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  • 1.
    Abbas, Khaled A
    et al.
    Egyptian National Institute of Transport.
    Al-Hosseiny, Ahmed T
    Egyptian National Institute of Transport.
    A generic approach for in depth statistical investigation of accident characteristics and causes2001Inngår i: Proceedings of the conference Traffic Safety on Three Continents: International conference in Moscow, Russia, 19-21 September, 2001 / [ed] Asp, Kenneth, Linköping: Statens väg- och transportforskningsinstitut, 2001, Vol. 18A:3, s. 13-Konferansepaper (Annet vitenskapelig)
    Abstract [en]

    The main aim of this research is to develop a generic approach for the utilization of statistical methods to conduct depth investigation of road accident characteristics and causes. This approach is applied in an effort to analyse the 1998 accident database for the main rural roads in Egypt. This database is composed of traffic accident data collected for 14 road sections representing nine major roads of the Egyptian rural road network. The proposed approach is composed of two main stages of analysis. Within each stage, several analytical steps are conducted. The first stage is mainly concerned with developing cluster bar charts, where different characteristics and causes of accidents are portrayed in relation to variations in the three main accident contributing factors, namely types of roads, vehicles and drivers. The second stage is concerned with conducting in-depth statistical analysis of the collected accident data. Within this stage, four levels of statistical investigations were conducted. These are meant to examine a number of issues.

  • 2.
    Abbaszadeh Shahri, Abbas
    et al.
    KTH, Skolan för arkitektur och samhällsbyggnad (ABE), Byggvetenskap.
    Larsson, Stefan
    KTH, Skolan för arkitektur och samhällsbyggnad (ABE), Byggvetenskap, Jord- och bergmekanik.
    Johansson, Fredrik
    KTH, Skolan för arkitektur och samhällsbyggnad (ABE), Byggvetenskap, Jord- och bergmekanik.
    Updated relations for the uniaxial compressive strength of marlstones based on P-wave velocity and point load index test2016Inngår i: INNOVATIVE INFRASTRUCTURE SOLUTIONS, ISSN 2364-4176, Vol. 1, nr 1, artikkel-id UNSP 17Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Although there are many proposed relations for different rock types to predict the uniaxial compressive strength (UCS) as a function of P-wave velocity (V-P) and point load index (Is), only a few of them are focused on marlstones. However, these studies have limitations in applicability since they are mainly based on local studies. In this paper, an attempt is therefore made to present updated relations for two previous proposed correlations for marlstones in Iran. The modification process is executed through multivariate regression analysis techniques using a provided comprehensive database for marlstones in Iran, including UCS, V-P and Is from publications and validated relevant sources comprising 119 datasets. The accuracy, appropriateness and applicability of the obtained modifications were tested by means of different statistical criteria and graph analyses. The conducted comparison between updated and previous proposed relations highlighted better applicability in the prediction of UCS using the updated correlations introduced in this study. However, the derived updated predictive models are dependent on rock types and test conditions, as they are in this study.

  • 3.
    Abdalmoaty, Mohamed
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik.
    Learning Stochastic Nonlinear Dynamical Systems Using Non-stationary Linear Predictors2017Licentiatavhandling, monografi (Annet vitenskapelig)
    Abstract [en]

    The estimation problem of stochastic nonlinear parametric models is recognized to be very challenging due to the intractability of the likelihood function. Recently, several methods have been developed to approximate the maximum likelihood estimator and the optimal mean-square error predictor using Monte Carlo methods. Albeit asymptotically optimal, these methods come with several computational challenges and fundamental limitations.

    The contributions of this thesis can be divided into two main parts. In the first part, approximate solutions to the maximum likelihood problem are explored. Both analytical and numerical approaches, based on the expectation-maximization algorithm and the quasi-Newton algorithm, are considered. While analytic approximations are difficult to analyze, asymptotic guarantees can be established for methods based on Monte Carlo approximations. Yet, Monte Carlo methods come with their own computational difficulties; sampling in high-dimensional spaces requires an efficient proposal distribution to reduce the number of required samples to a reasonable value.

    In the second part, relatively simple prediction error method estimators are proposed. They are based on non-stationary one-step ahead predictors which are linear in the observed outputs, but are nonlinear in the (assumed known) input. These predictors rely only on the first two moments of the model and the computation of the likelihood function is not required. Consequently, the resulting estimators are defined via analytically tractable objective functions in several relevant cases. It is shown that, under mild assumptions, the estimators are consistent and asymptotically normal. In cases where the first two moments are analytically intractable due to the complexity of the model, it is possible to resort to vanilla Monte Carlo approximations. Several numerical examples demonstrate a good performance of the suggested estimators in several cases that are usually considered challenging.

    Fulltekst (pdf)
    fulltext
  • 4.
    Abdumuminov, Shuhrat
    et al.
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation.
    Esteky, David Emanuel
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation.
    Black-Litterman Model: Practical Asset Allocation Model Beyond Traditional Mean-Variance2016Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
    Abstract [en]

    This paper consolidates and compares the applicability and practicality of Black-Litterman model versus traditional Markowitz Mean-Variance model. Although well-known model such as Mean-Variance is academically sound and popular, it is rarely used among asset managers due to its deficiencies. To put the discussion into context we shed light on the improvement made by Fisher Black and Robert Litterman by putting the performance and practicality of both Black- Litterman and Markowitz Mean-Variance models into test. We will illustrate detailed mathematical derivations of how the models are constructed and bring clarity and profound understanding of the intuition behind the models. We generate two different portfolios, composing data from 10-Swedish equities over the course of 10-year period and respectively select 30-days Swedish Treasury Bill as a risk-free rate. The resulting portfolios orientate our discussion towards the better comparison of the performance and applicability of these two models and we will theoretically and geometrically illustrate the differences. Finally, based on extracted results of the performance of both models we demonstrate the superiority and practicality of Black-Litterman model, which in our particular case outperform traditional Mean- Variance model.

    Fulltekst (pdf)
    fulltext
  • 5.
    Abodayeh, Kamaleldin
    et al.
    Prince Sultan Univ, Dept Math & Gen Sci, Riyadh, Saudi Arabia.
    Raza, Ali
    Air Univ, Dept Math, Stochat Anal & Optimizat Res Grp, PAF Complex E-9, Islamabad 44000, Pakistan.
    Arif, Muhammad Shoaib
    Air Univ, Dept Math, Stochat Anal & Optimizat Res Grp, PAF Complex E-9, Islamabad 44000, Pakistan.
    Rafiq, Muhammad
    Univ Cent Punjab, Fac Engn, Lahore, Pakistan.
    Bibi, Mairaj
    Comsats Univ, Dept Math, Chak Shahzad Campus Pk Rd, Islamabad, Pakistan.
    Mohsin, Muhammad
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    Stochastic Numerical Analysis for Impact of Heavy Alcohol Consumption on Transmission Dynamics of Gonorrhoea Epidemic2020Inngår i: CMC-COMPUTERS MATERIALS & CONTINUA, ISSN 1546-2218, Vol. 62, nr 3, s. 1125-1142Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    This paper aims to perform a comparison of deterministic and stochastic models. The stochastic modelling is a more realistic way to study the dynamics of gonorrhoea infection as compared to its corresponding deterministic model. Also, the deterministic solution is itself mean of the stochastic solution of the model. For numerical analysis, first, we developed some explicit stochastic methods, but unfortunately, they do not remain consistent in certain situations. Then we proposed an implicitly driven explicit method for stochastic heavy alcohol epidemic model. The proposed method is independent of the choice of parameters and behaves well in all scenarios. So, some theorems and simulations are presented in support of the article.

