Matematisk institutt
http://hdl.handle.net/10852/5
Wed, 17 Jan 2018 07:12:58 GMT
20180117T07:12:58Z

Evaluating properties of environmental contours
http://hdl.handle.net/10852/59492
Evaluating properties of environmental contours
Huseby, Arne; Vanem, Erik; Eskeland, Karoline
Environmental contours are widely used as a basis for e.g., ship design. The traditional approach to environmental contours is based on the wellknown Rosenblatt transformation. However, due to the effects of this transformation the probabilistic properties of the resulting environmental contour can be difficult to interpret. An alternative approach to environmental contours uses Monte Carlo simulations on the joint environmental model, and thus obtain a contour without the need for the Rosenblatt transformation. This contour have welldefined probabilistic properties, but may sometimes be overly conservative in certain areas. In this paper we give a precise definition of the concept of exceedence probability which is valid for all types of environmental contours. Moreover, we show how to estimate the exceedence probability of a given environmental contour, and use this to compare different approaches to contour construction. The methods are illustrated by numerical examples based on reallife data.
This is a accepted version of a chapter from the book Safety and Reliability. Theory and Applications. © CRC Publishing / Taylor & Francis Group
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/59492
20170101T00:00:00Z

Fano congruences of index 3 and alternating 3forms
http://hdl.handle.net/10852/59368
Fano congruences of index 3 and alternating 3forms
Ranestad, Kristian; Mezzetti, Emilia; De Poi, Pietro; Faenzi, Daniele
We study congruences of lines $X_\omega $ defined by a sufficiently general choice of an alternating 3form $\omega $ in $n+1$ dimensions, as Fano manifolds of index $3$ and dimension $n1$. These congruences include the $\mathrm{G}_2$variety for $n=6$ and the variety of reductions of projected $\mathbb{P}^2 \times \mathbb{P}^2$ for $n=7$.
We compute the degree of $X_\omega $ as the $n$th Fine number and study the Hilbert scheme of these congruences proving that the choice of $\omega $ bijectively corresponds to $X_\omega $ except when $n=5$. The fundamental locus of the congruence is also studied together with its singular locus: these varieties include the Coble cubic for $n=8$ and the Peskine variety for $n=9$.
The residual congruence $Y$ of $X_\omega $ with respect to a general linear congruence containing $X_\omega $ is analysed in terms of the quadrics containing the linear span of $X_\omega $. We prove that $Y$ is Cohen–Macaulay but nonGorenstein in codimension $4$. We also examine the fundamental locus $G$ of $Y$ of which we determine the singularities and the irreducible components.
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/59368
20170101T00:00:00Z

The Geometry of the Space of Curves of Genus 2
http://hdl.handle.net/10852/59364
The Geometry of the Space of Curves of Genus 2
Vodrup, Magnus Røen
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/59364
20170101T00:00:00Z

Latent Gaussian models to predict historical bycatch in commercial fishery
http://hdl.handle.net/10852/59360
Latent Gaussian models to predict historical bycatch in commercial fishery
Breivik, Olav Nikolai; Storvik, Geir Olve; Nedreaas, Kjell Harald
Knowledge about how many fish that have been killed due to bycatch is an important aspect of ensuring a sustainable ecosystem and fishery. We introduce a Bayesian spatiotemporal prediction method for historical bycatch that incorporates two sources of available data sets, fishery data and survey data. The model used assumes that occurrence of bycatch can be described as a loglinear combination of covariates and random effects modeled as Gaussian fields. Integrated Nested Laplace Approximations (INLA) is used for fast calculations. The method introduced is general, and is applied on bycatch of juvenile cod (Gadus morhua) in the Barents Sea shrimp (Pandalus borealis) fishery. In this fishery we compare our prediction method with the well known ratio and effort methods, and make a strong case that the Bayesian spatiotemporal method produces more reliable historical bycatch predictions compared to existing methods.
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/59360
20170101T00:00:00Z

