scholarly journals On generalized max-linear models in max-stable random fields

2017 ◽  
Vol 54 (3) ◽  
pp. 797-810
Author(s):  
Michael Falk ◽  
Maximilian Zott
Keyword(s):  
Random Field ◽  
Linear Model ◽  
Random Fields ◽  
Linear Models ◽  
Higher Dimensions ◽  
Natural Order ◽  
Stable Random Fields ◽  
Index Space

Abstract In practice, it is not possible to observe a whole max-stable random field. Therefore, we propose a method to reconstruct a max-stable random field in C([0, 1]k) by interpolating its realizations at finitely many points. The resulting interpolating process is again a max-stable random field. This approach uses a generalized max-linear model. Promising results have been established in the k = 1 case of Falk et al. (2015). However, the extension to higher dimensions is not straightforward since we lose the natural order of the index space.

scholarly journals Conditional sampling for spectrally discrete max-stable random fields

2011 ◽  
Vol 43 (2) ◽  
pp. 461-483 ◽  
Author(s):  
Yizao Wang ◽  
Stilian A. Stoev
Keyword(s):  
Random Fields ◽  
Linear Models ◽  
Conditional Sampling ◽  
Prediction Problem ◽  
Conditional Distributions ◽  
Spatial Extremes ◽  
Inference Problems ◽  
New Perspective ◽  
Stable Random Fields ◽  
Computational Solution

Max-stable random fields play a central role in modeling extreme value phenomena. We obtain an explicit formula for the conditional probability in general max-linear models, which include a large class of max-stable random fields. As a consequence, we develop an algorithm for efficient and exact sampling from the conditional distributions. Our method provides a computational solution to the prediction problem for spectrally discrete max-stable random fields. This work offers new tools and a new perspective to many statistical inference problems for spatial extremes, arising, for example, in meteorology, geology, and environmental applications.

scholarly journals Conditional sampling for spectrally discrete max-stable random fields

2011 ◽  
Vol 43 (02) ◽  
pp. 461-483 ◽  
Author(s):  
Yizao Wang ◽  
Stilian A. Stoev
Keyword(s):  
Random Fields ◽  
Linear Models ◽  
Conditional Sampling ◽  
Prediction Problem ◽  
Conditional Distributions ◽  
Spatial Extremes ◽  
Inference Problems ◽  
New Perspective ◽  
Stable Random Fields ◽  
Computational Solution

Max-stable random fields play a central role in modeling extreme value phenomena. We obtain an explicit formula for the conditional probability in general max-linear models, which include a large class of max-stable random fields. As a consequence, we develop an algorithm for efficient and exact sampling from the conditional distributions. Our method provides a computational solution to the prediction problem for spectrally discrete max-stable random fields. This work offers new tools and a new perspective to many statistical inference problems for spatial extremes, arising, for example, in meteorology, geology, and environmental applications.

A large sample test for the length of memory of stationary symmetric stable random fields via nonsingular ℤd-actions

2018 ◽  
Vol 55 (1) ◽  
pp. 179-195
Author(s):  
Ayan Bhattacharya ◽  
Parthanil Roy
Keyword(s):  
Random Field ◽  
Sample Size ◽  
Power Function ◽  
Ergodic Theory ◽  
Random Fields ◽  
Large Sample ◽  
Discrete Parameter ◽  
Sample Test ◽  
Block Maxima ◽  
Stable Random Fields

AbstractBased on the ratio of two block maxima, we propose a large sample test for the length of memory of a stationary symmetric α-stable discrete parameter random field. We show that the power function converges to 1 as the sample-size increases to ∞ under various classes of alternatives having longer memory in the sense of Samorodnitsky (2004). Ergodic theory of nonsingular ℤd-actions plays a very important role in the design and analysis of our large sample test.

scholarly journals Analysis of a Linear Model for Non-Synchronous Vibrations Near Stall

2021 ◽  
Vol 6 (3) ◽  
pp. 26
Author(s):  
Christoph Brandstetter ◽  
Sina Stapelfeldt
Keyword(s):  
Linear Model ◽  
Linear Models ◽  
Structural Vibration ◽  
Experimental Investigations ◽  
Vibration Modes ◽  
Critical Problem ◽  
Safety Critical ◽  
Unstable Vibration ◽  
Aero Engines ◽  
Lock In

Non-synchronous vibrations arising near the stall boundary of compressors are a recurring and potentially safety-critical problem in modern aero-engines. Recent numerical and experimental investigations have shown that these vibrations are caused by the lock-in of circumferentially convected aerodynamic disturbances and structural vibration modes, and that it is possible to predict unstable vibration modes using coupled linear models. This paper aims to further investigate non-synchronous vibrations by casting a reduced model for NSV in the frequency domain and analysing stability for a range of parameters. It is shown how, and why, under certain conditions linear models are able to capture a phenomenon, which has traditionally been associated with aerodynamic non-linearities. The formulation clearly highlights the differences between convective non-synchronous vibrations and flutter and identifies the modifications necessary to make quantitative predictions.

