensic (epi-)genetics, the marker selection and development of\nthe DNA methylation tool based on RFR and MPS as well as the results of the\nage-determination tool will be presented. Furthermore, the potential and (current)\nlimitations of the experimental and machine learning approach in respect to the\nimplementation into forensic investigations will be discussed. The here presented\nproject of the University of Amsterdam in cooperation with the Netherlands Fo-\nrensic Institute was funded by the NCTV grant of the Dutch Ministry of Security\nand Justice.
Higher Order Elicitability
Friday, 26.1.18, 12:00-13:00, Raum 404, Eckerstr. 1
Elicitability of a statistical functional means that it can be obtained as the minimizer of an expected loss function. Such a loss function leads to a natural way of forecast comparison or model selection, and allows for M-estimation and generalized regression.\n\nPrime examples of elicitable functionals are the mean or quantiles of a random variable. Independently, Weber (2006, Mathematical Finance) and Gneiting (2011, JASA) have shown that expected shortfall (ES), an important risk measure in banking and finance, is not elicitable. However, it turns out that ES is jointly elicitable with a certain quantile, that is, it is elicitable of second order.\n\nIn this talk, we present our results on higher order elicitability of ES and some other functionals, and we provide characterizations of the associated classes of consistent scoring functions. We illustrate the usefulness of scoring functions for forecast comparison.
Inference of biogeographical ancestry from SNP data -- an evaluation of selection methods and classifiers on a variety of SNP data sets
Wednesday, 7.3.18, 14:30-15:30, Raum 404, Eckerstr. 1
Single nucleotide polymorphism in DNA have proven to be suitable for inferring biogeographical ancestry of human individuals. Various methods have been developed and recent articles in this field focus on their advantages and evaluate their qualities in a variety of settings and under different aspects, such as the ability to predict admixture rates, the dependency on assumptions or handling different rates of missing data. This thesis includes three aspects that are heavily linked:\nFirst, we test forward selection algorithms to select a minimal sufficient or maybe even best subset of SNPs for ancestry prediction from a given set of SNPs that may not be preselected. We compare the quality of predictions on SNP sets chosen by forward selection with different methods with those on a SNP set selected using a procedure that is based on FST values. Secondly we introduce a novel version of a naive Bayesian classifier.Different versions of Bayesian classifiers have been developed for this purpose and they show good performances. Finally we use SNP data simulation software to systematically test our methods and compare the Bayesian classifier with logistic regression, which is an established method in eye color prediction from SNP data. We investigate the impact of parameters, such as migration and the number of islands, on the prediction performances and conclude the analysis with comparing the results to those on real data sets.