    Fulltekst (pdf)
    fulltext
  • 6.
    Abola, Benard
    et al.
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda.
    Biganda, Pitos
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Department of Mathematics, College of Natural and Applied Sciences, University of Dar es Salaam,Tanzania.
    Engström, Christopher
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Anguzu, Collins
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Department of Mathematics, Makerere University, Kampala, Uganda.
    Mango, John Magero
    Department of Mathematics, Makerere University, Kampala, Uganda.
    Kakuba, Gudwin
    Department of Mathematics, Makerere University, Kampala, Uganda.
    Silvestrov, Sergei
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    A Variant of Updating Page Rank in Evolving Tree graphs2019Inngår i: Proceedings of 18th Applied Stochastic Models and Data Analysis International Conference with the Demographics 2019 Workshop, Florence, Italy: 11-14 June, 2019 / [ed] Christos H. Skiadas, ISAST: International Society for the Advancement of Science and Technology , 2019, s. 31-49Konferansepaper (Fagfellevurdert)
    Abstract [en]

    PageRank update refers to the process of computing new PageRank values after change(s) (addition or removal of links/vertices) has occurred in real life networks. The purpose of the updating is to avoid recalculating the values from scratch. To efficiently carry out the update, we consider PageRank as the expected number of visits to target vertex if multiple random walks are performed, starting at each vertex once and weighing each of these walks by a weight value. Hence, it might be looked at as updating non-normalised PageRank. In the proposed approach, a scaled adjacency matrix is sequentially updated after every change and the levels of the vertices being updated as well. This enables sets of internal and sink vertices dependent on their roots or parents, thus vector-vector product can be performed sequentially since there are no infinite steps from one vertex to the other.

  • 7.
    Abola, Benard
    et al.
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda.
    Biganda, Pitos
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Department of Mathematics, College of Natural and Applied Sciences, University of Dar es Salaam,Tanzania.
    Engström, Christopher
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Mango, J. M.
    Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda.
    Kakuba, G.
    Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda.
    Silvestrov, Sergei
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    PageRank in evolving tree graphs2018Inngår i: Stochastic Processes and Applications: SPAS2017, Västerås and Stockholm, Sweden, October 4-6, 2017 / [ed] Sergei Silvestrov, Anatoliy Malyarenko, Milica Rančić, Springer, 2018, Vol. 271, s. 375-390Kapittel i bok, del av antologi (Fagfellevurdert)
    Abstract [en]

    In this article, we study how PageRank can be updated in an evolving tree graph. We are interested in finding how ranks of the graph can be updated simultaneously and effectively using previous ranks without resorting to iterative methods such as the Jacobi or Power method. We demonstrate and discuss how PageRank can be updated when a leaf is added to a tree, at least one leaf is added to a vertex with at least one outgoing edge, an edge added to vertices at the same level and forward edge is added in a tree graph. The results of this paper provide new insights and applications of standard partitioning of vertices of the graph into levels using breadth-first search algorithm. Then, one determines PageRanks as the expected numbers of random walk starting from any vertex in the graph. We noted that time complexity of the proposed method is linear, which is quite good. Also, it is important to point out that the types of vertex play essential role in updating of PageRank.

  • 8.
    Abola, Benard
    et al.
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda.
    Biganda, Pitos
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Department of Mathematics, College of Natural and Applied Sciences, University of Dar es Salaam,Tanzania.
    Silvestrov, Dmitrii
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Stockholm University, Sweden.
    Silvestrov, Sergei
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Mango, John
    Department of Mathematics, Makerere University, Kampala, Uganda.
    Kakuba, Gudwin
    Department of Mathematics, Makerere University, Kampala, Uganda.
    Nonlinearly  Perturbed Markov Chains  and  Information Networks2019Inngår i: Proceedings of 18th Applied Stochastic Models and Data Analysis International Conference with the Demographics 2019 Workshop, Florence, Italy: 11-14 June, 2019 / [ed] Christos H. Skiadas, ISAST: International Society for the Advancement of Science and Technology , 2019, s. 51-79Konferansepaper (Fagfellevurdert)
    Abstract [en]

    The paper is devoted to studies of perturbed Markov chains commonly used for description of information networks. In such models, the matrix of transition probabilities for the corresponding Markov chain is usually regularised by adding  a special damping matrix multiplied by a small damping (perturbation) parameter ε. In this paper, we present results of the detailed perturbation analysis of Markov chains with damping component and numerical experiments supporting and illustrating the results of this perturbation analysis.

  • 9.
    Abrahamson, Peter
    et al.
    Örebro universitet, Handelshögskolan vid Örebro universitet.
    Bodin, Daniel
    Örebro universitet, Handelshögskolan vid Örebro universitet.
    Behov av stödundervisning i grundskolan: En designbaserad analys av longitudinella data2008Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
  • 10.
    Abrahamsson, Linda
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Matematisk statistik.
    Statistical models of breast cancer tumour growth for mammography screening data2012Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
    Fulltekst (pdf)
    fulltext
  • 11.
    Abrahamsson, Per Anders
    et al.
    Uppsala universitet, Humanistisk-samhällsvetenskapliga vetenskapsområdet, Samhällsvetenskapliga fakulteten, Institutionen för informationsvetenskap. Uppsala universitet, Humanistisk-samhällsvetenskapliga vetenskapsområdet, Samhällsvetenskapliga fakulteten, Institutionen för informationsvetenskap.
    Adami, Hans Olov
    Taube, Adam
    Kim, KyungMann
    Zelen, Marvin
    Kulldorff, Martin
    Re: Long-term survival and mortality in prostate cancer treated with noncurative intent1995Inngår i: UROLGY, Vol. 154, s. 460-465Artikkel i tidsskrift (Fagfellevurdert)
  • 12.
    Abramowicz, Konrad
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Numerical analysis for random processes and fields and related design problems2011Doktoravhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    In this thesis, we study numerical analysis for random processes and fields. We investigate the behavior of the approximation accuracy for specific linear methods based on a finite number of observations. Furthermore, we propose techniques for optimizing performance of the methods for particular classes of random functions. The thesis consists of an introductory survey of the subject and related theory and four papers (A-D).

    In paper A, we study a Hermite spline approximation of quadratic mean continuous and differentiable random processes with an isolated point singularity. We consider a piecewise polynomial approximation combining two different Hermite interpolation splines for the interval adjacent to the singularity point and for the remaining part. For locally stationary random processes, sequences of sampling designs eliminating asymptotically the effect of the singularity are constructed.

    In Paper B, we focus on approximation of quadratic mean continuous real-valued random fields by a multivariate piecewise linear interpolator based on a finite number of observations placed on a hyperrectangular grid. We extend the concept of local stationarity to random fields and for the fields from this class, we provide an exact asymptotics for the approximation accuracy. Some asymptotic optimization results are also provided.

    In Paper C, we investigate numerical approximation of integrals (quadrature) of random functions over the unit hypercube. We study the asymptotics of a stratified Monte Carlo quadrature based on a finite number of randomly chosen observations in strata generated by a hyperrectangular grid. For the locally stationary random fields (introduced in Paper B), we derive exact asymptotic results together with some optimization methods. Moreover, for a certain class of random functions with an isolated singularity, we construct a sequence of designs eliminating the effect of the singularity.

