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| 2. |
- Auffray, Charles, et al.
(författare)
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Making sense of big data in health research: Towards an EU action plan
- 2016
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Ingår i: Genome Medicine. - : BIOMED CENTRAL LTD. - 1756-994X. ; 8:71
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Tidskriftsartikel (refereegranskat)abstract
- Medicine and healthcare are undergoing profound changes. Whole-genome sequencing and high-resolution imaging technologies are key drivers of this rapid and crucial transformation. Technological innovation combined with automation and miniaturization has triggered an explosion in data production that will soon reach exabyte proportions. How are we going to deal with this exponential increase in data production? The potential of "big data" for improving health is enormous but, at the same time, we face a wide range of challenges to overcome urgently. Europe is very proud of its cultural diversity; however, exploitation of the data made available through advances in genomic medicine, imaging, and a wide range of mobile health applications or connected devices is hampered by numerous historical, technical, legal, and political barriers. European health systems and databases are diverse and fragmented. There is a lack of harmonization of data formats, processing, analysis, and data transfer, which leads to incompatibilities and lost opportunities. Legal frameworks for data sharing are evolving. Clinicians, researchers, and citizens need improved methods, tools, and training to generate, analyze, and query data effectively. Addressing these barriers will contribute to creating the European Single Market for health, which will improve health arid healthcare for all Europearis.
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| 3. |
- Gut, Allan, et al.
(författare)
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A Maxtrimmed St. Petersburg Game
- 2016
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Ingår i: Journal of theoretical probability. - : Springer Science and Business Media LLC. - 0894-9840 .- 1572-9230. ; 29:1, s. 277-291
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Tidskriftsartikel (refereegranskat)abstract
- Let S-n, n >= 1, describe the successive sums of the payoffs in the classical St. Petersburg game. The celebrated Feller weak law states that s(n)/n log(2)n ->(p) 1 as n -> infinity It is also known that almost sure convergence fails. However, Csorgo and Simons (Stat Probab Lett 26: 65-73, 1996) have shown that almost sure convergence holds for trimmed sums, that is, for S-n - max(1 <= k <= n) X-k. Since our actual distribution is discrete there may be ties. Our main focus in this paper is on the "maxtrimmed sum", that is, the sum trimmed by the random number of observations that are equal to the largest one. We prove an analog of Martin-Lof's (J Appl Probab 22: 634-643, 1985) distributional limit theorem for maxtrimmed sums, but also for the simply trimmed ones, as well as for the "total maximum". In a final section, we interpret these findings in terms of sums of (truncated) Poisson random variables.
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| 4. |
- Gut, Allan, et al.
(författare)
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A pointwise limit theorem for counting processes of perturbed random walks with an application to repeated significance tests
- 2017
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Ingår i: Sequential Analysis. - : Informa UK Limited. - 0747-4946 .- 1532-4176. ; 36:2, s. 290-298
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Tidskriftsartikel (refereegranskat)abstract
- Hsu and Robbins (1947) introduced the concept of complete conver-gence as a complement to the Kolmogorov strong law in that they proved that Sigma(infinity)(n=1) P(|Sn| > n epsilon) < infinity provided the mean of the summands is zero and that the variance is finite. Later, Erdos proved the necessity (1949, 1950). Heyde (1975) proved that, under the same conditions, lim(epsilon)SE arrow 0 epsilon(2) Sigma(infinity)(n=1) P(|Sn| > n epsilon) = EX2, thereby opening an area of research that has been called precise asymptotics. Both results above have been extended and generalized in various directions. Kao (1978) proved a pointwise version of Heyde's result, viz. for the counting process N(epsilon) = Sigma(infinity)(n=1) 1{|Sn| > n epsilon}, he showed that lim(epsilon)SE arrow 0 epsilon N-2 (epsilon) ->(d) EX2 integral(infinity)(0) 1 {|W(u)| > u} du, where W(.) is the standard Wiener process. In this article, we prove an analog for perturbed random walks and illustrate how they enter naturally within the theory of repeated significance tests in exponential families.
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| 8. |
- Gut, Allan, et al.
(författare)
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An asymmetric Marcinkiewicz-Zygmund LLN for random fields
- 2009
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Ingår i: Statistics and Probability Letters. - : Elsevier BV. - 0167-7152 .- 1879-2103. ; 79:8, s. 1016-1020
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Tidskriftsartikel (refereegranskat)abstract
- The classical Marcinkiewicz-Zygmund law for i.i.d. random variables has been generalized by Gut [Gut, A., 1978. Marcinkiewicz laws and convergence rates in the law of large numbers for random variables with multidimensional indices. Ann. Probab. 6, 469-482] to random fields. Therein all indices have the same power in the normalization. Looking into some weighted means of random fields. such as Cesaro summation, it is of interest to generalize these laws to the case where different indices have different powers in the normalization. In this paper we give precise moment conditions for such laws.
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| 9. |
- Gut, Allan, et al.
(författare)
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An asymmetric St. Petersburg game with trimming
- 2018
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Ingår i: Advances in Applied Probability. - : Cambridge University Press (CUP). - 0001-8678 .- 1475-6064. ; 50:A, s. 115-129
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Tidskriftsartikel (refereegranskat)abstract
- Let S-n, n >= 1, be the successive sums of the payoffs in the classical St. Petersburg game. The celebrated Feller weak law states that S-n/(n log(2) n) ->(P) 1 as n ->infinity. In this paper we review some earlier results of ours and extend some of them as we consider an asymmetric St. Petersburg game, in which the distribution of the payoff X is given by P(X = sr(k-1)) = pq(k-1), k = 1, 2,..., where p + q = 1 and s, r > 0. Two main results are extensions of the Feller weak law and the convergence in distribution theorem of Martin-Lof (1985). Moreover, it is well known that almost-sure convergence fails, though Csorgo and Simons (1996) showed that almost-sure convergence holds for trimmed sums and also for sums trimmed by an arbitrary fixed number of maxima. In view of the discreteness of the distribution we focus on 'max-trimmed sums', that is, on the sums trimmed by the random number of observations that are equal to the largest one, and prove limit theorems for simply trimmed sums, for max-trimmed sums, as well as for the 'total maximum'. Analogues with respect to the random number of summands equal to the minimum are also obtained and, finally, for joint trimming.
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