| 1. |
- Cengiz, Cigdem, et al.
(författare)
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High-dimensional profile analysis
- 2020
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- The three tests of profile analysis: test of parallelism, test of level and test of flatness have been studied. Likelihood ratio tests have been derived. Firstly, a traditional setting, where the sample size is greater than the dimension of the parameter space, is considered. Then, all tests have been derived in a high-dimensional setting. In high-dimensional data analysis, it is required to use some techniques to tackle the problems which arise with the dimensionality. We propose a dimension reduction method using scores which was first proposed by Läuter et al. (1996).
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| 2. |
- Holmberg, Kaj, 1955-
(författare)
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Optimal proportional representation
- 2020
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In a democratic proportional election system, it is vital that the mandates in the parliament are allocated as proportionally as possible to the number of votes the parties got in the election. We formulate an optimization model for allocation of seats in a parliament so as to minimize the disproportionality. By applying separable programming techniques, we obtain an easily solvable problem, and present a method for solving it optimally. The obtained solution is the feasible solution that has the minimal disproportionality (with the measure chosen), even in the presence of a parliament threshold, which is not always the case for the practical procedures used in many countries. We apply the approach to real life data from the last three elections in Sweden, and show that the result is better, i.e. more proportional, than what was obtained with the modified Sainte-Laguë method, which is presently used. A natural suggestion would be to use our method instead.We also consider the issue about constituencies, and suggest a procedure, based on the same kind of optimization problem, for allocating mandates in the constituencies, without changing the overall allocation with respect to parties. The numbers of mandates for the constituencies are based on the number of votes given, not on estimated numbers of inhabitants entitled to vote. This removes the need for compensatory mandates, and makes the question about sizes of the constituencies less important.
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| 3. |
- Ngailo, Edward, 1982-, et al.
(författare)
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Approximation of misclassification probabilities in linear discriminant analysis with repeated measurements
- 2020
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In this paper, we propose approximations for the probabilities of misclassification in linear discriminant analysis when means follow a growth curve structure. The discriminant function can classify a new observation vector of p repeated measurements into one of two multivariate normal populations with equal covariance matrix. We derive certain relations of the statistics under consideration in order to obtain approximations of the misclassification errors. Finally, we perform Monte Carlo simulations to evaluate the performance of proposed results.
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| 4. |
- Ngailo, Edward, 1982-, et al.
(författare)
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Linear discriminant analysis via the Growth Curve model and restrictions on the mean space
- 2020
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- A linear classification function is applied when the means follow a Growth Curve model with restriction on the mean space. If the underlying assumption is that different groups in the experimental design follow different growth proles, a bilinear restriction on the mean space gives an Extended Growth Curve model. Given this restriction the approximations for the probability of misclassifications are derived. Moreover, a discriminant function is also derived when there exist rank restrictions on the mean parameters.
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| 5. |
- Nordström, Jan, 1953-, et al.
(författare)
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The number of boundary conditions for initial boundary value problems
- 2020
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Both the energy method and the Laplace transform method are frequently used for determining the number of boundary conditions required for a well posed initial boundary value problem.We show that these two distinctly dierent methods yield the same results.
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| 6. |
- Olsson, Per-Magnus, 1976-, et al.
(författare)
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Exploiting parallelization and synergy in derivative free optimization
- 2020
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Real life optimization often concerns difficult objective functions, in two aspects, namely that gradients are unavailable, and that evaluation of the objective function takes a long time. Such problems are often attacked with model building algorithms, where an approximation of the function is constructed and solved, in order to find a new promising point to evaluate. We study several ways of saving time by using parallel calculations in the context of model building algorithms, which is not trivial, since such algorithms are inherently sequential. We present a number of ideas that has been implemented and tested on a large number of known test functions, and a few new ones. The computational results reveal that some ideas are quite promising.
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| 7. |
- Ålund, Oskar, 1987-, et al.
(författare)
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Learning to Differentiate
- 2020
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Artificial neural networks together with associated computational libraries provide a powerful framework for constructing both classification and regression algorithms. In this paper we use neural networks to design linear and non-linear discrete differential operators. We show that neural network based operators can be used to construct stable discretizations of initial boundary-value problems by ensuring that the operators satisfy a discrete analogue of integration-byparts known as summation-by-parts. Furthermore we demonstrate the benefits of building the summation-by-parts property into the network by weight restriction, rather than enforcing it through a regularizer. We conclude that, if possible, known structural elements of an operation are best implemented as innate—rather than learned—properties of the network. The strategy developed in this work also opens the door for constructing stable differential operators on general meshes.
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