    In Paper D, we consider a Monte Carlo pricing method for arithmetic Asian options. An estimator is constructed using a piecewise constant approximation of an underlying asset price process. For a wide class of Lévy market models, we provide upper bounds for the discretization error and the variance of the estimator. We construct an algorithm for accurate simulations with controlled discretization and Monte Carlo errors, andobtain the estimates of the option price with a predetermined accuracy at a given confidence level. Additionally, for the Black-Scholes model, we optimize the performance of the estimator by using a suitable variance reduction technique.

    Fulltekst (pdf)
    fulltext
  • 13.
    Abramowicz, Konrad
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Arnqvist, Per
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Sjöstedt de Luna, Sara
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Secchi, Piercesare
    Vantini, Simone
    Vitelli, Valeria
    Was it snowing on lake Kassjön in January 4486 BC? Functional data analysis of sediment data2014Konferansepaper (Annet vitenskapelig)
  • 14.
    Abramowicz, Konrad
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Häger, Charlotte
    Umeå universitet, Medicinska fakulteten, Institutionen för samhällsmedicin och rehabilitering, Sjukgymnastik.
    Hérbert-Losier, Kim
    Swedish Winter Sports Research Centre Mid Sweden; University Department of Health Sciences, Östersund, Sweden.
    Pini, Alessia
    MOX – Department of Mathematics, Politecnico di Milano.
    Schelin, Lina
    Umeå universitet, Samhällsvetenskapliga fakulteten, Handelshögskolan vid Umeå universitet, Statistik. Umeå universitet, Medicinska fakulteten, Institutionen för samhällsmedicin och rehabilitering, Fysioterapi.
    Strandberg, Johan
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Vantini, Simone
    MOX – Department of Mathematics, Politecnico di Milano.
    An inferential framework for domain selection in functional anova2014Inngår i: Contributions in infinite-dimensional statistics and related topics / [ed] Bongiorno, E.G., Salinelli, E., Goia, A., Vieu, P, Esculapio , 2014Konferansepaper (Fagfellevurdert)
    Abstract [en]

    We present a procedure for performing an ANOVA test on functional data, including pairwise group comparisons. in a Scheff´e-like perspective. The test is based on the Interval Testing Procedure, and it selects intervals where the groups significantly differ. The procedure is applied on the 3D kinematic motion of the knee joint collected during a functional task (one leg hop) performed by three groups of individuals.

  • 15.
    Abramowicz, Konrad
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Häger, Charlotte
    Umeå universitet, Medicinska fakulteten, Institutionen för samhällsmedicin och rehabilitering, Fysioterapi.
    Pini, Alessia
    Umeå universitet, Samhällsvetenskapliga fakulteten, Handelshögskolan vid Umeå universitet, Statistik. Department of Statistical Sciences, Università Cattolica del Sacro Cuore, Milan, Italy.
    Schelin, Lina
    Umeå universitet, Medicinska fakulteten, Institutionen för samhällsmedicin och rehabilitering. Umeå universitet, Samhällsvetenskapliga fakulteten, Handelshögskolan vid Umeå universitet, Statistik.
    Sjöstedt de Luna, Sara
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Vantini, Simone
    Nonparametric inference for functional-on-scalar linear models applied to knee kinematic hop data after injury of the anterior cruciate ligament2018Inngår i: Scandinavian Journal of Statistics, ISSN 0303-6898, E-ISSN 1467-9469, Vol. 45, nr 4, s. 1036-1061Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Motivated by the analysis of the dependence of knee movement patterns during functional tasks on subject-specific covariates, we introduce a distribution-free procedure for testing a functional-on-scalar linear model with fixed effects. The procedure does not only test the global hypothesis on the entire domain but also selects the intervals where statistically significant effects are detected. We prove that the proposed tests are provided with an asymptotic control of the intervalwise error rate, that is, the probability of falsely rejecting any interval of true null hypotheses. The procedure is applied to one-leg hop data from a study on anterior cruciate ligament injury. We compare knee kinematics of three groups of individuals (two injured groups with different treatments and one group of healthy controls), taking individual-specific covariates into account.

    Fulltekst (pdf)
    fulltext
  • 16.
    Abramowicz, Konrad
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Schelin, Lina
    Umeå universitet, Samhällsvetenskapliga fakulteten, Handelshögskolan vid Umeå universitet, Statistik.
    Sjöstedt de Luna, Sara
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Strandberg, Johan
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Multiresolution clustering of dependent functional data with application to climate reconstruction2019Inngår i: Stat, E-ISSN 2049-1573, Vol. 8, nr 1, artikkel-id e240Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We propose a new nonparametric clustering method for dependent functional data, the double clustering bagging Voronoi method. It consists of two levels of clustering. Given a spatial lattice of points, a function is observed at each grid point. In the first‐level clustering, features of the functional data are clustered. The second‐level clustering takes dependence into account, by grouping local representatives, built from the resulting first‐level clusters, using a bagging Voronoi strategy. Depending on the distance measure used, features of the functions may be included in the second‐step clustering, making the method flexible and general. Combined with the clustering method, a multiresolution approach is proposed that searches for stable clusters at different spatial scales, aiming to capture latent structures. This provides a powerful and computationally efficient tool to cluster dependent functional data at different spatial scales, here illustrated by a simulation study. The introduced methodology is applied to varved lake sediment data, aiming to reconstruct winter climate regimes in northern Sweden at different time resolutions over the past 6,000 years.

  • 17.
    Abramowicz, Konrad
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Seleznjev, Oleg
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    On the error of the Monte Carlo pricing method for Asian option2008Inngår i: Journal of Numerical and Applied Mathematics, ISSN 0868-6912, Vol. 96, nr 1, s. 1-10Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We consider a Monte Carlo method to price a continuous arithmetic Asian option with a given precision. Piecewise constant approximation and plain simulation are used for a wide class of models based on L\'{e}vy processes. We give bounds of the possible discretization and simulation errors. The sufficient numbers of discretization points and simulations to obtain requested accuracy are derived. To demonstrate the general approach, the Black-Scholes model is studied in more detail. We undertake the case of continuous averaging and starting time zero,  but the obtained results can be applied to the discrete case  and generalized for any time before an execution date. Some numerical experiments and comparison to the PDE based method are also presented.

  • 18.
    Abramowicz, Konrad
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Seleznjev, Oleg
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Piecewise multilinear interpolation of a random field2013Inngår i: Advances in Applied Probability, ISSN 0001-8678, E-ISSN 1475-6064, Vol. 45, nr 4, s. 945-959Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We consider a piecewise-multilinear interpolation of a continuous random field on a d-dimensional cube. The approximation performance is measured using the integrated mean square error. Piecewise-multilinear interpolator is defined by N-field observations on a locations grid (or design). We investigate the class of locally stationary random fields whose local behavior is like a fractional Brownian field, in the mean square sense, and find the asymptotic approximation accuracy for a sequence of designs for large N. Moreover, for certain classes of continuous and continuously differentiable fields, we provide the upper bound for the approximation accuracy in the uniform mean square norm.

  • 19.
    Abramowicz, Konrad
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Seleznjev, Oleg
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Stratified Monte Carlo quadrature for continuous random fields2015Inngår i: Methodology and Computing in Applied Probability, ISSN 1387-5841, E-ISSN 1573-7713, Vol. 17, nr 1, s. 59-72Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We consider the problem of numerical approximation of integrals of random fields over a unit hypercube. We use a stratified Monte Carlo quadrature and measure the approximation performance by the mean squared error. The quadrature is defined by a finite number of stratified randomly chosen observations with the partition generated by a rectangular grid (or design). We study the class of locally stationary random fields whose local behavior is like a fractional Brownian field in the mean square sense and find the asymptotic approximation accuracy for a sequence of designs for large number of the observations. For the H¨older class of random functions, we provide an upper bound for the approximation error. Additionally, for a certain class of isotropic random functions with an isolated singularity at the origin, we construct a sequence of designs eliminating the effect of the singularity point.

