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Relevant bibliographies by topics / Extremes of Gaussian processes

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Academic literature on the topic 'Extremes of Gaussian processes'

Author: Grafiati

Published: 4 June 2021

Last updated: 20 February 2023

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Journal articles on the topic "Extremes of Gaussian processes"

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Gong, K., and X. Z. Chen. "Estimating extremes of combined two Gaussian and non-Gaussian response processes." International Journal of Structural Stability and Dynamics 14, no. 03 (February 16, 2014): 1350076. http://dx.doi.org/10.1142/s0219455413500764.

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Assessment of structural performance under stochastic dynamic loadings requires estimation of the extremes of stochastic response components and the resultant responses as their linear and nonlinear combinations. This paper addresses the evaluations and combination rules for the extremes of scalar and vectorial resultant responses from two response components that may show non-Gaussian characteristics. The non-Gaussian response process is modeled as a translation process from an underlying Gaussian process. The mean crossing rates and extreme value distributions of resultant responses are calculated following the theory for vector-valued Gaussian processes. An extensive parameter study is conducted concerning the influence of statistical moments of non-Gaussian response components on the extremes of resultant responses. It is revealed that the existing combination rules developed for Gaussian processes are not applicable to the case of non-Gaussian process. New combination rules are suggested that permit predictions of the extremes of resultant responses directly from the extremes of response components.

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Dębicki, K., K. M. Kosiński, M. Mandjes, and T. Rolski. "Extremes of multidimensional Gaussian processes." Stochastic Processes and their Applications 120, no. 12 (December 2010): 2289–301. http://dx.doi.org/10.1016/j.spa.2010.08.010.

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Kabluchko, Zakhar. "Extremes of independent Gaussian processes." Extremes 14, no. 3 (April 6, 2010): 285–310. http://dx.doi.org/10.1007/s10687-010-0110-x.

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Piterbarg, V. I. "Large extremes of Gaussian chaos processes." Doklady Mathematics 93, no. 2 (March 2016): 145–47. http://dx.doi.org/10.1134/s1064562416020058.

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Kabluchko, Zakhar. "Extremes of space–time Gaussian processes." Stochastic Processes and their Applications 119, no. 11 (November 2009): 3962–80. http://dx.doi.org/10.1016/j.spa.2009.08.001.

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Dȩbicki, Krzysztof, Enkelejd Hashorva, and Longmin Wang. "Extremes of vector-valued Gaussian processes." Stochastic Processes and their Applications 130, no. 9 (September 2020): 5802–37. http://dx.doi.org/10.1016/j.spa.2020.04.008.

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Bai, Long, Krzysztof Dȩbicki, Enkelejd Hashorva, and Lanpeng Ji. "Extremes of threshold-dependent Gaussian processes." Science China Mathematics 61, no. 11 (September 5, 2018): 1971–2002. http://dx.doi.org/10.1007/s11425-017-9225-7.

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Toro, Gabriel R., and C. Allin Cornell. "Extremes of Gaussian Processes with Bimodal Spectra." Journal of Engineering Mechanics 112, no. 5 (May 1986): 465–84. http://dx.doi.org/10.1061/(asce)0733-9399(1986)112:5(465).

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Huesler, Juerg, Vladimir Piterbarg, and Yueming Zhang. "Extremes of Gaussian Processes with Random Variance." Electronic Journal of Probability 16 (2011): 1254–80. http://dx.doi.org/10.1214/ejp.v16-904.

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Bai, Long. "Extremes of Gaussian chaos processes with trend." Journal of Mathematical Analysis and Applications 473, no. 2 (May 2019): 1358–76. http://dx.doi.org/10.1016/j.jmaa.2019.01.026.

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Dissertations / Theses on the topic "Extremes of Gaussian processes"

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Kratz, Marie. "Some contributions in probability and statistics of extremes." Habilitation à diriger des recherches, Université Panthéon-Sorbonne - Paris I, 2005. http://tel.archives-ouvertes.fr/tel-00239329.

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Stewart, Michael Ian. "Asymptotic methods for tests of homogeneity for finite mixture models." Thesis, The University of Sydney, 2002. http://hdl.handle.net/2123/855.