Latent gaussian models to decide on spatial closures for bycatch management in the barents sea shrimp fishery
http://hdl.handle.net/10852/59359
Latent gaussian models to decide on spatial closures for bycatch management in the barents sea shrimp fishery
Breivik, Olav Nikolai; Storvik, Geir Olve; Nedreaas, Kjell Harald
In the Barents Sea and adjacent water, fishing grounds are closed for shrimp fishing by the Norwegian Directorate of Fisheries Monitoring and Surveillance Service (MSS) if the expected number of juvenile fish caught are predicted to exceed a certain limit per kilogram shrimp (Pandalus borealis). Today, a simple ratio estimator, which does not fully utilize all data available, is in use. In this paper, we construct a Bayesian hierarchical spatiotemporal model for improved prediction of the bycatch ratio in the Barents Sea shrimp fishery. More predictable bycatch will be an advantage for the MSS because of more correct decisions and better resource allocation and also for the fishermen because of more predictable fishing grounds. The model assumes that the occurrence of shrimp and juvenile Atlantic cod (Gadus morhua) can be modeled by linked regression models containing several covariates (including 0group abundance estimates) and random effects modeled as Gaussian fields. Integrated nested Laplace approximations is applied for fast calculation. The method is applied to prediction of the bycatch ratio for Atlantic cod.
Fri, 01 Jan 2016 00:00:00 GMT
http://hdl.handle.net/10852/59359
20160101T00:00:00Z

EuroForMix: An open source software based on a continuous model to evaluate STR DNA profiles from a mixture of contributors with artefacts
http://hdl.handle.net/10852/59358
EuroForMix: An open source software based on a continuous model to evaluate STR DNA profiles from a mixture of contributors with artefacts
Bleka, Øyvind; Storvik, Geir Olve; Gill, Peter
We have released a software named EuroForMix to analyze STR DNA profiles in a userfriendly graphical user interface. The software implements a model to explain the allelic peak height on a continuous scale in order to carry out weightofevidence calculations for profiles which could be from a mixture of contributors. Through a properly parameterized model we are able to do inference on mixture proportions, the peak height properties, stutter proportion and degradation. In addition, EuroForMix includes models for allele dropout, allele dropin and subpopulation structure. EuroForMix supports two inference approaches for likelihood ratio calculations. The first approach uses maximum likelihood estimation of the unknown parameters. The second approach is Bayesian based which requires prior distributions to be specified for the parameters involved. The user may specify any number of known and unknown contributors in the model, however we find that there is a practical computing time limit which restricts the model to a maximum of four unknown contributors.
EuroForMix is the first freely open source, continuous model (accommodating peak height, stutter, dropin, dropout, population substructure and degradation), to be reported in the literature. It therefore serves an important purpose to act as an unrestricted platform to compare different solutions that are available. The implementation of the continuous model used in the software showed close to identical results to the Rpackage DNAmixtures, which requires a HUGIN Expert license to be used. An additional feature in EuroForMix is the ability for the user to adapt the Bayesian inference framework by incorporating their own prior information.
Fri, 01 Jan 2016 00:00:00 GMT
http://hdl.handle.net/10852/59358
20160101T00:00:00Z

A comparative study of qualitative and quantitative models used to interpret complex STR DNA profiles
http://hdl.handle.net/10852/59357
A comparative study of qualitative and quantitative models used to interpret complex STR DNA profiles
Bleka, Øyvind; Benschop, Corina C G; Storvik, Geir Olve; Gill, Peter
The investigation of the performance of models to interpret complex DNA profiles is best undertaken using real DNA profiles. Here we used a data set to reflect the variety typically encountered in real casework. The “crimestains” were constructed from known individuals and comprised a total of 59 diverse samples: pristine DNA/DNA extracted from blood, 2–3 person mixtures, degradation/nodegradation, differences in allele sharing, dropout/no dropout, etc. Two siblings were also included in the testset in order to challenge the systems. Two kinds of analyses were performed, namely tests on whether a person of interest is a contributor based on weightofevidence (likelihood ratio) calculations, and deconvolution test to estimate the profile of unknown constituent parts. The weightofevidence analyses compared LRmix Studio with EuroForMix including exploration of the effect of applying an ad hoc stutterfilter. For the deconvolution analysis we compared EuroForMix with LoCIMtool. When we classified persons of interests into being true contributors or noncontributors, we found that EuroForMix, overall, returned a higher true positive rate for the same false positive levels compared to LRmix. In particular, in cases with an unknown major component, EuroForMix was more discriminating for mixtures where the person of interest was a minor contributor. Comparing deconvolution of major contributors we found that EuroForMix overall performed better than LoCIMtool.
Fri, 01 Jan 2016 00:00:00 GMT
http://hdl.handle.net/10852/59357
20160101T00:00:00Z

