scholarly journals High level excursion set geometry for non-Gaussian infinitely divisible random fields

2013 ◽  
Vol 41 (1) ◽  
pp. 134-169 ◽  
Author(s):  
Robert J. Adler ◽  
Gennady Samorodnitsky ◽  
Jonathan E. Taylor
Keyword(s):  
Random Fields ◽  
Infinitely Divisible ◽  
Excursion Set ◽  
Non Gaussian ◽  
High Level

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 Random Fields with Pólya Correlation Structure

2014 ◽  
Vol 51 (4) ◽  
pp. 1037-1050 ◽  
Author(s):  
Richard Finlay ◽  
Eugene Seneta
Keyword(s):  
Random Fields ◽  
Cross Correlation ◽  
Marginal Distribution ◽  
Gaussian Random Fields ◽  
Correlation Structure ◽  
Finite Variance ◽  
Infinitely Divisible ◽  
New Class ◽  
Joint Characteristic ◽  
Non Gaussian

We construct random fields with Pólya-type autocorrelation function and dampened Pólya cross-correlation function. The marginal distribution of the random fields may be taken as any infinitely divisible distribution with finite variance, and the random fields are fully characterized in terms of their joint characteristic function. This makes available a new class of non-Gaussian random fields with flexible correlation structure for use in modeling and estimation.

Random Fields with Pólya Correlation Structure

2014 ◽  
Vol 51 (04) ◽  
pp. 1037-1050 ◽  
Author(s):  
Richard Finlay ◽  
Eugene Seneta
Keyword(s):  
Random Fields ◽  
Cross Correlation ◽  
Marginal Distribution ◽  
Gaussian Random Fields ◽  
Correlation Structure ◽  
Finite Variance ◽  
Infinitely Divisible ◽  
New Class ◽  
Joint Characteristic ◽  
Non Gaussian

We construct random fields with Pólya-type autocorrelation function and dampened Pólya cross-correlation function. The marginal distribution of the random fields may be taken as any infinitely divisible distribution with finite variance, and the random fields are fully characterized in terms of their joint characteristic function. This makes available a new class of non-Gaussian random fields with flexible correlation structure for use in modeling and estimation.

Learning for infinitely divisible GARCH models in option pricing

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Fumin Zhu ◽  
Michele Leonardo Bianchi ◽  
Young Shin Kim ◽  
Frank J. Fabozzi ◽  
Hengyu Wu
Keyword(s):  
Option Pricing ◽  
Stock Returns ◽  
Bayesian Learning ◽  
Space Structure ◽  
Estimation Methods ◽  
Garch Models ◽  
Learning Approaches ◽  
Infinitely Divisible ◽  
Asymmetric Garch ◽  
Non Gaussian

AbstractThis paper studies the option valuation problem of non-Gaussian and asymmetric GARCH models from a state-space structure perspective. Assuming innovations following an infinitely divisible distribution, we apply different estimation methods including filtering and learning approaches. We then investigate the performance in pricing S&P 500 index short-term options after obtaining a proper change of measure. We find that the sequential Bayesian learning approach (SBLA) significantly and robustly decreases the option pricing errors. Our theoretical and empirical findings also suggest that, when stock returns are non-Gaussian distributed, their innovations under the risk-neutral measure may present more non-normality, exhibit higher volatility, and have a stronger leverage effect than under the physical measure.

scholarly journals Robust Image Labeling Using Conditional Random Fields

2021 ◽  
Author(s):  
Maryam Nematollahi Arani
Keyword(s):  
Object Recognition ◽  
Mixture Models ◽  
Random Fields ◽  
Conditional Random Fields ◽  
Semantic Gap ◽  
Visual Features ◽  
Image Labeling ◽  
Low Level ◽  
Robust Image ◽  
High Level

Object recognition has become a central topic in computer vision applications such as image search, robotics and vehicle safety systems. However, it is a challenging task due to the limited discriminative power of low-level visual features in describing the considerably diverse range of high-level visual semantics of objects. Semantic gap between low-level visual features and high-level concepts are a bottleneck in most systems. New content analysis models need to be developed to bridge the semantic gap. In this thesis, algorithms based on conditional random fields (CRF) from the class of probabilistic graphical models are developed to tackle the problem of multiclass image labeling for object recognition. Image labeling assigns a specific semantic category from a predefined set of object classes to each pixel in the image. By well capturing spatial interactions of visual concepts, CRF modeling has proved to be a successful tool for image labeling. This thesis proposes novel approaches to empowering the CRF modeling for robust image labeling. Our primary contributions are twofold. To better represent feature distributions of CRF potentials, new feature functions based on generalized Gaussian mixture models (GGMM) are designed and their efficacy is investigated. Due to its shape parameter, GGMM can provide a proper fit to multi-modal and skewed distribution of data in nature images. The new model proves more successful than Gaussian and Laplacian mixture models. It also outperforms a deep neural network model on Corel imageset by 1% accuracy. Further in this thesis, we apply scene level contextual information to integrate global visual semantics of the image with pixel-wise dense inference of fully-connected CRF to preserve small objects of foreground classes and to make dense inference robust to initial misclassifications of the unary classifier. Proposed inference algorithm factorizes the joint probability of labeling configuration and image scene type to obtain prediction update equations for labeling individual image pixels and also the overall scene type of the image. The proposed context-based dense CRF model outperforms conventional dense CRF model by about 2% in terms of labeling accuracy on MSRC imageset and by 4% on SIFT Flow imageset. Also, the proposed model obtains the highest scene classification rate of 86% on MSRC dataset.

scholarly journals Cerebral cortex classification by conditional random fields applied to intraoperative thermal imaging

2016 ◽  
Vol 2 (1) ◽  
pp. 475-478
Author(s):  
Nico Hoffmann ◽  
Edmund Koch ◽  
Uwe Petersohn ◽  
Matthias Kirsch ◽  
Gerald Steiner
Keyword(s):  
Cerebral Cortex ◽  
Random Fields ◽  
Conditional Random Fields ◽  
Intraoperative Imaging ◽  
A Priori ◽  
Approaches To Learning ◽  
Time Frequency ◽  
Classification Framework ◽  
Preprocessing Technique ◽  
High Level

AbstractIntraoperative thermal neuroimaging is a novel intraoperative imaging technique for the characterization of perfusion disorders, neural activity and other pathological changes of the brain. It bases on the correlation of (sub-)cortical metabolism and perfusion with the emitted heat of the cortical surface. In order to minimize required computational resources and prevent unwanted artefacts in subsequent data analysis workflows foreground detection is a important preprocessing technique to differentiate pixels representing the cerebral cortex from background objects. We propose an efficient classification framework that integrates characteristic dynamic thermal behaviour into this classification task to include additional discriminative features. The first stage of our framework consists of learning this representation of characteristic thermal time-frequency behaviour. This representation models latent interconnections in the time-frequency domain that cover specific, yet a priori unknown, thermal properties of the cortex. In a second stage these features are then used to classify each pixel’s state with conditional random fields. We quantitatively evaluate several approaches to learning high-level features and their impact to the overall prediction accuracy. The introduction of high-level features leads to a significant accuracy improvement compared to a baseline classifier.

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