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We present limit theory for tests of homogeneity for finite mixture models. More specifically, we derive the asymptotic distribution of certain random quantities used for testing that a mixture of two distributions is in fact just a single distribution. Our methods apply to cases where the mixture component distributions come from one of a wide class of one-parameter exponential families, both continous and discrete. We consider two random quantities, one related to testing simple hypotheses, the other composite hypotheses. For simple hypotheses we consider the maximum of the standardised score process, which is itself a test statistic. For composite hypotheses we consider the maximum of the efficient score process, which is itself not a statistic (it depends on the unknown true distribution) but is asymptotically equivalent to certain common test statistics in a certain sense. We show that we can approximate both quantities with the maximum of a certain Gaussian process depending on the sample size and the true distribution of the observations, which when suitably normalised has a limiting distribution of the Gumbel extreme value type. Although the limit theory is not practically useful for computing approximate p-values, we use Monte-Carlo simulations to show that another method suggested by the theory, involving using a Studentised version of the maximum-score statistic and simulating a Gaussian process to compute approximate p-values, is remarkably accurate and uses a fraction of the computing resources that a straight Monte-Carlo approximation would.

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Stewart, Michael Ian. "Asymptotic methods for tests of homogeneity for finite mixture models." University of Sydney. Mathematics and Statistics, 2002. http://hdl.handle.net/2123/855.

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We present limit theory for tests of homogeneity for finite mixture models. More specifically, we derive the asymptotic distribution of certain random quantities used for testing that a mixture of two distributions is in fact just a single distribution. Our methods apply to cases where the mixture component distributions come from one of a wide class of one-parameter exponential families, both continous and discrete. We consider two random quantities, one related to testing simple hypotheses, the other composite hypotheses. For simple hypotheses we consider the maximum of the standardised score process, which is itself a test statistic. For composite hypotheses we consider the maximum of the efficient score process, which is itself not a statistic (it depends on the unknown true distribution) but is asymptotically equivalent to certain common test statistics in a certain sense. We show that we can approximate both quantities with the maximum of a certain Gaussian process depending on the sample size and the true distribution of the observations, which when suitably normalised has a limiting distribution of the Gumbel extreme value type. Although the limit theory is not practically useful for computing approximate p-values, we use Monte-Carlo simulations to show that another method suggested by the theory, involving using a Studentised version of the maximum-score statistic and simulating a Gaussian process to compute approximate p-values, is remarkably accurate and uses a fraction of the computing resources that a straight Monte-Carlo approximation would.

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Schmid, Christoph Manuel. "Extreme values of Gaussian processes and a heterogeneous multi agents model." [S.l.] : [s.n.], 2002. http://www.zb.unibe.ch/download/eldiss/02schmid_c.pdf.

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Engelke, Sebastian. "Brown-Resnick Processes: Analysis, Inference and Generalizations." Doctoral thesis, Niedersächsische Staats- und Universitätsbibliothek Göttingen, 2012. http://hdl.handle.net/11858/00-1735-0000-000D-F1B3-2.

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Skolidis, Grigorios. "Transfer learning with Gaussian processes." Thesis, University of Edinburgh, 2012. http://hdl.handle.net/1842/6271.

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Transfer Learning is an emerging framework for learning from data that aims at intelligently transferring information between tasks. This is achieved by developing algorithms that can perform multiple tasks simultaneously, as well as translating previously acquired knowledge to novel learning problems. In this thesis, we investigate the application of Gaussian Processes to various forms of transfer learning with a focus on classification problems. This process initiates with a thorough introduction to the framework of Transfer learning, providing a clear taxonomy of the areas of research. Following that, we continue by reviewing the recent advances on Multi-task learning for regression with Gaussian processes, and compare the performance of some of these methods on a real data set. This review gives insights about the strengths and weaknesses of each method, which acts as a point of reference to apply these methods to other forms of transfer learning. The main contributions of this thesis are reported in the three following chapters. The third chapter investigates the application of Multi-task Gaussian processes to classification problems. We extend a previously proposed model to the classification scenario, providing three inference methods due to the non-Gaussian likelihood the classification paradigm imposes. The forth chapter extends the multi-task scenario to the semi-supervised case. Using labeled and unlabeled data, we construct a novel covariance function that is able to capture the geometry of the distribution of each task. This setup allows unlabeled data to be utilised to infer the level of correlation between the tasks. Moreover, we also discuss the potential use of this model to situations where no labeled data are available for certain tasks. The fifth chapter investigates a novel form of transfer learning called meta-generalising. The question at hand is if, after training on a sufficient number of tasks, it is possible to make predictions on a novel task. In this situation, the predictor is embedded in an environment of multiple tasks but has no information about the origins of the test task. This elevates the concept of generalising from the level of data to the level of tasks. We employ a model based on a hierarchy of Gaussian processes, in a mixtures of expert sense, to make predictions based on the relation between the distributions of the novel and the training tasks. Each chapter is accompanied with a thorough experimental part giving insights about the potentials and the limits of the proposed methods.