On the choice and influence of the number of boosting steps for highdimensional linear Coxmodels
http://hdl.handle.net/10852/59345
On the choice and influence of the number of boosting steps for highdimensional linear Coxmodels
Seibold, Heidi; Bernau, Christoph; Boulesteix, AnneLaure; De Bin, Riccardo
In biomedical research, boostingbased regression approaches have gained much attention in the last decade. Their intrinsic variable selection procedure and ability to shrink the estimates of the regression coefficients toward 0 make these techniques appropriate to fit prediction models in the case of highdimensional data, e.g. gene expressions. Their prediction performance, however, highly depends on specific tuning parameters, in particular on the number of boosting iterations to perform. This crucial parameter is usually selected via crossvalidation. The crossvalidation procedure may highly depend on a completely random component, namely the considered fold partition. We empirically study how much this randomness affects the results of the boosting techniques, in terms of selected predictors and prediction ability of the related models. We use four publicly available data sets related to four different diseases. In these studies, the goal is to predict survival endpoints when a large number of continuous candidate predictors are available. We focus on two well known boosting approaches implemented in the Rpackages CoxBoost and mboost, assuming the validity of the proportional hazards assumption and the linearity of the effects of the predictors. We show that the variability in selected predictors and prediction ability of the model is reduced by averaging over several repetitions of crossvalidation in the selection of the tuning parameters.
The final version of this research has been published in Computational Statistics. © 2017 Springer Verlag
Mon, 01 Jan 2018 00:00:00 GMT
http://hdl.handle.net/10852/59345
20180101T00:00:00Z

Handling codependence issues in resamplingbased variable selection procedures: a simulation study
http://hdl.handle.net/10852/59344
Handling codependence issues in resamplingbased variable selection procedures: a simulation study
De Bin, Riccardo; Sauerbrei, Willi
If a number of candidate variables are available, variable selection is a key task aiming to identify those candidates which influence the outcome of interest. Methods as backward elimination, forward selection, etc. are often implemented, despite their drawbacks. One of these drawbacks is the instability of their results with respect to small perturbations in the data. To handle this issue, resamplingbased procedures have been introduced; using a resampling technique, e.g. bootstrap, these procedures generate several pseudosamples that are used to compute the inclusion frequency of each variable, i.e. the proportion of pseudosamples in which the variable is selected. Based on the inclusion frequencies, it is possible to discriminate between relevant and irrelevant variables. These procedures may fail in case of correlated variables. To deal with this issue, two procedures based on 2×2 tables of inclusion frequencies have been developed in the literature. In this paper we analyse the behaviours of these two procedures and the role of their tuning parameters in an extensive simulation study.
Mon, 01 Jan 2018 00:00:00 GMT
http://hdl.handle.net/10852/59344
20180101T00:00:00Z