  • 20.
    Abramowizc, Konrad
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Arnqvist, Per
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Secchi, Piercesare
    Politecnico di Milano, Italy.
    Sjöstedt de Luna, Sara
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Vantini, Simone
    Politecnico di Milano, Italy.
    Vitelli, Valeria
    Oslo University, Norway.
    Clustering misaligned dependent curves applied to varved lake sediment for climate reconstruction2017Inngår i: Stochastic environmental research and risk assessment (Print), ISSN 1436-3240, E-ISSN 1436-3259, Vol. 31, nr 1, s. 71-85Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper we introduce a novel functional clustering method, the Bagging Voronoi K-Medoid Aligment (BVKMA) algorithm, which simultaneously clusters and aligns spatially dependent curves. It is a nonparametric statistical method that does not rely on distributional or dependency structure assumptions. The method is motivated by and applied to varved (annually laminated) sediment data from lake Kassjön in northern Sweden, aiming to infer on past environmental and climate changes. The resulting clusters and their time dynamics show great potential for seasonal climate interpretation, in particular for winter climate changes.

  • 21.
    Abramsson, Evelina
    et al.
    Umeå universitet, Samhällsvetenskapliga fakulteten, Handelshögskolan vid Umeå universitet, Statistik.
    Grind, Kajsa
    Umeå universitet, Samhällsvetenskapliga fakulteten, Handelshögskolan vid Umeå universitet, Statistik.
    Skattning av kausala effekter med matchat fall-kontroll data2017Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
    Fulltekst (pdf)
    fulltext
  • 22.
    Achcar, JA
    et al.
    Uppsala universitet, Humanistisk-samhällsvetenskapliga vetenskapsområdet, Samhällsvetenskapliga fakulteten, Institutionen för informationsvetenskap.
    Agrawal, MC
    Anand, KN
    Ali, MM
    Ali, MM
    Bagui, SC
    Baker, RD
    Balamurali, S
    Balasooriya, U
    Bansal, AK
    Barry, J
    Bonett, DG
    Box, G
    Carling, K
    Caudill, SB
    Chakraborti, S
    Chatfield, C
    Chatterjee, S
    Cornell, JA
    Cox, D
    Draper, NR
    Ehrenberg, A
    Finney, DJ
    25 years of applied statistics1998Inngår i: JOURNAL OF APPLIED STATISTICS, ISSN 0266-4763, Vol. 25, nr 1, s. 3-22Artikkel i tidsskrift (Fagfellevurdert)
  • 23. Adami, Hans-Olov
    et al.
    Bergström, Reinhold
    Uppsala universitet, Humanistisk-samhällsvetenskapliga vetenskapsområdet, Samhällsvetenskapliga fakulteten, Institutionen för informationsvetenskap.
    Weiderpass, Elisabete
    Persson, Ingemar
    Barlow, Lotti
    McLaughlin, Joseph K.
    Risk for endometrial cancer following breast cancer: A prospective study in Sweden1997Inngår i: Cancer Causes & Control, Vol. 8, s. 821-827Artikkel i tidsskrift (Fagfellevurdert)
  • 24. Adami, H-O
    et al.
    Bergström, R
    Uppsala universitet, Humanistisk-samhällsvetenskapliga vetenskapsområdet, Samhällsvetenskapliga fakulteten, Institutionen för informationsvetenskap.
    Engholm, G
    Nyrén, O
    Wolk, A
    Ekbom, A
    Englund, A
    Baron, J
    A prospective study of smoking and risk of prostate cancer1996Inngår i: Int J Cancer, Vol. 67, s. 764-768Artikkel i tidsskrift (Fagfellevurdert)
  • 25.
    Adami, J
    et al.
    Uppsala universitet, Humanistisk-samhällsvetenskapliga vetenskapsområdet, Samhällsvetenskapliga fakulteten, Institutionen för informationsvetenskap.
    Nyren, O
    Bergstrom, R
    Ekbom, A
    McLaughlin, JK
    Hogman, C
    Fraumeni, JF
    Glimelius, B
    Blood transfusion and non-Hodgkin lymphoma: Lack of association1997Inngår i: ANNALS OF INTERNAL MEDICINE, ISSN 0003-4819, Vol. 127, nr 5, s. 365-&Artikkel i tidsskrift (Fagfellevurdert)
  • 26.
    Adesina, Owolabi Abiona
    Blekinge Tekniska Högskola, Sektionen för ingenjörsvetenskap.
    Statistical Modelling and the Fokker-Planck Equation2008Independent thesis Advanced level (degree of Master (One Year))Oppgave
    Abstract [en]

    A stochastic process or sometimes called random process is the counterpart to a deterministic process in theory. A stochastic process is a random field, whose domain is a region of space, in other words, a random function whose arguments are drawn from a range of continuously changing values. In this case, Instead of dealing only with one possible 'reality' of how the process might evolve under time (as is the case, for example, for solutions of an ordinary differential equation), in a stochastic or random process there is some indeterminacy in its future evolution described by probability distributions. This means that even if the initial condition (or starting point) is known, there are many possibilities the process might go to, but some paths are more probable and others less. However, in discrete time, a stochastic process amounts to a sequence of random variables known as a time series. Over the past decades, the problems of synergetic are concerned with the study of macroscopic quantitative changes of systems belonging to various disciplines such as natural science, physical science and electrical engineering. When such transition from one state to another take place, fluctuations i.e. (random process) may play an important role. Fluctuations in its sense are very common in a large number of fields and nearly every system is subjected to complicated external or internal influences that are often termed noise or fluctuations. Fokker-Planck equation has turned out to provide a powerful tool with which the effects of fluctuation or noise close to transition points can be adequately be treated. For this reason, in this thesis work analytical and numerical methods of solving Fokker-Planck equation, its derivation and some of its applications will be carefully treated. Emphasis will be on both for one variable and N- dimensional cases.

    Fulltekst (pdf)
    FULLTEXT01
  • 27.
    Adler, Jonas
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Lunz, Sebastian
    Univ Cambridge, Dept Appl Math & Theoret Phys, Cambridge, England..
    Banach Wasserstein GAN2018Inngår i: Advances in Neural Information Processing Systems 31 (NIPS 2018) / [ed] Bengio, S Wallach, H Larochelle, H Grauman, K CesaBianchi, N Garnett, R, Neural Information Processing Systems (NIPS) , 2018Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Wasserstein Generative Adversarial Networks (WGANs) can be used to generate realistic samples from complicated image distributions. The Wasserstein metric used in WGANs is based on a notion of distance between individual images, which induces a notion of distance between probability distributions of images. So far the community has considered l(2) as the underlying distance. We generalize the theory of WGAN with gradient penalty to Banach spaces, allowing practitioners to select the features to emphasize in the generator. We further discuss the effect of some particular choices of underlying norms, focusing on Sobolev norms. Finally, we demonstrate a boost in performance for an appropriate choice of norm on CIFAR-10 and CelebA.

