Matematisk institutt
http://hdl.handle.net/10852/5
Wed, 12 Dec 2018 18:26:50 GMT
20181212T18:26:50Z

Parametric or nonparametric: The FIC approach
http://hdl.handle.net/10852/65861
Parametric or nonparametric: The FIC approach
Jullum, Martin; Hjort, Nils Lid
Should one rely on a parametric or nonparametric model when analysing a given data set? This classic question cannot be answered by traditional model selection criteria like AIC and BIC, since a nonparametric model has no likelihood. The purpose of the present paper is to develop a focused information criterion (FIC) for comparing general nonnested parametric models with a nonparametric alternative. It relies in part on the notion of a focus parameter, a population quantity of particular interest in the statistical analysis. The FIC compares and ranks candidate models based on estimated precision of the different modelbased estimators for the focus parameter. It has earlier been developed for several classes of problems, but mainly involving parametric models. The new FIC, including also nonparametrics, is novel also in the mathematical context, being derived without the local neighbourhood asymptotics underlying previous versions of FIC. Certain averageweighted versions, called AFIC, allowing several focus parameters to be considered simultaneously, are also developed. We concentrate on the standard i.i.d. setting and certain direct extensions thereof, but also sketch further generalisations to other types of data. Theoretical and simulationbased results demonstrate desirable properties and satisfactory performance.
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/65861
20170101T00:00:00Z

Bifurcation Analysis of a Certain HodgkinHuxley Model Depending on Multiple Bifurcation Parameters
http://hdl.handle.net/10852/65821
Bifurcation Analysis of a Certain HodgkinHuxley Model Depending on Multiple Bifurcation Parameters
Erhardt, André Henrik
In this paper, we study the dynamics of a certain HodgkinHuxley model describing the action potential (AP) of a cardiac muscle cell for a better understanding of the occurrence of a special type of cardiac arrhythmia, the socalled early afterdepolarisations (EADs). EADs are pathological voltage oscillations during the repolarisation or plateau phase of cardiac APs. They are considered as potential precursors to cardiac arrhythmia and are often associated with deficiencies in potassium currents or enhancements in the calcium or sodium currents, e.g., induced by ion channel diseases, drugs or stress. Our study is focused on the enhancement in the calcium current to identify regions, where EADs related to enhanced calcium current appear. To this aim, we study the dynamics of the model using bifurcation theory and numerical bifurcation analysis. Furthermore, we investigate the interaction of the potassium and calcium current. It turns out that a suitable increasing of the potassium current adjusted the EADs related to an enhanced calcium current. Thus, one can use our result to balance the EADs in the sense that an enhancement in the potassium currents may compensate the effect of enhanced calcium currents.
Mon, 01 Jan 2018 00:00:00 GMT
http://hdl.handle.net/10852/65821
20180101T00:00:00Z

Investigating the Advantages of Having a Tensor Product Finite Element Software
http://hdl.handle.net/10852/65786
Investigating the Advantages of Having a Tensor Product Finite Element Software
Tharmanathan, Nithusha
Mon, 01 Jan 2018 00:00:00 GMT
http://hdl.handle.net/10852/65786
20180101T00:00:00Z

A posteriori error estimation for multiplenetwork poroelasticity
http://hdl.handle.net/10852/65762
A posteriori error estimation for multiplenetwork poroelasticity
Ødegaard, Emilie Eliseussen
Mon, 01 Jan 2018 00:00:00 GMT
http://hdl.handle.net/10852/65762
20180101T00:00:00Z

