A kernel-based spectral model for non-Gaussian spatio-temporal processes

2002 ◽  
Vol 2 (4) ◽  
pp. 299-314 ◽  
Author(s):  
Christopher K Wikle
Keyword(s):  
Spectral Model ◽  
Spatio Temporal ◽  
Non Gaussian

scholarly journals Learning on dynamic statistical manifolds

2020 ◽  
Vol 476 (2239) ◽  
pp. 20200213 ◽  
Author(s):  
F. Boso ◽  
D. M. Tartakovsky
Keyword(s):  
Loss Function ◽  
Uncertainty Propagation ◽  
Cumulative Distribution ◽  
Computationally Efficient ◽  
Random System ◽  
Statistical Manifolds ◽  
Hyperbolic Balance Laws ◽  
Leibler Divergence ◽  
Spatio Temporal ◽  
Non Gaussian

Hyperbolic balance laws with uncertain (random) parameters and inputs are ubiquitous in science and engineering. Quantification of uncertainty in predictions derived from such laws, and reduction of predictive uncertainty via data assimilation, remain an open challenge. That is due to nonlinearity of governing equations, whose solutions are highly non-Gaussian and often discontinuous. To ameliorate these issues in a computationally efficient way, we use the method of distributions, which here takes the form of a deterministic equation for spatio-temporal evolution of the cumulative distribution function (CDF) of the random system state, as a means of forward uncertainty propagation. Uncertainty reduction is achieved by recasting the standard loss function, i.e. discrepancy between observations and model predictions, in distributional terms. This step exploits the equivalence between minimization of the square error discrepancy and the Kullback–Leibler divergence. The loss function is regularized by adding a Lagrangian constraint enforcing fulfilment of the CDF equation. Minimization is performed sequentially, progressively updating the parameters of the CDF equation as more measurements are assimilated.

scholarly journals A Non‐Gaussian Spatio‐Temporal Model for Daily Wind Speeds Based on a Multi‐Variate Skew‐ t Distribution

2018 ◽  
Vol 40 (3) ◽  
pp. 312-326 ◽  
Author(s):  
Felipe Tagle ◽  
Stefano Castruccio ◽  
Paola Crippa ◽  
Marc G. Genton
Keyword(s):  
Wind Speeds ◽  
Temporal Model ◽  
Spatio Temporal ◽  
Non Gaussian ◽  
T Distribution

scholarly journals Bounds on the Sum-Rate of MIMO Causal Source Coding Systems with Memory under Spatio-Temporal Distortion Constraints

Entropy ◽  
2020 ◽  
Vol 22 (8) ◽  
pp. 842
Author(s):  
Photios A. Stavrou ◽  
Jan Østergaard ◽  
Mikael Skoglund
Keyword(s):  
Gaussian Noise ◽  
Rate Distortion ◽  
Source Model ◽  
Upper Bounds ◽  
Optimal Test ◽  
Test Channel ◽  
Noise Process ◽  
Channel Realization ◽  
Spatio Temporal ◽  
Non Gaussian

In this paper, we derive lower and upper bounds on the OPTA of a two-user multi-input multi-output (MIMO) causal encoding and causal decoding problem. Each user’s source model is described by a multidimensional Markov source driven by additive i.i.d. noise process subject to three classes of spatio-temporal distortion constraints. To characterize the lower bounds, we use state augmentation techniques and a data processing theorem, which recovers a variant of rate distortion function as an information measure known in the literature as nonanticipatory ϵ-entropy, sequential or nonanticipative RDF. We derive lower bound characterizations for a system driven by an i.i.d. Gaussian noise process, which we solve using the SDP algorithm for all three classes of distortion constraints. We obtain closed form solutions when the system’s noise is possibly non-Gaussian for both users and when only one of the users is described by a source model driven by a Gaussian noise process. To obtain the upper bounds, we use the best linear forward test channel realization that corresponds to the optimal test channel realization when the system is driven by a Gaussian noise process and apply a sequential causal DPCM-based scheme with a feedback loop followed by a scaled ECDQ scheme that leads to upper bounds with certain performance guarantees. Then, we use the linear forward test channel as a benchmark to obtain upper bounds on the OPTA, when the system is driven by an additive i.i.d. non-Gaussian noise process. We support our framework with various simulation studies.