  • 28.
    Adler, Jonas
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.). Elekta, Box 7593, 103 93 Stockholm, Sweden.
    Ringh, Axel
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Öktem, Ozan
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Karlsson, Johan
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Learning to solve inverse problems using Wasserstein lossManuskript (preprint) (Annet vitenskapelig)
    Abstract [en]

    We propose using the Wasserstein loss for training in inverse problems. In particular, we consider a learned primal-dual reconstruction scheme for ill-posed inverse problems using the Wasserstein distance as loss function in the learning. This is motivated by miss-alignments in training data, which when using standard mean squared error loss could severely degrade reconstruction quality. We prove that training with the Wasserstein loss gives a reconstruction operator that correctly compensates for miss-alignments in certain cases, whereas training with the mean squared error gives a smeared reconstruction. Moreover, we demonstrate these effects by training a reconstruction algorithm using both mean squared error and optimal transport loss for a problem in computerized tomography.

  • 29. Adolfson, Malin
    et al.
    Laseen, Stefan
    Linde, Jesper
    Villani, Mattias
    Stockholms universitet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    Empirical properties of closed- and open-economy DSGE models of the Euro area2008Inngår i: Macroeconomic dynamics (Print), ISSN 1365-1005, E-ISSN 1469-8056, Vol. 12, s. 2-19Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper, we compare the empirical proper-ties of closed- and open-economy DSGE models estimated on Euro area data. The comparison is made along several dimensions; we examine the models in terms of their marginal likelihoods, forecasting performance, variance decompositions, and their transmission mechanisms of monetary policy.

  • 30. Adolfson, Malin
    et al.
    Linde, Jesper
    Villani, Mattias
    Stockholms universitet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    Forecasting performance of an open economy DSGE model2007Inngår i: Econometric Reviews, ISSN 0747-4938, E-ISSN 1532-4168, Vol. 26, nr 04-feb, s. 289-328Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    This paper analyzes the forecasting performance of an open economy dynamic stochastic general equilibrium (DSGE) model, estimated with Bayesian methods, for the Euro area during 1994Q1-2002Q4. We compare the DSGE model and a few variants of this model to various reduced form forecasting models such as vector autoregressions (VARs) and vector error correction models (VECM), estimated both by maximum likelihood and, two different Bayesian approaches, and traditional benchmark models, e.g., the random. walk. The accuracy of point forecasts, interval forecasts and the predictive distribution as a whole are assessed in, an out-of-sample rolling event evaluation using several univariate and multivariate measures. The results show that the open economy DSGE model compares well with more empirical models and thus that the tension between, rigor and fit in older generations of DSGE models is no longer present. We also critically examine the role of Bayesian model probabilities and other frequently used low-dimensional summaries, e.g., the log determinant statistic, as measures of overall forecasting performance.

  • 31.
    Adolfsson, Chandra
    Örebro universitet, Institutionen för ekonomi, statistik och informatik.
    Utvärdering av granskningssystem för SCB:s undersökningar Kortperiodisk Sysselsättningsstatistik och Konjunkturstatistik över Vakanser2007Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
    Abstract [sv]

    I denna studie har undersökningarna Kortperiodisk Sysselsättningsstatistiks (KS) och Konjunkturstatistik över Vakansers (KV) befintliga granskningssystem utvärderats med avseende på hur effektivt det är. Processdata har framställts och analyserats. Resultaten tyder på att många av de inkomna blanketterna med misstänkt felaktiga uppgifter inte rättas upp, utan tvingas igenom trots att granskningssystemet ej accepterade uppgifterna. Det befintliga granskningssystemet har en högre träffsäkerhet avseende KS-undersökningen, men både KS och KV skulle kunnas granskas mer effektivt.

    För att utvärdera det befintliga granskningssystemet ytterligare användes en poängfunktion. Till studien fanns tillgång till både helt ogranskat material och helt granskat material och dessa material användes i poängfunktionen. Det uppräknade ogranskade värdet för varje objekt jämfördes med det uppräknade granskade värdet och ställdes i relation till respektive skattade branschtotal. De poängsatta blanketterna rangordnades sedan. Därefter analyserades materialet för att försöka finna var det skulle vara lämpligt att sätta det tröskelvärde som skulle skilja det material som ”egentligen” skulle ha behövts granskas från det som kunde ha lämnats orört. Att sätta tröskelvärdet är svårt. Här gjordes det godtyckligt utifrån kriterierna att det fel som införs i skattningarna för att allt material inte granskas skulle hållas så lågt som möjligt samt att antalet blanketter som skulle behöva granskas manuellt av produktionsgruppen också skulle hållas så lågt som möjligt. Även här visade det sig att det befintliga granskningssystemet inte är så effektivt som önskas. När resultaten från denna del av utvärderingen analyserades upptäcktes problem som beror på blankettutformningen. Skulle blanketterna ses över och åtgärdas skulle det fel som införs för att allt material inte granskas kunna minskas avsevärt. Genom att minska det införda felet kan tröskelvärdet förmodligen sättas på en ny nivå vilket medför att omfattningen av granskningen skulle minska ytterligare.

    Hur skulle då ett mer effektivt granskningssystem kunna se ut? I den här studien har valet fallit på att testa ”significance editing” på KS-undersökningen, det som på svenska kallas för effektgranskning. En poängfunktion användes även här, denna tilldelar de inkomna blanketterna varsin poäng och dessa poäng rangordnas därefter. Efter att poängen rangordnats bestäms en gräns, ett tröskelvärde, och de blanketter med en poäng som överstiger tröskelvärdet granskas och rättas upp av produktionsgruppen. De blanketter med en poäng som understiger det satta tröskelvärdet rättas inte upp, utan behåller sina originalvärden. Poängfunktionen jämför det inkomna ogranskade, uppräknade, värdet med ett uppräknat ”förväntat” värde och ställer denna differens i relation till den skattade branschtotalen. Svårigheten ligger ofta i att hitta ett bra förväntat värde och detta problem uppstår ideligen i urvalsundersökningar. Tanken med effektgranskning är att omfattningen av granskningen ska minska och den granskning som utförs ska ha effekt på slutresultatet.

    Det var inte lätt att hitta ett bra förväntat värde på den tid som stod till förfogande. Två problem som snabbt upptäcktes var dels att i KS-undersökningen finns inte uträknade säsongs- eller trendfaktorer per variabel. Dessutom byttes en mycket stor del av urvalet ut till kvartal 2 (som denna studie har avgränsats till att behandla). Detta har fått till följd att cirka hälften av objekten i urvalet inte går att följa bakåt i tiden eftersom de inte ingått i urvalet tidigare. I studien har respektive stratums medelvärde använts som förväntat värde. Resultaten visar att det valda förväntade värdet inte skulle ha använts i praktiken, men det fungerar bra i syfte att illustrera hur det i praktiken skulle kunna gå till att införa en mer effektiv granskning.

    Fulltekst (pdf)
    FULLTEXT01
  • 32.
    Adolfsson, Per
    et al.
    Örebro universitet, Handelshögskolan vid Örebro Universitet.
    Ivic, Marijo
    Örebro universitet, Handelshögskolan vid Örebro Universitet.
    Ett försök till att statistiskt modellera matchutfall för fotbollens division 1 för herrar i Sverige2012Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
  • 33.
    Adriansson, Nils
    et al.
    Uppsala universitet, Humanistisk-samhällsvetenskapliga vetenskapsområdet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    Mattsson, Ingrid
    Uppsala universitet, Humanistisk-samhällsvetenskapliga vetenskapsområdet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    Forecasting GDP Growth, or How Can Random Forests Improve Predictions in Economics?2015Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
    Abstract [en]

    GDP is used to measure the economic state of a country and accurate forecasts of it is therefore important. Using the Economic Tendency Survey we investigate forecasting quarterly GDP growth using the data mining technique Random Forest. Comparisons are made with a benchmark AR(1) and an ad hoc linear model built on the most important variables suggested by the Random Forest. Evaluation by forecasting shows that the Random Forest makes the most accurate forecast supporting the theory that there are benefits to using Random Forests on economic time series. 