Investigation of Nanoparticles in Zebrafish using Particle Tracking Velocimetry.
http://hdl.handle.net/10852/65706
Investigation of Nanoparticles in Zebrafish using Particle Tracking Velocimetry.
Farhad, Shako
Cancer is a major public health problem worldwide where it is the second leading cause of death. To improve safety and efficacy of anticancer drugs with less side effects, nanoparticles (NPs) have been studied heavily. The concept of selectively detecting and destroying cancer cells with NPs is very exciting, but from the past 10 years only 0.7\% (median) of the administered NP dose is found to be delivered to a solid tumour. To best be able to study the flow and distribution of fluorescent NPs in vivo, the zebrafish model has become very popular as it is optically transparent for easy imaging. Particle Image Velocimetry (PIV) is a nonintrusive optical measurement method, which gives velocity fields resolved in both time and space. Using PIV as the backbone a Particle Tracking Velocimetry (PTV) code was developed to track NPs varying in scale from 100 nm to 1200 nm. The mean and STD percentage of nanoparticle trajectories that are likely to end up in the vein margin within the next frame decreases with nanoparticle size (800 nm, 400 nm, 200 nm). Distribution of nanoparticle trajectories throughout the vein in relation to different nanoparticle sizes needs more data to determine anything conclusively.; Cancer is a major public health problem worldwide where it is the second leading cause of death. To improve safety and efficacy of anticancer drugs with less side effects, nanoparticles (NPs) have been studied heavily. The concept of selectively detecting and destroying cancer cells with NPs is very exciting, but from the past 10 years only 0.7\% (median) of the administered NP dose is found to be delivered to a solid tumour. To best be able to study the flow and distribution of fluorescent NPs in vivo, the zebrafish model has become very popular as it is optically transparent for easy imaging. Particle Image Velocimetry (PIV) is a nonintrusive optical measurement method, which gives velocity fields resolved in both time and space. Using PIV as the backbone a Particle Tracking Velocimetry (PTV) code was developed to track NPs varying in scale from 100 nm to 1200 nm. The mean and STD percentage of nanoparticle trajectories that are likely to end up in the vein margin within the next frame decreases with nanoparticle size (800 nm, 400 nm, 200 nm). Distribution of nanoparticle trajectories throughout the vein in relation to different nanoparticle sizes needs more data to determine anything conclusively.
Mon, 01 Jan 2018 00:00:00 GMT
http://hdl.handle.net/10852/65706
20180101T00:00:00Z

Pricing Perpetual American Options with Linear Programming
http://hdl.handle.net/10852/65671
Pricing Perpetual American Options with Linear Programming
Bakke, Jan Aleksander Olsen
This master thesis will demonstrate how to price perpetual American options with linear programming. American options are used both for hedging and speculation, and being able to price derivatives, without creating arbitrage opportunities, are of importance. First we introduce a deterministic security market model and exploit the mathematical structure. Then European and American put and call options are presented. With dynamic programming we show how to price American options. Dynamic programming is based on an idea that an investor would act optimally at all trading dates and the objective is yielding the maximum profit, despite the risk of not knowing the true future value of the option. With this technique, we investigate perpetual American options on a ternary Markov chain model. Perpetual options are without an expiration date. Markov chain models are only dependent of the current state when determining the future value, thus simplifying the computations. The solution, based on dynamic programming, is the smallest payoff that is greater than the discounted expected value of the option at the next trading date. The value and the payoff must not be confused, as an investor may be willing to pay more than the payoff today, if the value of the option might rise in the future. The solution is obtained by formulating the problem as an optimization problem and then using linear programming theory.
Mon, 01 Jan 2018 00:00:00 GMT
http://hdl.handle.net/10852/65671
20180101T00:00:00Z

Mode jumping MCMC for Bayesian variable selection in GLMM
http://hdl.handle.net/10852/65654
Mode jumping MCMC for Bayesian variable selection in GLMM
Hubin, Aliaksandr; Storvik, Geir Olve
Generalized linear mixed models (GLMM) are used for inference and prediction in a wide range of different applications providing a powerful scientific tool. An increasing number of sources of data are becoming available, introducing a variety of candidate explanatory variables for these models. Selection of an optimal combination of variables is thus becoming crucial. In a Bayesian setting, the posterior distribution of the models, based on the observed data, can be viewed as a relevant measure for the model evidence. The number of possible models increases exponentially in the number of candidate variables. Moreover, the space of models has numerous local extrema in terms of posterior model probabilities. To resolve these issues a novel MCMC algorithm for the search through the model space via efficient mode jumping for GLMMs is introduced. The algorithm is based on that marginal likelihoods can be efficiently calculated within each model. It is recommended that either exact expressions or precise approximations of marginal likelihoods are applied. The suggested algorithm is applied to simulated data, the famous U.S. crime data, protein activity data and epigenetic data and is compared to several existing approaches.
Mon, 01 Jan 2018 00:00:00 GMT
http://hdl.handle.net/10852/65654
20180101T00:00:00Z

Varieties of apolar subschemes of toric surfaces
http://hdl.handle.net/10852/65644
Varieties of apolar subschemes of toric surfaces
Ranestad, Kristian; Gallet, Matteo; Villamizar, Nelly
Powersum varieties, also called varieties of sums of powers, have provided examples of interesting relations between varieties since their first appearance in the 19th century. One of the most useful tools to study them is apolarity, a notion originally related to the action of differential operators on the polynomial ring. In this work we make explicit how one can see apolarity in terms of the Cox ring of a variety. In this way powersum varieties are a special case of varieties of apolar schemes; we explicitly describe examples of such varieties in the case of two toric surfaces, when the Cox ring is particularly wellbehaved.
Mon, 01 Jan 2018 00:00:00 GMT
http://hdl.handle.net/10852/65644
20180101T00:00:00Z