Detection of influential points as a byproduct of resamplingbased variable selection procedures
http://hdl.handle.net/10852/59343
Detection of influential points as a byproduct of resamplingbased variable selection procedures
De Bin, Riccardo; Boulesteix, AnneLaure; Sauerbrei, Willi
Influential points can cause severe problems when deriving a multivariable regression model. A novel approach to check for such points is proposed, based on the variable inclusion matrix, a simple way to summarize results from resamplingbased variable selection procedures. The variable inclusion matrix reports whether a variable (column) is included in a regression model fitted on a pseudosample (row) generated from the original data (e.g., bootstrap sample or subsample). It is used to study the variable selection stability, to derive weights for model averaged predictors and in others investigations. Concentrating on variable selection, it also allows understanding whether the presence of a specific observation has an influence on the selection of a variable. From the variable inclusion matrix, indeed, the inclusion frequency (Ifrequency) of each variable can be computed only in the pseudosamples (i.e., rows) which contain the specific observation. When the procedure is repeated for each observation, it is possible to check for influential points through the distribution of the Ifrequencies, visualized in a boxplot, or through a Grubbs’ test. Outlying values in the former case and significant results in the latter point to observations having an influence on the selection of a specific variable and therefore on the finally selected model. This novel approach is illustrated in two real data examples.
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/59343
20170101T00:00:00Z

IPFLASSO: Integrative L1Penalized Regression with Penalty Factors for Prediction Based on MultiOmics Data
http://hdl.handle.net/10852/59342
IPFLASSO: Integrative L1Penalized Regression with Penalty Factors for Prediction Based on MultiOmics Data
Boulesteix, AnneLaure; De Bin, Riccardo; Jiang, Xiaoyu; Fuchs, Mathias
As modern biotechnologies advance, it has become increasingly frequent that different modalities of highdimensional molecular data (termed “omics” data in this paper), such as gene expression, methylation, and copy number, are collected from the same patient cohort to predict the clinical outcome. While prediction based on omics data has been widely studied in the last fifteen years, little has been done in the statistical literature on the integration of multiple omics modalities to select a subset of variables for prediction, which is a critical task in personalized medicine. In this paper, we propose a simple penalized regression method to address this problem by assigning different penalty factors to different data modalities for feature selection and prediction. The penalty factors can be chosen in a fully datadriven fashion by crossvalidation or by taking practical considerations into account. In simulation studies, we compare the prediction performance of our approach, called IPFLASSO (Integrative LASSO with Penalty Factors) and implemented in the R package ipflasso, with the standard LASSO and sparse group LASSO. The use of IPFLASSO is also illustrated through applications to two reallife cancer datasets. All data and codes are available on the companion website to ensure reproducibility.
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/59342
20170101T00:00:00Z

Stochastic modeling of photovoltaic power generation and electricity prices
http://hdl.handle.net/10852/59335
Stochastic modeling of photovoltaic power generation and electricity prices
Benth, Fred Espen; Ibrahim, Noor Adilah
In recent years, renewable energy has gained importance in producing power in many markets. The aim of this article is to model photovoltaic (PV) production for three transmission operators in Germany. PV power can only be generated during sun hours and the cloud cover will determine its overall production. Therefore, we propose a model that takes into account the sun intensity as a seasonal function. We model the deseasonalized data by an autoregressive process to capture the stochastic dynamics in the data. We present two applications based on our suggested model. First, we build a relationship between electricity spot prices and PV production where the higher the volume of PV production, the lower the power prices. As a further application, we discuss virtual power plant derivatives and energy quanto options.
This is a submitted version of an article which will be published in the Journal of Energy Markets. © Incisive Media
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/59335
20170101T00:00:00Z

Sensitivity Analysis of Prices of Claims in Turbulent Markets
http://hdl.handle.net/10852/59263
Sensitivity Analysis of Prices of Claims in Turbulent Markets
Coffie, Emmanuel
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/59263
20170101T00:00:00Z

Simulating sleep.
http://hdl.handle.net/10852/59260
Simulating sleep.
Grobovs, Janis
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/59260
20170101T00:00:00Z

A white noise approach to insider trading
http://hdl.handle.net/10852/59180
A white noise approach to insider trading
Øksendal, Bernt; Røse, Elin Engen
We present a new approach to the optimal portfolio problem for an insider with logarithmic utility. Our method is based on white noise theory, stochastic forward integrals, HidaMalliavin calculus and the Donsker delta function.
Thu, 01 Jan 2015 00:00:00 GMT
http://hdl.handle.net/10852/59180
20150101T00:00:00Z