    Fulltekst (pdf)
    fulltext
  • 34.
    Agerbeg, Jens
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Statistical Learning and Analysis on Homology-Based Features2020Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
    Abstract [en]

    Stable rank has recently been proposed as an invariant to encode the result of persistent homology, a method used in topological data analysis. In this thesis we develop methods for statistical analysis as well as machine learning methods based on stable rank. As stable rank may be viewed as a mapping to a Hilbert space, a kernel can be constructed from the inner product in this space. First, we investigate this kernel in the context of kernel learning methods such as support-vector machines. Next, using the theory of kernel embedding of probability distributions, we give a statistical treatment of the kernel by showing some of its properties and develop a two-sample hypothesis test based on the kernel. As an alternative approach, a mapping to a Euclidean space with learnable parameters can be conceived, serving as an input layer to a neural network. The developed methods are first evaluated on synthetic data. Then the two-sample hypothesis test is applied on the OASIS open access brain imaging dataset. Finally a graph classification task is performed on a dataset collected from Reddit.

    Fulltekst (pdf)
    fulltext
  • 35.
    Agering, Harald
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    True risk of illiquid investments2018Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
    Abstract [en]

    Alternative assets are becoming a considerable portion of global financial markets. Some of these alternative assets are highly illiquid, and as such they may require more intricate methods for calculating risk and performance statistics accurately. Research on hedge funds has established a pattern of risk being understated and various measures of performance being overstated due to illiquidity of the assets. This paper sets out to prove the existence of such bias and presents methods for removing it. Four mathematical methods aiming to adjust statistics for sparse return series were considered, and an implementation was carried out for data on private equity, real estate and infrastructure assets. The results indicate that there are in general substantial adjustments made to the risk and performance statistics of the illiquid assets when using these methods. In particular, the volatility and market exposure were adjusted upwards while manager skill and risk-adjusted performance were adjusted downwards.

    Fulltekst (pdf)
    fulltext
  • 36.
    Aghababa, Somayeh
    Linnéuniversitetet, Fakulteten för teknik (FTK), Institutionen för matematik (MA).
    Extremal dependency:The GARCH(1,1) model and an Agent based model2013Independent thesis Advanced level (degree of Master (One Year)), 20 poäng / 30 hpOppgave
    Abstract [en]

    This thesis focuses on stochastic processes and some of their properties are investigated which are necessary to determine the tools, the extremal index and the extremogram. Both mathematical tools measure extremal dependency within random time series. Two different models are introduced and related properties are discussed. The probability function of the Agent based model is surveyed explicitly and strong stationarity is proven. Data sets for both processes are simulated and clustering of the data is investigated with two different methods. Finally an estimation of the extremogram is used to interpret dependency of extremes within the data.

    Fulltekst (pdf)
    fulltext
  • 37.
    Aghanavesi, Somayeh
    et al.
    Högskolan Dalarna, Akademin Industri och samhälle, Mikrodataanalys.
    Memedi, Mevludin
    Högskolan Dalarna, Akademin Industri och samhälle, Datateknik.
    Dougherty, Mark
    Högskolan Dalarna, Akademin Industri och samhälle, Mikrodataanalys.
    Nyholm, Dag
    Westin, Jerker
    Högskolan Dalarna, Akademin Industri och samhälle, Datateknik.
    Verification of a method for measuring Parkinson’s disease related temporal irregularity in spiral drawings2017Inngår i: Sensors, ISSN 1424-8220, E-ISSN 1424-8220, Vol. 17, nr 10, artikkel-id 2341Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Parkinson's disease (PD) is a progressive movement disorder caused by the death of dopamine-producing cells in the midbrain. There is a need for frequent symptom assessment, since the treatment needs to be individualized as the disease progresses. The aim of this paper was to verify and further investigate the clinimetric properties of an entropy-based method for measuring PD-related upper limb temporal irregularities during spiral drawing tasks. More specifically, properties of a temporal irregularity score (TIS) for patients at different stages of PD, and medication time points were investigated. Nineteen PD patients and 22 healthy controls performed repeated spiral drawing tasks on a smartphone. Patients performed the tests before a single levodopa dose and at specific time intervals after the dose was given. Three movement disorder specialists rated videos of the patients based on the unified PD rating scale (UPDRS) and the Dyskinesia scale. Differences in mean TIS between the groups of patients and healthy subjects were assessed. Test-retest reliability of the TIS was measured. The ability of TIS to detect changes from baseline (before medication) to later time points was investigated. Correlations between TIS and clinical rating scores were assessed. The mean TIS was significantly different between healthy subjects and patients in advanced groups (p-value = 0.02). Test-retest reliability of TIS was good with Intra-class Correlation Coefficient of 0.81. When assessing changes in relation to treatment, TIS contained some information to capture changes from Off to On and wearing off effects. However, the correlations between TIS and clinical scores (UPDRS and Dyskinesia) were weak. TIS was able to differentiate spiral drawings drawn by patients in an advanced stage from those drawn by healthy subjects, and TIS had good test-retest reliability. TIS was somewhat responsive to single-dose levodopa treatment. Since TIS is an upper limb high-frequency-based measure, it cannot be detected during clinical assessment.

    Fulltekst (pdf)
    fulltext
  • 38.
    Agram, Nacira
    et al.
    University of Oslo, Norway;University of Biskra, Algeria.
    Oksendal, Bernt
    University of Oslo, Norway.
    Model uncertainty stochastic mean-field control2019Inngår i: Stochastic Analysis and Applications, ISSN 0736-2994, E-ISSN 1532-9356, Vol. 37, nr 1, s. 36-56Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We consider the problem of optimal control of a mean-field stochasticdifferential equation (SDE) under model uncertainty. The model uncertaintyis represented by ambiguity about the law LðXðtÞÞ of the stateX(t) at time t. For example, it could be the law LPðXðtÞÞ of X(t) withrespect to the given, underlying probability measure P. This is the classicalcase when there is no model uncertainty. But it could also be thelaw LQðXðtÞÞ with respect to some other probability measure Q or,more generally, any random measure lðtÞ on R with total mass 1. Werepresent this model uncertainty control problem as a stochastic differentialgame of a mean-field related type SDE with two players. Thecontrol of one of the players, representing the uncertainty of the lawof the state, is a measure-valued stochastic process lðtÞ and the controlof the other player is a classical real-valued stochastic process u(t).This optimal control problem with respect to random probability processeslðtÞ in a non-Markovian setting is a new type of stochastic controlproblems that has not been studied before. By constructing a newHilbert space M of measures, we obtain a sufficient and a necessarymaximum principles for Nash equilibria for such games in the generalnonzero-sum case, and for saddle points in zero-sum games. As anapplication we find an explicit solution of the problem of optimal consumptionunder model uncertainty of a cash flow described by amean-field related type SDE.