Metoder og metodiske utfordringer for matchede kohortstudier
http://hdl.handle.net/10852/65639
Metoder og metodiske utfordringer for matchede kohortstudier
Johansen, Lena Rogstad
Når man estimerer effekten av en bestemt behandling eller eksponering på utfall i kohortstudier, og observasjonsstudier generelt, gir ikke standard metoder korrekte resultater i nærvær av ukontrollert konfundering. Matching er en teknikk som korrigerer for dette. I denne oppgaven studerer vi først og fremst i hvilken grad det er mulig å analysere matchede (også kalt tilordnede) kohortstudier når man ignorerer matchingsvariablene (konfunderingsvariablene) under forskjellige modellforutsetninger. Vi ser også på hvor mange ikkeeksponerte individer man bør velge per eksponert individ. Det viser seg at den estimerte sammenhengen mellom eksponering og utfall i nærvær versus fravær av matchingsvariablene avhenger av modellen for levetidene. Ettersom denne er både ukjent og ukontrollerbar i virkeligheten bør man beholde matchingsvariablene i analysen, såfremt det er mulig. Dessuten synes det å være lite å vinne på å velge flere enn ti ikkeeksponerte individer per eksponert individ.
Mon, 01 Jan 2018 00:00:00 GMT
http://hdl.handle.net/10852/65639
20180101T00:00:00Z

Bayesian model configuration, selection and averaging in complex regression contexts
http://hdl.handle.net/10852/65638
Bayesian model configuration, selection and averaging in complex regression contexts
Hubin, Aliaksandr
In this PhD thesis problems of Bayesian model selection and model averaging are addressed in various regression contexts. The approaches developed within the thesis are based on the idea of marginalizing out parameters from the likelihood. This allows to work on the marginal space of models, which simplifies the search algorithms significantly. For the linear models an efficient mode jumping Monte Carlo Markov chain (MJMCMC) algorithm was suggested. The approach performed very well on simulated and real data. Further, the algorithm was extended to work with logic regressions, where one has a feature space consisting of various complicated logical expressions, which makes enumeration of all features computationally and memory infeasible in most of the cases. The genetically modified MJMCMC (GMJMCMC) algorithm was suggested to tackle this issue. The algorithm combines the idea of keeping and updating the populations of highly predictive logical expressions combined with MJMCMC for the efficient exploration of the model space. Several simulation and real data studies show that logical expressions of high orders can be recovered with large power and low false discovery rate. Moreover, the GMJMCMC approach is adapted to make inference within the class of deep Bayesian regression models (which is a suggested in the thesis extension of various machine and statistical learning models like artificial neural networks, classification and regression trees, logic regressions and linear models). The reversible GMJMCMC, named RGMJMCMC, is also suggested. It makes transitions between the populations of variables in a way that satisfies the detailed balance equation. Based on several examples, it is shown that the DBRM approach can be efficient for both inference and prediction in various applications. In particular, two ground physical laws (planetary mass law and third Kepler’s law) were recovered from the data with large power and low false discovery rate. Three classification examples were also studied, where the comparison to other popular machine and statistical learning approaches was performed. Finally, a thorough study comparing different Bayesian approaches to genome wide association was done. It was shown that the developed in this thesis approaches can be efficiently applied to data with a huge number of covariates.
Mon, 01 Jan 2018 00:00:00 GMT
http://hdl.handle.net/10852/65638
20180101T00:00:00Z

Algebraic Ktheory of quotient stacks
http://hdl.handle.net/10852/65574
Algebraic Ktheory of quotient stacks
Krishna, Amalendu; Ravi, Charanya
We prove some fundamental results like localization, excision, Nisnevich descent, and the regular blowup formula for the algebraic Ktheory of certain stack quotients of schemes with affine group scheme actions. We show that the homotopy Ktheory of such stacks is homotopy invariant. This implies a similar homotopy invariance property of the algebraic Ktheory with coefficients.
Mon, 01 Jan 2018 00:00:00 GMT
http://hdl.handle.net/10852/65574
20180101T00:00:00Z