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Blitvic, Natasa. "Two-parameter noncommutative Gaussian processes." Thesis, Massachusetts Institute of Technology, 2012. http://hdl.handle.net/1721.1/78440.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2012.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 225-237).
The reality of billion-user networks and multi-terabyte data sets brings forth the need for accurate and computationally tractable descriptions of large random structures, such as random matrices or random graphs. The modern mathematical theory of free probability is increasingly giving rise to analysis tools specifically adapted to such large-dimensional regimes and, more generally, non-commutative probability is emerging as an area of interdisciplinary interest. This thesis develops a new non-commutative probabilistic framework that is both a natural generalization of several existing frameworks (viz. free probability, q-deformed probability) and a setting in which to describe a broader class of random matrix limits. From the practical perspective, this new setting is particularly interesting in its ability to characterize the behavior of large random objects that asymptotically retain a certain degree of commutative structure and therefore fall outside the scope of free probability. The type of commutative structure considered is modeled on the two-parameter families of generalized harmonic oscillators found in physics and the presently introduced framework may be viewed as a two-parameter deformation of classical probability. Specifically, we introduce (1) a generalized Non-commutative Central Limit Theorem giving rise to a two-parameter deformation of the classical Gaussian statistics and (2) a two-parameter continuum of non-commutative probability spaces in which to realize these statistics. The framework that emerges has a remarkably rich combinatorial structure and bears upon a number of well-known mathematical objects, such as a quantum deformation of the Airy function, that had not previously played a prominent role in a probabilistic setting. Finally, the present framework paves the way to new types of asymptotic results, by providing more general asymptotic theorems and revealing new layers of structure in previously known results, notably in the "correlated process version" of Wigner's Semicircle Law.
by Natasha Blitvić.
Ph.D.

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Feng, Shimin. "Sensor fusion with Gaussian processes." Thesis, University of Glasgow, 2014. http://theses.gla.ac.uk/5626/.

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This thesis presents a new approach to multi-rate sensor fusion for (1) user matching and (2) position stabilisation and lag reduction. The Microsoft Kinect sensor and the inertial sensors in a mobile device are fused with a Gaussian Process (GP) prior method. We present a Gaussian Process prior model-based framework for multisensor data fusion and explore the use of this model for fusing mobile inertial sensors and an external position sensing device. The Gaussian Process prior model provides a principled mechanism for incorporating the low-sampling-rate position measurements and the high-sampling-rate derivatives in multi-rate sensor fusion, which takes account of the uncertainty of each sensor type. We explore the complementary properties of the Kinect sensor and the built-in inertial sensors in a mobile device and apply the GP framework for sensor fusion in the mobile human-computer interaction area. The Gaussian Process prior model-based sensor fusion is presented as a principled probabilistic approach to dealing with position uncertainty and the lag of the system, which are critical for indoor augmented reality (AR) and other location-aware sensing applications. The sensor fusion helps increase the stability of the position and reduce the lag. This is of great benefit for improving the usability of a human-computer interaction system. We develop two applications using the novel and improved GP prior model. (1) User matching and identification. We apply the GP model to identify individual users, by matching the observed Kinect skeletons with the sensed inertial data from their mobile devices. (2) Position stabilisation and lag reduction in a spatially aware display application for user performance improvement. We conduct a user study. Experimental results show the improved accuracy of target selection, and reduced delay from the sensor fusion system, allowing the users to acquire the target more rapidly, and with fewer errors in comparison with the Kinect filtered system. They also reported improved performance in subjective questions. The two applications can be combined seamlessly in a proxemic interaction system as identification of people and their positions in a room-sized environment plays a key role in proxemic interactions.

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Aguilar, Tamara Alejandra Fernandez. "Gaussian processes for survival analysis." Thesis, University of Oxford, 2017. http://ora.ox.ac.uk/objects/uuid:b5a7a3b2-d1bd-40f1-9b8d-dbb2b9cedd29.

