| 1. |
- Hsing, T. L., et al.
(författare)
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Remembering Ross Leadbetter: some personal recollections
- 2023
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Ingår i: Extremes. - 1386-1999 .- 1572-915X. ; In Press
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- Ross Leadbetter had had a broad and deep influence on the development of probabilistic and statistical theory of extreme values and on the application of extreme-value methods. He has been an inspiration and a friend for many of us. This editorial collects thirteen personal recollections of Ross and his work. An account of his career and some of his work can be found in the IMS Obituary “Ross Leadbetter 1931–2022”.
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| 2. |
- Lindgren, Georg, et al.
(författare)
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Effective persistency evaluation via exact excursion distributions for random processes and fields
- 2022
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Ingår i: Journal of Physics Communications. - : IOP Publishing. - 2399-6528. ; 6
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Tidskriftsartikel (refereegranskat)abstract
- Finding the probability that a stochastic system stays in a certain region of its state space over a specified time—a long-standing problem both in computational physics and in applied and theoretical mathematics—is approached through the extended and multivariate Rice formula. In principle, it applies to any smooth process multivariate both in argument and in value given that efficient numerical implementations of the high-dimensional integration are available. The computational method offers an exact integral representation yielding remarkably accurate results and provides an alternative method of computing persistency probability and exponent for a physical system. It can be viewed as an implementation of path integration for a smooth Gaussian process with an arbitrary covariance. Its high accuracy is due to efficient computation of expectations with respect to high-dimensional nearly singular Gaussian distributions. For Gaussian processes, the computations are effective and more precise than those based on the Rice series expansions and the independent interval approximation. For the benchmark diffusion process, it produces the persistency exponent that is essentially the same as the recently obtained analytical value and surpasses accuracy, interpretability as well as control of the error, previous methods including the independent or Markovian approximation. The method solves the two-step excursion dependence for a stationary differentiable Gaussian process, in both theoretical and numerical sense. The solution is based on exact expressions for the probability density for one and two successive excursion lengths. The numerical routine RIND computes the densities using recent advances in scientific computing and is easily accessible for a general covariance function, via a simple numerical interface. The work offers also analytical results that explain the effectiveness of the implemented methodology and elaborates its utilization for non-Gaussian processes.
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| 3. |
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| 4. |
- Beckman, Stig-Inge, et al.
(författare)
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Alarm characteristics for a flood warning system with deterministic components
- 1990
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Ingår i: Journal of Time Series Analysis. - : Wiley. - 0143-9782 .- 1467-9892. ; 11:1, s. 1-18
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Tidskriftsartikel (refereegranskat)abstract
- A method for evaluating a predictor-based alarm system is studied in this paper. The predictor is composed of a deterministic component reflecting external information and a statistically based component for the error between the measurements and the external predictor. The aim of the predictor study is twofold: it is a means of interpreting the connections between the alarm and the catastrophe, and it can be used to select suitable alarm levels. As an application, the performance of a water-level predictor as part of a flood warning system has been evaluated. The result of this analysis shows that an alarm system which operates when the predictor reaches a certain level will tend to give either too many alarms or alarms that are out of phase with the catastrophe.''
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| 5. |
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| 6. |
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| 7. |
- Grage, Halfdan, et al.
(författare)
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Level crossing prediction with neural networks
- 2010
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Ingår i: Methodology and Computing in Applied Probability. - : Springer Science and Business Media LLC. - 1573-7713 .- 1387-5841. ; 63:Online First, s. 623-645
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Tidskriftsartikel (refereegranskat)abstract
- A level crossing predictor or alarm system with prediction horizon k is said to be optimal if it, at time t detects that an upcrossing will occur at time t + k, with a certain high probability and simultaneously gives a minimum number of false alarms. For a Gaussian stationary process, the optimal level crossing predictor can be explicitly specified in terms of the predicted value of the process itself and of its derivative. To the authors knowledge this simple optimal solution has not been used to any substantial degree. In this paper it is shown how a neural network can be trained to approximate an optimal alarm system arbitrarily well. As in other methods of parametrization, the choice of model structure, as well as an appropriate representation of data, are crucial for a good result. Comparative studies are presented for two Gaussian ARMA-processes, for which the optimal predictor can be derived theoretically. These studies confirm that a properly trained neural network can indeed approximate an optimal alarm system quite well – with due attention paid to the problems of model structure and representation of data. The technique is also tested on a strongly non-Gaussian Duffing process with satisfactory results.
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| 8. |
- Guttorp, Peter, et al.
(författare)
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Karl Pearson and the Scandinavian school of statistics
- 2009
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Ingår i: International Statistical Review. - : Wiley. - 1751-5823 .- 0306-7734. ; 77:1, s. 64-71
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Forskningsöversikt (refereegranskat)abstract
- The relationship between Karl Pearson and the Scandinavian statisticians was more of a competitive than a collaborative nature. We describe the leading statisticians and stochasticists of the Scandinavian school, and relate some of their work to the work of Pearson.
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| 9. |
- Holmquist, Björn, et al.
(författare)
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Correlation measures for circular data
- 1985
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Ingår i: Contributions to probability and statistics in honour of Gunnar Blom. ; , s. 157-168
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Bokkapitel (refereegranskat)
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| 10. |
- Holst, Ulla, et al.
(författare)
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Recursive estimation in mixture models with Markov regime
- 1991
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Ingår i: IEEE Transactions on Information Theory. - 0018-9448. ; 37:6, s. 1683-1690
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Tidskriftsartikel (refereegranskat)abstract
- A recursive algorithm is proposed for estimation of parameters in mixture models, where the observations are governed by a hidden Markov chain. The performance of the algorithm is studied by simulations of a symmetric normal mixture. The algorithm seems to be stable and produce approximately normally distributed estimates, provided the adaptive matrix is kept well conditioned.
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