Optimizing warnings for slippery runways based on weather data
http://hdl.handle.net/10852/65564
Optimizing warnings for slippery runways based on weather data
Huseby, Arne; Rabbe, Marit
Slippery runways represent a significant risk to aircrafts especially during the winter season. In order to apply the appropriate braking action, the pilots need reliable information about the runway conditions. Unfortunately the accuracy of runway reports can sometimes be unsatisfactory. In order to obtain more precise and uptodate information about the current conditions, a warning system based on various types of weather data was suggested by Huseby & Rabbe (2012). See also Huseby & Rabbe (2008) and Huseby et al. (2010). The system is based on a set of scenarios known to cause slippery conditions. By monitoring meteorological parameters like air and ground temperature, humidity, visibility and precipitation, and comparing these to the given scenarios, the system can issue warnings to the ground personnel. This system is currently being used on 16 Norwegian airports. In the present paper this warning system is reviewed. Ideally, the warning system should issue warnings whenever the estimated runway conditions are medium or worse. At the same time the system should not issue warnings when the runway conditions are good. Thus, there are two types of errors we need to take into consideration. Type 1 errors occur when the system does not issue a warning even though the conditions are medium or worse, while Type 2 errors occur if a warning is issued when the conditions are good. When designing the system, we need to find the optimal balance between these types of errors taking into account that a Type 1 error to a certain degree is considered to be worse than a Type 2 error. The paper describes how the system can be optimized using a combination of weather data and flight data.
© 2018 Taylor & Francis
Mon, 01 Jan 2018 00:00:00 GMT
http://hdl.handle.net/10852/65564
20180101T00:00:00Z

Buffered environmental contours
http://hdl.handle.net/10852/65563
Buffered environmental contours
Dahl, Kristina Rognlien; Huseby, Arne
The main idea of this paper is to use the notion of buffered failure probability from probabilistic structural design, first introduced by Rockafellar & Royset (2010), to introduce buffered environmental contours. Classical environmental contours are used in structural design in order to obtain upper bounds on the failure probabilities of a large class of designs. The purpose of buffered failure probabilities is the same. However, in contrast to classical environmental contours, this new concept does not just take into account failure vs. functioning, but also to which extent the system is failing. For example, this is relevant when considering the risk of flooding: We are not just interested in knowing whether a river has flooded. The damages caused by the flooding greatly depends on how much the water has risen above the standard level.
© 2018 Taylor & Francis
Mon, 01 Jan 2018 00:00:00 GMT
http://hdl.handle.net/10852/65563
20180101T00:00:00Z

Partial monitoring of multistage systems
http://hdl.handle.net/10852/65562
Partial monitoring of multistage systems
Skutlaberg, Kristina; Huseby, Arne; Natvig, Bent
For large multicomponent systems it is typically too costly to monitor the entire system constantly. In the present paper we consider a case where a component is unobserved in a time interval [0, T]. Here T is a stochastic variable with a distribution which depends om the structure of the system and the lifetime distribution of the other components. Thus, different systems will result in different distributions of T, the main focus of the paper is on how the unobserved period of time affects what we learn about the unobserved component during this period. We analyse this by considering three different cases. In the first case we consider both T as well as the state of the unobserved component at time T as given. In the second case we allow the state of the unobserved component at time T to be stochastic, while in the third case both T and the state are treated as stochastic variable. In all cases we study the problem using preposterior analysis. That is, we investigate how much information we can expect to get by the end of the time interval [0, T]. The methodology is also illustrated on a more complete example.
Mon, 01 Jan 2018 00:00:00 GMT
http://hdl.handle.net/10852/65562
20180101T00:00:00Z

Wake potential of a dust particle in magnetised plasmas
http://hdl.handle.net/10852/65458
Wake potential of a dust particle in magnetised plasmas
Miloch, Wojciech Jacek; Darian, Diako; Mortensen, Mikael
The electric potential distribution around a dust particle immersed in a magnetised supersonic plasma flow is studied by numerical simulations. It is shown that with increasing magnetisation of plasma, the peak in the wake potential gets smaller and moves upstream. For strong magnetisation, the trailing peak in the potential distribution vanishes and the potential becomes more isotropic. The results agree qualitatively with the linear response approach. The numerical simulations are carried out with a particleincell code.
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/65458
20170101T00:00:00Z