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Survival analysis is an old area of statistics dedicated to the study of time-to-event random variables. Typically, survival data have three important characteristics. First, the response is a waiting time until the occurrence of a predetermined event. Second, the response can be "censored", meaning that we do not observe its actual value but a bound for it. Last, the presence of covariates. While there exists some feasible parametric methods for modelling this type of data, they usually impose very strong assumptions on the real complexity of the response and how it interacts with the covariates. While these assumptions allow us to have tractable inference schemes, we lose inference power and overlook important relationships in the data. Due to the inherent limitations of parametric models, it is natural to consider non-parametric approaches. In this thesis, we introduce a novel Bayesian non-parametric model for survival data. The model is based on using a positive map of a Gaussian process with stationary covariance function as prior over the so-called hazard function. This model is thoughtfully studied in terms of prior behaviour and posterior consistency. Alternatives to incorporate covariates are discussed as well as an exact and tractable inference scheme.

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Beck, Daniel Emilio. "Gaussian processes for text regression." Thesis, University of Sheffield, 2017. http://etheses.whiterose.ac.uk/17619/.

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Text Regression is the task of modelling and predicting numerical indicators or response variables from textual data. It arises in a range of different problems, from sentiment and emotion analysis to text-based forecasting. Most models in the literature apply simple text representations such as bag-of-words and predict response variables in the form of point estimates. These simplifying assumptions ignore important information coming from the data such as the underlying uncertainty present in the outputs and the linguistic structure in the textual inputs. The former is particularly important when the response variables come from human annotations while the latter can capture linguistic phenomena that go beyond simple lexical properties of a text. In this thesis our aim is to advance the state-of-the-art in Text Regression by improving these two aspects, better uncertainty modelling in the response variables and improved text representations. Our main workhorse to achieve these goals is Gaussian Processes (GPs), a Bayesian kernelised probabilistic framework. GP-based regression models the response variables as well-calibrated probability distributions, providing additional information in predictions which in turn can improve subsequent decision making. They also model the data using kernels, enabling richer representations based on similarity measures between texts. To be able to reach our main goals we propose new kernels for text which aim at capturing richer linguistic information. These kernels are then parameterised and learned from the data using efficient model selection procedures that are enabled by the GP framework. Finally we also capitalise on recent advances in the GP literature to better capture uncertainty in the response variables, such as multi-task learning and models that can incorporate non-Gaussian variables through the use of warping functions. Our proposed architectures are benchmarked in two Text Regression applications: Emotion Analysis and Machine Translation Quality Estimation. Overall we are able to obtain better results compared to baselines while also providing uncertainty estimates for predictions in the form of posterior distributions. Furthermore we show how these models can be probed to obtain insights about the relation between the data and the response variables and also how to apply predictive distributions in subsequent decision making procedures.

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Books on the topic "Extremes of Gaussian processes"

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Hida, Takeyuki. Gaussian processes. Providence, R.I: American Mathematical Society, 1993.

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Hida, Takeyuki. Gaussian processes. Providence, R.I: American Mathematical Society, 1993.

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service), SpringerLink (Online, ed. Lectures on Gaussian Processes. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012.

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Lifshits, Mikhail. Lectures on Gaussian Processes. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-24939-6.

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Marcus, Michael B. Markov processes, Gaussian processes, and local times. New York: Cambridge University Press, 2006.

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I, Williams Christopher K., ed. Gaussian processes for machine learning. Cambridge, Mass: MIT Press, 2006.

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Rasmussen, Carl Edward. Gaussian processes for machine learning. Cambridge, MA: MIT Press, 2005.

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Nagoya Lévy Seminar (3rd 1990 Nagoya-shi, Japan). Gaussian random fields. Edited by Hida Takeyuki 1927-, Itō Kiyosi 1915-, International Conference on Gaussian Random Fields (1990 : Nagoya-shi, Japan), and International Congress of Mathematicians. (1990 : Kyoto, Japan). Singapore: World Scientific, 1991.

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Lifshit͡s, M. A. Gaussian random functions. Dordrecht: Kluwer Academic Publishers, 1995.

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S, Taqqu Murad, ed. Stable non-Gaussian random processes: Stochastic models with infinite variance. New York: Chapman & Hall, 1994.