scholarly journals Toward an assessment of the hydrological components variability in green infrastructures: Pilot site of the Green Wave (Champs-sur-Marne)

2018 ◽  
pp. 34-42 ◽  
Author(s):  
Pierre-Antoine Versini ◽  
Auguste Gires ◽  
George Fitton ◽  
Ioulia Tchiguirinskaia ◽  
Daniel Schertzer
Keyword(s):  
Temporal Variability ◽  
Continuous Monitoring ◽  
Specific Model ◽  
Interesting Case ◽  
Pilot Site ◽  
Spatio Temporal ◽  
Non Gaussian ◽  
Measurement Campaigns ◽  
Velocity Water

The Green Wave (GW) site is located in the heart of the Paris-East Cluster for Science and Technology (Champs-sur-Marne, France). Initially designed on aesthetic criteria, this large wavy-form vegetated roof (1 ha) is a particularly interesting case study regarding hydrological and thermic issues. Since 2013, several measurement campaigns have been conducted during the Blue Green Dream project to investigate and better understand its hydrological behaviour. Rainfall, humidity, wind velocity, water content and temperature have been particularly studied. The data collected have been used to study the spatio-temporal variability of these variables. Results have shown they are all characterized by a non-gaussian distribution and a scaling behaviour. These results have justified the implementation of a continuous monitoring of the GW. It will serve to develop a specific model simulating its hydrological behaviour and able to assess green roof performances.

scholarly journals Data Assimilation in Spatio-Temporal Models with Non-Gaussian Initial States—The Selection Ensemble Kalman Model

2020 ◽  
Vol 10 (17) ◽  
pp. 5742
Author(s):  
Maxime Conjard ◽  
Henning Omre
Keyword(s):  
Posterior Distribution ◽  
Prior Distribution ◽  
Temporal Data ◽  
Initial State ◽  
Gaussian Distributions ◽  
Temporal Models ◽  
Parameter Field ◽  
Spatio Temporal ◽  
Non Gaussian

Assimilation of spatio-temporal data poses a challenge when allowing non-Gaussian features in the prior distribution. It becomes even more complex with nonlinear forward and likelihood models. The ensemble Kalman model and its many variants have proven resilient when handling nonlinearity. However, owing to the linearized updates, conserving the non-Gaussian features in the posterior distribution remains an issue. When the prior model is chosen in the class of selection-Gaussian distributions, the selection Ensemble Kalman model provides an approach that conserves non-Gaussianity in the posterior distribution. The synthetic case study features the prediction of a parameter field and the inversion of an initial state for the diffusion equation. By using the selection Kalman model, it is possible to represent multimodality in the posterior model while offering a 20 to 30% reduction in root mean square error relative to the traditional ensemble Kalman model.

DYNAMICS AND UNIVERSALITY OF AN ISOTHERMAL COMBUSTION PROBLEM IN 2D

2006 ◽  
Vol 18 (03) ◽  
pp. 285-310 ◽  
Author(s):  
Y. W. QI
Keyword(s):  
Lewis Number ◽  
Large Time Behavior ◽  
Nonlinear Pdes ◽  
Regularity Of Solutions ◽  
Group Method ◽  
Time Behavior ◽  
The Cauchy Problem ◽  
Spatio Temporal ◽  
Non Gaussian ◽  
Isothermal Combustion

In this paper, the Cauchy problem of the system [Formula: see text] is studied, where x ∈ R2, m ≥ 1 and d > 0 is the Lewis number. This system models isothermal combustion (see [7]), and auto-catalytic chemical reaction. We show the global existence and regularity of solutions with non-negative initial values having mild decay as |x| → ∞. More importantly, we establish the exact spatio-temporal profiles for such solutions. In particular, we prove that for m = 1, the exact large time behavior of solutions is characterized by a universal, non-Gaussian spatio-temporal profile, with anomalous exponents, due to the fact that quadratic nonlinearity is critical in 2D. Our approach is a combination of iteration using Renormalization Group method, which has been developed into a very powerful tool in the study of nonlinear PDEs largely by the pioneering works of Bricmont, Kupiainen and Lin [6], Bricmont, Kupiainen and Xin, [7], (see also [9]) and key estimates using the PDE method.

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