Simulating runup on steep slopes with operational Boussinesq models; capabilities, spurious effects and instabilities
http://hdl.handle.net/10852/65321
Simulating runup on steep slopes with operational Boussinesq models; capabilities, spurious effects and instabilities
Løvholt, Finn; Lynett, P.; Pedersen, Geir Kleivstul
Tsunamis induced by rock slides plunging into fjords constitute a severe threat to local coastal communities. The rock slide impact may give rise to highly nonlinear waves in the near field, and because the wave lengths are relatively short, frequency dispersion comes into play. Fjord systems are rugged with steep slopes, and modeling nonlinear dispersive waves in this environment with simultaneous runup is demanding. We have run an operational Boussinesqtype TVD (total variation diminishing) model using different runup formulations. Two different tests are considered, inundation on steep slopes and propagation in a trapezoidal channel. In addition, a set of Lagrangian models serves as reference models. Demanding test cases with solitary waves with amplitudes ranging from 0.1 to 0.5 were applied, and slopes were ranging from 10 to 50°. Different runup formulations yielded clearly different accuracy and stability, and only some provided similar accuracy as the reference models. The test cases revealed that the model was prone to instabilities for large nonlinearity and fine resolution. Some of the instabilities were linked with false breaking during the first positive inundation, which was not observed for the reference models. None of the models were able to handle the bore forming during drawdown, however. The instabilities are linked to shortcrested undulations on the grid scale, and appear on fine resolution during inundation. As a consequence, convergence was not always obtained. It is reason to believe that the instability may be a general problem for Boussinesq models in fjords.
Tue, 01 Jan 2013 00:00:00 GMT
http://hdl.handle.net/10852/65321
20130101T00:00:00Z

Optimal control with delayed information flow of systems driven by GBrownian motion
http://hdl.handle.net/10852/65220
Optimal control with delayed information flow of systems driven by GBrownian motion
Biagini, Francesca; MeyerBrandis, Thilo; Øksendal, Bernt; Paczka, Krzysztof
In this paper, we study strongly robust optimal control problems under volatility uncertainty. In the Gframework, we adapt the stochastic maximum principle to find necessary and sufficient conditions for the existence of a strongly robust optimal control.
Mon, 01 Jan 2018 00:00:00 GMT
http://hdl.handle.net/10852/65220
20180101T00:00:00Z

Poisson and Martin boundaries of discrete quantum groups: a noncommutative and categorical perspective
http://hdl.handle.net/10852/65045
Poisson and Martin boundaries of discrete quantum groups: a noncommutative and categorical perspective
Malacarne, Sara
Quantum groups are a noncommutative extension of the notion of a group and first appeared in the context of quantum mechanics. Now the theory of quantum groups has further developed and has become interesting in its own right. In this work we study compact and discrete quantum groups, the latter in connection with random walks and probabilistic boundaries.
Random walks on classical groups have been extensively studied and the associated probabilistic boundaries which encode information on their asymptotic behaviour, that is, what happens after an infinite number steps, have been obtained in a number of cases. In this work we concentrate on the quantum setting where the theory is still not so clear. We compute these boundaries for particular discrete quantum groups using both a functional analytic and categorical approach. It turns out in fact that the interconnection between the two offers a very powerful tool for gaining insights into this topic.
Mon, 01 Jan 2018 00:00:00 GMT
http://hdl.handle.net/10852/65045
20180101T00:00:00Z

Optimal spline spaces for L2 nwidth problems with boundary conditions
http://hdl.handle.net/10852/64835
Optimal spline spaces for L2 nwidth problems with boundary conditions
Floater, Michael S.; Sande, Espen
In this paper we show that, with respect to the L2 norm, three classes of functions in Hr(0,1) , defined by certain boundary conditions, admit optimal spline spaces of all degrees ≥r−1 , and all these spline spaces have uniform knots.
Mon, 01 Jan 2018 00:00:00 GMT
http://hdl.handle.net/10852/64835
20180101T00:00:00Z

Alternating Sign Matrices, Related (0, 1)Matrices, and the Smith Normal Form
http://hdl.handle.net/10852/64834
Alternating Sign Matrices, Related (0, 1)Matrices, and the Smith Normal Form
Brualdi, R.A.; Dahl, Geir
We investigate the Smith Normal Form (SNF) of alternating sign matrices (ASMs) and related matrices of 0’s and 1’s ((0, 1)matrices). We identify certain classes of ASMs and (0, 1)matrices whose SNFs are (0, 1)matrices. We relate some of our work to various ranks, in particular, the (0, 1)rank of a (0, 1)matrix, that is, the bipartite partition number of a bipartite graph.
Mon, 01 Jan 2018 00:00:00 GMT
http://hdl.handle.net/10852/64834
20180101T00:00:00Z