  • 39.
    Ahlberg, Daniel
    et al.
    Stockholm Univ, Dept Math, S-10691 Stockholm, Sweden.
    Deijfen, Maria
    Stockholm Univ, Dept Math, S-10691 Stockholm, Sweden.
    Janson, Svante
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Analys och sannolikhetsteori.
    Competing first passage percolation on random graphs with finite variance degrees2019Inngår i: Random structures & algorithms (Print), ISSN 1042-9832, E-ISSN 1098-2418, Vol. 55, nr 3, s. 545-559Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We study the growth of two competing infection types on graphs generated by the configuration model with a given degree sequence. Starting from two vertices chosen uniformly at random, the infection types spread via the edges in the graph in that an uninfected vertex becomes type 1 (2) infected at rate lambda(1) (lambda(2)) times the number of nearest neighbors of type 1 (2). Assuming (essentially) that the degree of a randomly chosen vertex has finite second moment, we show that if lambda(1) = lambda(2), then the fraction of vertices that are ultimately infected by type 1 converges to a continuous random variable V is an element of (0,1), as the number of vertices tends to infinity. Both infection types hence occupy a positive (random) fraction of the vertices. If lambda(1) not equal lambda(2), on the other hand, then the type with the larger intensity occupies all but a vanishing fraction of the vertices. Our results apply also to a uniformly chosen simple graph with the given degree sequence.

  • 40.
    Ahlberg, Daniel
    et al.
    Stockholm Univ, Dept Math, SE-10691 Stockholm, Sweden.
    Griffiths, Simon
    PUC Rio, Dept Matemat, BR-22451900 Gavea, RJ, Brazil.
    Janson, Svante
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Analys och sannolikhetsteori.
    Morris, Robert
    Inst Nacl Matemat Pura & Aplicada, Estr Dona Castorina 110, BR-22460320 Rio De Janeiro, Brazil.
    Competition in growth and urns2019Inngår i: Random structures & algorithms (Print), ISSN 1042-9832, E-ISSN 1098-2418, Vol. 54, nr 2, s. 211-227Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We study survival among two competing types in two settings: a planar growth model related to two-neighbor bootstrap percolation, and a system of urns with graph-based interactions. In the planar growth model, uncolored sites are given a color at rate 0, 1 or infinity, depending on whether they have zero, one, or at least two neighbors of that color. In the urn scheme, each vertex of a graph G has an associated urn containing some number of either blue or red balls ( but not both). At each time step, a ball is chosen uniformly at random from all those currently present in the system, a ball of the same color is added to each neighboring urn, and balls in the same urn but of different colors annihilate on a one-for-one basis. We show that, for every connected graph G and every initial configuration, only one color survives almost surely. As a corollary, we deduce that in the two-type growth model on Z(2), one of the colors only infects a finite number of sites with probability one. We also discuss generalizations to higher dimensions and multi-type processes, and list a number of open problems and conjectures.

  • 41.
    Ahlberg, Daniel
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Analys och sannolikhetsteori. Inst Nacl Matemat Pura & Aplicada, Estr Dona Castorina 110, BR-22460320 Rio De Janeiro, Brazil.;Uppsala Univ, Dept Math, SE-75106 Uppsala, Sweden..
    Steif, Jeffrey E.
    Univ Gothenburg, Chalmers Univ Technol, Math Sci, SE-41296 Gothenburg, Sweden..
    Pete, Gabor
    Hungarian Acad Sci, Renyi Inst, 13-15 Realtanoda U, H-1053 Budapest, Hungary.;Budapest Univ Technol & Econ, Inst Math, 1 Egry Jozsef U, H-1111 Budapest, Hungary..
    Scaling limits for the threshold window: When does a monotone Boolean function flip its outcome?2017Inngår i: Annales de l'I.H.P. Probabilites et statistiques, ISSN 0246-0203, E-ISSN 1778-7017, Vol. 53, nr 4, s. 2135-2161Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Consider a monotone Boolean function f : {0, 1}(n) -> {0, 1} and the canonical monotone coupling {eta(p) : p is an element of [0, 1]} of an element in {0, 1}(n) chosen according to product measure with intensity p is an element of [0, 1]. The random point p is an element of [0, 1] where f (eta(p)) flips from 0 to 1 is often concentrated near a particular point, thus exhibiting a threshold phenomenon. For a sequence of such Boolean functions, we peer closely into this threshold window and consider, for large n, the limiting distribution (properly normalized to be nondegenerate) of this random point where the Boolean function switches from being 0 to 1. We determine this distribution for a number of the Boolean functions which are typically studied and pay particular attention to the functions corresponding to iterated majority and percolation crossings. It turns out that these limiting distributions have quite varying behavior. In fact, we show that any nondegenerate probability measure on R arises in this way for some sequence of Boolean functions.

  • 42.
    Ahlberg, Daniel
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Analys och sannolikhetsteori. Inst Matematica Pura & Aplicada, Estr Dona Castorina 110, BR-22460320 Rio De Janeiro, Brazil.
    Tassion, Vincent
    Univ Geneva, 2-4 Rue Lievre, CH-1211 Geneva, Switzerland.
    Teixeira, Augusto
    Inst Matematica Pura & Aplicada, Estr Dona Castorina 110, BR-22460320 Rio De Janeiro, Brazil.
    Sharpness of the phase transition for continuum percolation in R22018Inngår i: Probability theory and related fields, ISSN 0178-8051, E-ISSN 1432-2064, Vol. 172, nr 1-2, s. 525-581Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We study the phase transition of random radii Poisson Boolean percolation: Around each point of a planar Poisson point process, we draw a disc of random radius, independently for each point. The behavior of this process is well understood when the radii are uniformly bounded from above. In this article, we investigate this process for unbounded (and possibly heavy tailed) radii distributions. Under mild assumptions on the radius distribution, we show that both the vacant and occupied sets undergo a phase transition at the same critical parameter.c. Moreover, For. <.c, the vacant set has a unique unbounded connected component and we give precise bounds on the one-arm probability for the occupied set, depending on the radius distribution. At criticality, we establish the box-crossing property, implying that no unbounded component can be found, neither in the occupied nor the vacant sets. We provide a polynomial decay for the probability of the one-arm events, under sharp conditions on the distribution of the radius. For. >.c, the occupied set has a unique unbounded component and we prove that the one-arm probability for the vacant decays exponentially fast. The techniques we develop in this article can be applied to other models such as the Poisson Voronoi and confetti percolation.

  • 43.
    Ahlberg, Daniel
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Analys och sannolikhetsteori. Inst Nacl Matemat Pura & Aplicada, Rio De Janeiro, RJ, Brazil;Stockholm Univ, Dept Math, SE-10691 Stockholm, Sweden;Stockholm Univ, Dept Math, SE-10691 Stockholm, Sweden.
    Tykesson, Johan
    Chalmers Univ Technol, Dept Math, SE-41296 Gothenburg, Sweden;Univ Gothenburg, Gothenburg, Sweden.
    Gilbert´s disc model with geostatical marking2018Inngår i: Advances in Applied Probability, ISSN 0001-8678, E-ISSN 1475-6064, Vol. 50, nr 4, s. 1075-1094Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We study a variant of Gilbert's disc model, in which discs are positioned at the points of a Poisson process in R-2 with radii determined by an underlying stationary and ergodic random field phi: R-2 -> [0, infinity), independent of the Poisson process. This setting, in which the random field is independent of the point process, is often referred to as geostatistical marking. We examine how typical properties of interest in stochastic geometry and percolation theory, such as coverage probabilities and the existence of long-range connections, differ between Gilbert's model with radii given by some random field and Gilbert's model with radii assigned independently, but with the same marginal distribution. Among our main observations we find that complete coverage of R(2 )does not necessarily happen simultaneously, and that the spatial dependence induced by the random field may both increase as well as decrease the critical threshold for percolation.

