Institutt for matematikk og statistikk

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Institutt for matematikk og statistikk

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• Artikler, rapporter og annet (matematikk og statistikk) [63]
• Mastergradsoppgaver i matematikk [11]
• Mastergradsoppgaver i statistikk [4]
• Mastergradsoppgaver i teknologi - industriell matematikk [4]

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• A Two-Component Generalization of the Integrable rdDym Equation

  Morozov, Oleg (Journal article; Tidsskriftartikkel; Peer reviewed, 2012)

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  Abstract:	We find a two-component generalization of the integrable case of rdDym equation. The reductions of this system include the general rdDym equation, the Boyer-Finley equation, and the deformed Boyer-Finley equation. Also we find a Bäcklund transformation between our generalization and Bodganov's two-component generalization of the universal hierarchy equatio
  URI:	http://hdl.handle.net/10037/5059

  File(s) in this item: 1

  article.pdf   (225.8Kb)
• A modelling approach to assessing the timescale uncertainties in proxy series with chronological errors

  Divine, D.V; Godtliebsen, F.; Rue, H. (Journal article; Tidsskriftartikkel; Peer reviewed, 2012)

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  Abstract:

  The paper proposes an approach to assessment of timescale errors in proxy-based series with chronological uncertainties. The method relies on approximation of the physical process(es) forming a proxy archive by a random Gamma process. Parameters of the process are partly data-driven and partly determined from prior assumptions. For a particular case of a linear accumulation model and absolutely dated tie points an analytical solution is found suggesting the Beta-distributed probability density on age estimates along the length of a proxy archive. In a general situation of uncertainties in the ages of the tie points the proposed method employs MCMC simulations of age-depth profiles yielding empirical confidence intervals on the constructed piecewise linear best guess timescale. It is suggested that the approach can be further extended to a more general case of a time-varying expected accumulation between the tie points. The approach is illustrated by using two ice and two lake/marine sediment cores representing the typical examples of paleoproxy archives with age models based on tie points of mixed origin

  URI:

  http://hdl.handle.net/10037/5055

  File(s) in this item: 1

  article.pdf   (1.483Mb)
• SDiff(2) and uniqueness of the Plebanski equation

  Kruglikov, Boris; Morozov, Oleg (Journal article; Tidsskriftartikkel; Peer reviewed, 2012)

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  Abstract:

  The group of area preserving diffeomorphisms showed importance in the problems of self-dual gravity and integrability theory. We discuss how representations of this infinite-dimensional Lie group can arise in mathematical physics from pure local considerations. Then using Lie algebra extensions and cohomology we derive the second Plebański equation and its geometry. We do not use Kähler or other additional structures but obtain the equation solely from the geometry of area preserving transformations group. We conclude that the Plebański equation is Lie remarkable.

  URI:

  http://hdl.handle.net/10037/4965

  File(s) in this item: 1

  article.pdf   (541.2Kb)
• Causality in Scale Space as an Approach to Change Detection

  Skrøvseth, Stein Olav; Godtliebsen, Fred; Bellika, Johan Gustav (Journal article; Tidsskriftartikkel; Peer reviewed, 2012)

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  Abstract:

  Kernel density estimation and kernel regression are useful ways to visualize and assess the structure of data. Using these techniques we define a temporal scale space as the vector space spanned by bandwidth and a temporal variable. In this space significance regions that reflect a significant derivative in the kernel smooth similar to those of SiZer (Significant Zero-crossings of derivatives) are indicated. Significance regions are established by hypothesis tests for significant gradient at every point in scale space. Causality is imposed onto the space by restricting to kernels with left-bounded or finite support and shifting kernels forward. We show that these adjustments to the methodology enable early detection of changes in time series constituting live surveillance systems of either count data or unevenly sampled measurements. Warning delays are comparable to standard techniques though comparison shows that other techniques may be better suited for single-scale problems. Our method reliably detects change points even with little to no knowledge about the relevant scale of the problem. Hence the technique will be applicable for a large variety of sources without tailoring. Furthermore this technique enables us to obtain a retrospective reliable interval estimate of the time of a change point rather than a point estimate. We apply the technique to disease outbreak detection based on laboratory confirmed cases for pertussis and influenza as well as blood glucose concentration obtained from patients with diabetes type 1.

  URI:

  http://hdl.handle.net/10037/4961

  File(s) in this item: 1

  article.pdf   (775.5Kb)
• On hybrid classification using model assisted posterior estimates

  Ghosh, Anil K.; Godtliebsen, Fred (Journal article; Tidsskriftartikkel; Peer reviewed, 2012)

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  Abstract:

  Traditional parametric and nonparametric classifiers used for statistical pattern recognition have their own strengths and limitations. While parametric methods assume some specific parametric models for density functions or posterior probabilities of competing classes, nonparametric methods are free from such assumptions. So, when these model assumptions are correct, parametric methods outperform nonparametric classifiers, especially when the training sample is small. But, violations of these assumptions often lead to poor performance by parametric classifiers, where nonparametric methods work well. In this article, we make an attempt to overcome these limitations of parametric and nonparametric approaches and combine their strengths. The resulting classifiers, denoted the hybrid classifiers, perform like parametric classifiers when the model assumptions are valid, but unlike parametric classifiers, they also provide safeguards against possible deviations from parametric model assumptions. In this article, we propose some multiscale methods for hybrid classification, and their performance is evaluated using several simulated and benchmark data sets.

  URI:

  http://hdl.handle.net/10037/4948

  File(s) in this item: 1

  article.pdf   (3.990Mb)

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