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Book chapters on the topic "Extremes of Gaussian processes"

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Falk, Michael, Rolf-Dieter Reiss, and Jürg Hüsler. "Extremes of Gaussian Processes." In Laws of Small Numbers: Extremes and Rare Events, 273–96. Basel: Birkhäuser Basel, 2004. http://dx.doi.org/10.1007/978-3-0348-7791-6_10.

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Falk, Michael, Jürg Hüsler, and Rolf-Dieter Reiss. "Extremes of Gaussian Processes." In Laws of Small Numbers: Extremes and Rare Events, 381–418. Basel: Springer Basel, 2010. http://dx.doi.org/10.1007/978-3-0348-0009-9_10.

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Stamatovic, Sinisa. "Extremes of Gaussian Processes." In International Encyclopedia of Statistical Science, 496–98. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-04898-2_245.

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Berman, Simeon M. "A Central Limit Theorem for Extreme Sojourn Times of Stationary Gaussian Processes." In Lecture Notes in Statistics, 81–99. New York, NY: Springer New York, 1989. http://dx.doi.org/10.1007/978-1-4612-3634-4_8.

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Azencott, Robert, and Didier Dacunha-Castelle. "Gaussian Processes." In Series of Irregular Observations, 10–17. New York, NY: Springer New York, 1986. http://dx.doi.org/10.1007/978-1-4612-4912-2_3.

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Todorovic, Petar. "Gaussian Processes." In An Introduction to Stochastic Processes and Their Applications, 92–105. New York, NY: Springer New York, 1992. http://dx.doi.org/10.1007/978-1-4613-9742-7_4.

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Adler, Robert J., and Jonathan E. Taylor. "Gaussian Processes." In Lecture Notes in Mathematics, 13–35. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-19580-8_2.

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Bryc, Wlodzimierz. "Gaussian processes." In The Normal Distribution, 109–21. New York, NY: Springer New York, 1995. http://dx.doi.org/10.1007/978-1-4612-2560-7_9.

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Gusak, Dmytro, Alexander Kukush, Alexey Kulik, Yuliya Mishura, and Andrey Pilipenko. "Gaussian processes." In Theory of Stochastic Processes, 59–70. New York, NY: Springer New York, 2009. http://dx.doi.org/10.1007/978-0-387-87862-1_6.

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Lee, Herbert K. H. "Gaussian Processes." In International Encyclopedia of Statistical Science, 575–77. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-04898-2_271.

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Conference papers on the topic "Extremes of Gaussian processes"

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Leira, Bernt J. "Combination of Multiple Extreme Bending Moment Components." In ASME 2012 31st International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/omae2012-83528.

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A procedure for estimating the combined load effect for processes with different zero-crossing periods is described. The procedure is illustrated by application to the combination of wave-induced bending moments. The basic formulations related to the distribution of maxima and extremes for a scalar Gaussian process are first reviewed. Subsequently, an outline of the procedure for multi-component processes is given. The developed formulation is then applied for analysis of the combined bending moment load effect. Two cases of such combinations are addressed (i) A case with widely different velocity variances (ii) A case involving a non-linear combination of the bending moments. A geometric approach to the interpretation and derivation of associated load effect combination factors is also demonstrated.

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Smith, Mark, Steven Reece, Stephen Roberts, and Iead Rezek. "Online Maritime Abnormality Detection Using Gaussian Processes and Extreme Value Theory." In 2012 IEEE 12th International Conference on Data Mining (ICDM). IEEE, 2012. http://dx.doi.org/10.1109/icdm.2012.137.

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Grosskopf, Michael, Earl Lawrence, Ayan Biswas, Li Tang, Kelin Rumsey, Luke Van Roekel, and Nathan Urban. "In-Situ Spatial Inference on Climate Simulations with Sparse Gaussian Processes." In ISAV'21: In Situ Infrastructures for Enabling Extreme-Scale Analysis and Visualization. New York, NY, USA: ACM, 2021. http://dx.doi.org/10.1145/3490138.3490140.

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Sun, Schyler C., and Weisi Guo. "Forecasting Wireless Demand with Extreme Values using Feature Embedding in Gaussian Processes." In 2021 IEEE 93rd Vehicular Technology Conference (VTC2021-Spring). IEEE, 2021. http://dx.doi.org/10.1109/vtc2021-spring51267.2021.9449040.