  • 44.
    Ahlberg, Fredrik
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Application of the Ordered Lorenz Curve in the Analysis of a Non-Life Insurance Portfolio2019Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
    Abstract [en]

    Insurance analysts have a great variety of assessment tools at their disposal in order to ensure a healthy insurance portfolio. To describe the financial income and loss distribution of the insurance portfolio one of the more fundamental mathematical instrument is the Lorenz curve. A measure developed in the early 19th centrury by Max O. Lorenz which intended to describe a population’s income distribution in a macro perspective. By developing further on this method with guidance from the article by Frees, Meyers and Cummings, [5], a link between the Lorenz curve and the insurance portfolio’s risk segment will be investigated.

    By constructing an insurance rating function which determine an insurance expected loss, depending on the policyholders characteristics, ordering the premium and loss distributions by its relative loss the intent is to identify profitable blocks along the ordered Lorenz curve. With this insight an analyst can redefine the portfolio structure and highlight the desirable characteristics which define a policyholder. In order to keep up with the competition an insurer has to, in the long run, create a sustainable, profitable portfolio with lowering the risk of occurring greater insurance claims.

    Fulltekst (pdf)
    fulltext
  • 45.
    Ahlgren, Marcus
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Claims Reserving using Gradient Boosting and Generalized Linear Models2018Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
    Abstract [en]

    One fundamental function of an insurance company revolves around calculating the expected claims costs for which the insurer has to compensate its policyholders for. This is the process of claims reserving which is practised by actuaries using statistical methods. Over the last few decades statistical learning methods have become increasingly popular due to their ability to find complex patterns in any type of data. However, they have not been widely adapted within the insurance sector. In this thesis we evaluate the capability of claims reserving with the method of gradient boosting, a non-parametric statistical learning method that has proven to be successful within multiple other disciplines which has made it very popular. The gradient boosting technique is compared with the generalized linear model(GLM) which is widely used for modelling claims. We compare the models by using a claims data set provided by Länsförsäkringar AB which allows us to train the models and evaluate their performance on data not yet seen by the models. The models were implemented using R. The results show that the GLM has a lower prediction error. Also, the gradient boosting method requires more fine tuning to handle claims data properly while the GLM already possesses certain features that makes it suitable for claims reserving without making as many adjustments in the model implementation. The advantage of capturing complex dependencies in data is not fully utilized in this thesis since we only work with 6 predictor variables. It is more likely that gradient boosting can compete with GLM when predicting more complicated claims.

    Fulltekst (pdf)
    fulltext
  • 46.
    Ahlgren, Markus
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Internal Market Risk Modelling for Power Trading Companies2015Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
    Abstract [en]

    Since the financial crisis of 2008, the risk awareness has increased in the -financial sector. Companies are regulated with regards to risk exposure. These regulations are driven by the Basel Committee that formulates broad supervisory standards, guidelines and recommends statements of best practice in banking supervision. In these regulations companies are regulated with own funds requirements for market risks.

    This thesis constructs an internal model for risk management that, according to the "Capital Requirements Regulation" (CRR) respectively the "Fundamental Review of the Trading Book" (FRTB), computes the regulatory capital requirements for market risks. The capital requirements according to CRR and FRTB are compared to show how the suggested move to an expected shortfall (ES) based model in FRTB will affect the capital requirements. All computations are performed with data that have been provided from a power trading company to make the results fit reality. In the results, when comparing the risk capital requirements according to CRR and FRTB for a power portfolio with only linear assets, it shows that the risk capital is higher using the value-at-risk (VaR) based model. This study shows that the changes in risk capital mainly depend on the different methods of calculating the risk capital according to CRR and FRTB respectively and minor on the change of risk measure.

    Fulltekst (pdf)
    fulltext
  • 47.
    Ahlinder, Jon
    et al.
    Totalförsvarets Forskningsinstitut, FOI, Stockholm, Sweden.
    Nordgaard, Anders
    Swedish National Forensic Centre (NFC), Linköping, Sweden.
    Wiklund Lindström, Susanne
    Totalförsvarets Forskningsinstitut, FOI, Stockholm, Sweden.
    Chemometrics comes to court: evidence evaluation of chem–bio threat agent attacks2015Inngår i: Journal of Chemometrics, ISSN 0886-9383, E-ISSN 1099-128X, Vol. 29, nr 5, s. 267-276Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Forensic statistics is a well-established scientific field whose purpose is to statistically analyze evidence in order to support legal decisions. It traditionally relies on methods that assume small numbers of independent variables and multiple samples. Unfortunately, such methods are less applicable when dealing with highly correlated multivariate data sets such as those generated by emerging high throughput analytical technologies. Chemometrics is a field that has a wealth of methods for the analysis of such complex data sets, so it would be desirable to combine the two fields in order to identify best practices for forensic statistics in the future. This paper provides a brief introduction to forensic statistics and describes how chemometrics could be integrated with its established methods to improve the evaluation of evidence in court.

    The paper describes how statistics and chemometrics can be integrated, by analyzing a previous know forensic data set composed of bacterial communities from fingerprints. The presented strategy can be applied in cases where chemical and biological threat agents have been illegally disposed.

  • 48.
    Ahmad, M. Rauf
    Uppsala universitet, Humanistisk-samhällsvetenskapliga vetenskapsområdet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    A homogeneity test of large dimensional covariance matrices under non-normality2018Inngår i: Kybernetika (Praha), ISSN 0023-5954, E-ISSN 1805-949X, Vol. 54, nr 5, s. 908-920Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A test statistic for homogeneity of two or more covariance matrices is presented when the distributions may be non-normal and the dimension may exceed the sample size. Using the Frobenius norm of the difference of null and alternative hypotheses, the statistic is constructed as a linear combination of consistent, location-invariant, estimators of trace functions that constitute the norm. These estimators are defined as U-statistics and the corresponding theory is exploited to derive the normal limit of the statistic under a few mild assumptions as both sample size and dimension grow large. Simulations are used to assess the accuracy of the statistic.

  • 49.
    Ahmad, M. Rauf
    Uppsala universitet, Humanistisk-samhällsvetenskapliga vetenskapsområdet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    A significance test of the RV coefficient in high dimensions2019Inngår i: Computational Statistics & Data Analysis, ISSN 0167-9473, E-ISSN 1872-7352, Vol. 131, s. 116-130Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The RV coefficient is an important measure of linear dependence between two multivariate data vectors. Using unbiased and computationally efficient estimators of its components, a modification to the RV coefficient is proposed, and used to construct a test of significance for the true coefficient. The modified estimator improves the accuracy of the original and, along with the test, can be applied to data with arbitrarily large dimensions, possibly exceeding the sample size, and the underlying distribution need only have finite fourth moment. Exact and asymptotic properties are studied under fairly general conditions. The accuracy of the modified estimator and the test is shown through simulations under a variety of parameter settings. In comparisons against several existing methods, both the proposed estimator and the test exhibit similar performance to the distance correlation. Several real data applications are also provided.

  • 50.
    Ahmad, M. Rauf
    Uppsala universitet, Humanistisk-samhällsvetenskapliga vetenskapsområdet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    A unified approach to testing mean vectors with large dimensions2019Inngår i: AStA Advances in Statistical Analysis, ISSN 1863-8171, E-ISSN 1863-818X, Vol. 103, nr 4, s. 593-618Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A unified testing framework is presented for large-dimensional mean vectors of one or several populations which may be non-normal with unequal covariance matrices. Beginning with one-sample case, the construction of tests, underlying assumptions and asymptotic theory, is systematically extended to multi-sample case. Tests are defined in terms of U-statistics-based consistent estimators, and their limits are derived under a few mild assumptions. Accuracy of the tests is shown through simulations. Real data applications, including a five-sample unbalanced MANOVA analysis on count data, are also given.

    Fulltekst (pdf)
    fulltext
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