A Maximum Principle for MeanField SDEs with Time Change
http://hdl.handle.net/10852/59114
A Maximum Principle for MeanField SDEs with Time Change
Di Nunno, Giulia; Haferkorn, Hannes Hagen
Time change is a powerful technique for generating noises and providing flexible models. In the framework of time changed Brownian and Poisson random measures we study the existence and uniqueness of a solution to a general meanfield stochastic differential equation. We consider a meanfield stochastic control problem for meanfield controlled dynamics and we present a necessary and a sufficient maximum principle. For this we study existence and uniqueness of solutions to meanfield backward stochastic differential equations in the context of time change. An example of a centralised control in an economy with specialised sectors is provided.
The final version of this research has been published in Applied Mathematics and Optimization. © 2017 Springer Verlag
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/59114
20170101T00:00:00Z

A BSPLINELIKE BASIS FOR THE POWELLSABIN 12SPLIT BASED ON SIMPLEX SPLINES
http://hdl.handle.net/10852/59094
A BSPLINELIKE BASIS FOR THE POWELLSABIN 12SPLIT BASED ON SIMPLEX SPLINES
Cohen, Elaine; Lyche, Tom; Riesenfeld, Richard F
We introduce a simplex spline basis for a space of C^1quadratics on the wellknown PowellSabin 12split triangular region. Among its many important desirable properties, we show that it has an associated recurrence relation for evaluation and differentiation. Also developed are a Marsdenlike identity, quasiinterpolants, approximation methods exhibiting unconditional stability, a subdivision scheme, and smoothness conditions across macroelement edges.
This research has been published in Mathematics of Computation. © 2013 American Mathematical Society
Tue, 01 Jan 2013 00:00:00 GMT
http://hdl.handle.net/10852/59094
20130101T00:00:00Z

The stability of parabolic problems with nonstandard p(x,t)growth
http://hdl.handle.net/10852/59077
The stability of parabolic problems with nonstandard p(x,t)growth
Erhardt, André H
In this paper, we study weak solutions to the following nonlinear parabolic partial differential equation ∂tu−diva(x,t,∇u)+λ(up(x,t)−2u)=0inΩT, where λ≥0 and ∂tu denote the partial derivative of u with respect to the time variable t, while ∇u denotes the one with respect to the space variable x. Moreover, the vectorfield a(x,t,⋅) satisfies certain nonstandard p(x,t) growth and monotonicity conditions. In this manuscript, we establish the existence of a unique weak solution to the corresponding Dirichlet problem. Furthermore, we prove the stability of this solution, i.e., we show that two weak solutions with different initial values are controlled by these initial values.
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/59077
20170101T00:00:00Z

Cinfinityregularization by Noise of Singular ODE's
http://hdl.handle.net/10852/59066
Cinfinityregularization by Noise of Singular ODE's
Baños, David Ruiz; Proske, Frank Norbert
In this paper we construct a new type of noise of fractional nature that has a strong regularizing effect on differential equations. We consider an equation with this noise with a highly irregular coefficient. We employ a new method to prove existence and uniqueness of global strong solutions where classical methods fail because of the ”roughness” and nonMarkovianity of the driving process. In addition, we prove the rather remarkable property that such solutions are infinitely many times classically differentiable with respect to the initial condition in spite of the vector field being discontinuous. This opens a fundamental question on studying certain classes of interesting partial differential equations perturbed by this noise.
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/59066
20170101T00:00:00Z

Equivariant vector bundles, their derived category and Ktheory on affine schemes
http://hdl.handle.net/10852/58925
Equivariant vector bundles, their derived category and Ktheory on affine schemes
Krishna, Amalendu; Ravi, Charanya
Let GG be an affine group scheme over a noetherian commutative ring RR. We show that every GGequivariant vector bundle on an affine toric scheme over RR with GGaction is equivariantly extended from Spec ( R ) Spec(R) for several cases of RR and GG. We show that, given two affine schemes with group scheme actions, an equivalence of the equivariant derived categories implies isomorphism of the equivariant KKtheories as well as equivariant K'K′theories.
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/58925
20170101T00:00:00Z