scholarly journals A Cascaded Unsupervised Model for PoS Tagging

2021 ◽  
Vol 20 (1) ◽  
pp. 1-23
Author(s):  
Necva Bölücü ◽  
Burcu Can
Keyword(s):  
Linear Model ◽  
Language Processing ◽  
Bayesian Model ◽  
Linear Models ◽  
Syntactic Category ◽  
Semantic Parsing ◽  
Pos Tagging ◽  
Part Of Speech ◽  
Sentence Level ◽  
Log Linear

Part of speech (PoS) tagging is one of the fundamental syntactic tasks in Natural Language Processing, as it assigns a syntactic category to each word within a given sentence or context (such as noun, verb, adjective, etc.). Those syntactic categories could be used to further analyze the sentence-level syntax (e.g., dependency parsing) and thereby extract the meaning of the sentence (e.g., semantic parsing). Various methods have been proposed for learning PoS tags in an unsupervised setting without using any annotated corpora. One of the widely used methods for the tagging problem is log-linear models. Initialization of the parameters in a log-linear model is very crucial for the inference. Different initialization techniques have been used so far. In this work, we present a log-linear model for PoS tagging that uses another fully unsupervised Bayesian model to initialize the parameters of the model in a cascaded framework. Therefore, we transfer some knowledge between two different unsupervised models to leverage the PoS tagging results, where a log-linear model benefits from a Bayesian model’s expertise. We present results for Turkish as a morphologically rich language and for English as a comparably morphologically poor language in a fully unsupervised framework. The results show that our framework outperforms other unsupervised models proposed for PoS tagging.

scholarly journals Identification and isotropy characterization of deformed random fields through excursion sets

2018 ◽  
Vol 50 (3) ◽  
pp. 706-725
Author(s):  
Julie Fournier
Keyword(s):  
Random Field ◽  
Euler Characteristic ◽  
Random Fields ◽  
Weak Form ◽  
Invariance Property ◽  
Basic Domain ◽  
Excursion Sets ◽  
The Mean ◽  
Isotropic Random

Abstract A deterministic application θ:ℝ2→ℝ2 deforms bijectively and regularly the plane and allows the construction of a deformed random field X∘θ:ℝ2→ℝ from a regular, stationary, and isotropic random field X:ℝ2→ℝ. The deformed field X∘θ is, in general, not isotropic (and not even stationary), however, we provide an explicit characterization of the deformations θ that preserve the isotropy. Further assuming that X is Gaussian, we introduce a weak form of isotropy of the field X∘θ, defined by an invariance property of the mean Euler characteristic of some of its excursion sets. We prove that deformed fields satisfying this property are strictly isotropic. In addition, we are able to identify θ, assuming that the mean Euler characteristic of excursion sets of X∘θ over some basic domain is known.

scholarly journals Excursion sets of infinitely divisible random fields with convolution equivalent Lévy measure

2017 ◽  
Vol 54 (3) ◽  
pp. 833-851 ◽  
Author(s):  
Anders Rønn-Nielsen ◽  
Eva B. Vedel Jensen
Keyword(s):  
Random Field ◽  
Large Class ◽  
Random Fields ◽  
Lévy Measure ◽  
Infinitely Divisible ◽  
Excursion Sets ◽  
Excursion Set ◽  
Fixed Radius ◽  
Asymptotic Probability ◽  
The Right

Abstract We consider a continuous, infinitely divisible random field in ℝd, d = 1, 2, 3, given as an integral of a kernel function with respect to a Lévy basis with convolution equivalent Lévy measure. For a large class of such random fields, we compute the asymptotic probability that the excursion set at level x contains some rotation of an object with fixed radius as x → ∞. Our main result is that the asymptotic probability is equivalent to the right tail of the underlying Lévy measure.

scholarly journals Autoregressive Models of the Random fields—A Survey

2020 ◽  
pp. 1-9
Keyword(s):  
Random Fields ◽  
Linear Models ◽  
Estimation Methods ◽  
Suitable Model ◽  
Main Mode ◽  
One Dimensional ◽  
Non Linear ◽  
The Status ◽  
Ar Models ◽  
Shed Light

Autoregressive (AR) random fields are widely use to describe changes in the status of real-physical objects and implemented for analyzing linear & non-linear models. AR models are Markov processes with a higher order dependence for one-dimensional time series. Actually, various estimation methods were used in order to evaluate the autoregression parameters. Although in many applications background knowledge can often shed light on the search for a suitable model, but other applications lack this knowledge and often require the type of trial errors to choose a model. This article presents a brief survey of the literatures related to the linear and non-linear autoregression models, including several extensions of the main mode models and the models developed. The use of autoregression to describe such system requires that they be of sufficiently high orders which leads to increase the computational costs.

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