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Wang, Jie, Xiangyuan Zheng, and Qingdong He. "Artificial Intelligence Applied to Extreme Value Prediction of Non-Gaussian Processes with Bandwidth Effect and Non-monotonicity." In 2021 IEEE International Conference on Artificial Intelligence and Computer Applications (ICAICA). IEEE, 2021. http://dx.doi.org/10.1109/icaica52286.2021.9498204.

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Lua, James, and E. Thomas Mover. "First-Excursion Probability and Response Peak Distribution of a Nonlinear Structure Under Non-Gaussian Non-Stationary Loadings." In ASME 1998 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1998. http://dx.doi.org/10.1115/imece1998-0392.

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Abstract Probabilistic methods have been used recently for the reliability assessment and design of ship structures because of the presence of various uncertainties in structural configuration, material properties, and environmental and operating conditions. Among these uncertainties, random dynamic loads induced by either sea waves or slamming play a significant role in reliability-based ship structural design. The present state-of-the-art probabilistic method for ship design is based on a linear structural response model subjected to stationary Gaussian random processes. However, under extreme operating conditions, the ship structural response may not be linear due to the initiation and evolution of multiple local damage, such as local plastic deformation, stiffener tripping, panel buckling, or fracture. In addition, the complexity of fluid-structure interaction phenomena may render the assumptions on the loading process (stationary and Gaussian) invalid. Under this study, we developed a simulation based probabilistic analysis framework for a nonlinear dynamic structural system under non-Gaussian non-stationary loadings. The general simulation based probabilistic analysis framework (SIMLAB) is formulated by integrating 1) random variable generating modules; 2) random process generation modules; and 3) user selected deterministic solver and limit state function. The developed random process simulation module is able to generate a Gaussian, non-Gaussian, stationary, or non-stationary process. To demonstrate the applicability of the developed tool for a structural dynamic system with random variables and random processes, a free-free beam subjected to a sea wave induced random process is solved by integrating a structural dynamics code, DYNA3D, with the developed probabilistic analysis framework. The limit state function is formulated based on the first crossing of a beam Von Mises stress at an integration point above a safe threshold. In order to validate the accuracy of SIMLAB, a linear beam structure subjected to a stationary Gaussian process is considered first and the simulated statistical distributions of peak and extreme response variables are compared with analytical predictions. The effect of material nonlinearity on probability of failure and peak statistics is explored by using an elastoplastic beam model subjected to a random excitation. Results on probability of failure and peak statistics are compared with the corresponding statistical models for a linear structure. The great versatility of the simulation based probabilistic analysis framework provides us a solid foundation for the development of more advanced probabilistic analysis tools for reliability-based ship design.

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Cetin, Ali, Trond Pytte, and Sveinung Eriksrud. "Determination of Short Term Extreme Response Values for Temporary Riser Systems: A Practical Approach." In ASME 2016 35th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/omae2016-54763.

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Operation limits for temporary riser system are determined according to some probability of exceedance of a relevant variable. Accordingly, consistent statistical analysis and probability modelling of the data is required. The common industry approach is to rely on the classical narrow-banded Gaussian process assumption when considering time series of variables of interest. Thus, the time series peaks are characterized by means of the Rayleigh distribution and the relevant extreme values are estimated based on this. However, non-linearities present in riser systems may yield non-Gaussian (wide-banded) processes, rendering the classical approach inappropriate. In the present work, an approximate and practical method is presented to address above issue. It is demonstrated that the approximate method is capable of consistently estimating the relevant extreme values, even where the classical method comes short.

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Kislov, Denis, and Alexander S. Shalin. "Optomechanical manipulation of nanoparticles with a magnetic response in a Gaussian beam." In INTERNATIONAL CONFERENCE ON PHYSICS AND CHEMISTRY OF COMBUSTION AND PROCESSES IN EXTREME ENVIRONMENTS (COMPHYSCHEM’20-21) and VI INTERNATIONAL SUMMER SCHOOL “MODERN QUANTUM CHEMISTRY METHODS IN APPLICATIONS”. AIP Publishing, 2020. http://dx.doi.org/10.1063/5.0031717.

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Agarwal, Puneet, William Walker, and Kenneth Bhalla. "Estimation of Most Probable Maximum From Short-Duration or Undersampled Time-Series Data." In ASME 2015 34th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/omae2015-41701.

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The most probable maximum (MPM) is the extreme value statistic commonly used in the offshore industry. The extreme value of vessel motions, structural response, and environment are often expressed using the MPM. For a Gaussian process, the MPM is a function of the root-mean square and the zero-crossing rate of the process. Accurate estimates of the MPM may be obtained in frequency domain from spectral moments of the known power spectral density. If the MPM is to be estimated from the time-series of a random process, either from measurements or from simulations, the time series data should be of long enough duration, sampled at an adequate rate, and have an ensemble of multiple realizations. This is not the case when measured data is recorded for an insufficient duration, or one wants to make decisions (requiring an estimate of the MPM) in real-time based on observing the data only for a short duration. Sometimes, the instrumentation system may not be properly designed to measure the dynamic vessel motions with a fine sampling rate, or it may be a legacy instrumentation system. The question then becomes whether the short-duration and/or the undersampled data is useful at all, or if some useful information (i.e., an estimate of MPM) can be extracted, and if yes, what is the accuracy and uncertainty of such estimates. In this paper, a procedure for estimation of the MPM from the short-time maxima, i.e., the maximum value from a time series of short duration (say, 10 or 30 minutes), is presented. For this purpose pitch data is simulated from the vessel RAOs (response amplitude operators). Factors to convert the short-time maxima to the MPM are computed for various non-exceedance levels. It is shown that the factors estimated from simulation can also be obtained from the theory of extremes of a Gaussian process. Afterwards, estimation of the MPM from the short-time maxima is explored for an undersampled process; however, undersampled data must not be used and only the adequately sampled data should be utilized. It is found that the undersampled data can be somewhat useful and factors to convert the short-time maxima to the MPM can be derived for an associated non-exceedance level. However, compared to the adequately sampled data, the factors for the undersampled data are less useful since they depend on more variables and have more uncertainty. While the vessel pitch data was the focus of this paper, the results and conclusions are valid for any adequately sampled narrow-banded Gaussian process.

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Dhaka, Akash Kumar, Michael Riis Andersen, Pablo Garcia Moreno, and Aki Vehtari. "Scalable Gaussian Process for Extreme Classification." In 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP). IEEE, 2020. http://dx.doi.org/10.1109/mlsp49062.2020.9231675.

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Reports on the topic "Extremes of Gaussian processes"

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Beder, Jay H. Sieves for Gaussian Processes. Fort Belvoir, VA: Defense Technical Information Center, November 1985. http://dx.doi.org/10.21236/ada166055.

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2

Samorodnitsky, Gennady. Continuity of Gaussian Processes. Fort Belvoir, VA: Defense Technical Information Center, August 1986. http://dx.doi.org/10.21236/ada174738.

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3

Berman, Simeon M. Sojourns and Extremes of Stochastic Processes. Fort Belvoir, VA: Defense Technical Information Center, September 1989. http://dx.doi.org/10.21236/ada245005.

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Berman, Simeon M. Sojourns, Extremes, and Self-Intersections of Stochastic Processes. Fort Belvoir, VA: Defense Technical Information Center, September 1992. http://dx.doi.org/10.21236/ada257251.

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Chernozhukov, Victor, Denis Chetverikov, and Kengo Kato. Gaussian approximation of suprema of empirical processes. Institute for Fiscal Studies, December 2012. http://dx.doi.org/10.1920/wp.cem.2012.4412.

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Chernozhukov, Victor, Denis Chetverikov, and Kengo Kato. Gaussian approximation of suprema of empirical processes. The IFS, December 2013. http://dx.doi.org/10.1920/wp.cem.2013.7513.

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Chernozhukov, Victor, Denis Chetverikov, and Kengo Kato. Gaussian approximation of suprema of empirical processes. The IFS, August 2016. http://dx.doi.org/10.1920/wp.cem.2016.4116.

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Beder, J. Sieves and a Filter for Gaussian Processes. Fort Belvoir, VA: Defense Technical Information Center, April 1985. http://dx.doi.org/10.21236/ada158762.

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Taniguchi, M., P. R. Krishnaiah, and R. Chao. Normalizing Transformations of Some Statistics of Gaussian ARMA Processes. Fort Belvoir, VA: Defense Technical Information Center, February 1986. http://dx.doi.org/10.21236/ada170184.

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Stetzler, Steven, and Michael Grosskopf. Fast Emulation of Expensive Simulations using Approximate Gaussian Processes. Office of Scientific and Technical Information (OSTI), August 2021. http://dx.doi.org/10.2172/1811874.

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