Gaussian Markov Random Field

Image segmentation is one of the essential problems in computer vision and image processing. It works by partitioning a digital image into multiple regions or sets. The increasing importance of image segmentation in multiple issues and applications has motivated the researchers to propose and improve algorithms that support image segmentation process. There are many methods for image segmentation. In this paper, we use thresholding technique with genetic algorithm to find optimal thresholds between the various objects and the background.

A method to reconstruct fields, source strengths and physical parameters based on Gaussian process regression is presented for the case where data are known to fulfill a given linear differential equation with localized sources. The approach is applicable to a wide range of data from physical measurements and numerical simulations. It is based on the well-known invariance of the Gaussian under linear operators, in particular differentiation. Instead of using a generic covariance function to represent data from an unknown field, the space of possible covariance functions is restricted to allow only Gaussian random fields that fulfill the homogeneous differential equation. The resulting tailored kernel functions lead to more reliable regression compared to using a generic kernel and makes some hyperparameters directly interpretable. For differential equations representing laws of physics such a choice limits realizations of random fields to physically possible solutions. Source terms ...

Summary The paper describes Bayesian analysis for agricultural field experiments, a topic that has received very little previous attention, despite a vast frequentist literature. Adoption of the Bayesian paradigm simplifies the interpretation of the results, especially in ranking and selection. Also, complex formulations can be analysed with comparative ease, by using Markov chain Monte Carlo methods. A key ingredient in the approach is the need for spatial representations of the unobserved fertility patterns. This is discussed in detail. Problems caused by outliers and by jumps in fertility are tackled via hierarchical t formulations that may find use in other contexts. The paper includes three analyses of variety trials for yield and one example involving binary data; none is entirely straightforward. Some comparisons with frequentist analyses are made.

Realistic and accurate reconstructions of past vegetation cover are necessary to study past environmental changes. This is important since the effects of human land-use changes (e.g. agriculture, deforestation and afforestation/reforestation) on biodiversity and climate are still under debate. Over the last decade, development, validation, and application of pollen-vegetation relationship models have made it possible to estimate plant abundance from fossil pollen data at both local and regional scales. In particular, the REVEALS model has been applied to produce datasets of past regional plant cover at 1 • spatial resolution at large subcontinental scales (North America, Europe, and China). However, such reconstructions are spatially discontinuous due to the discrete and irregular geographical distribution of sites (lakes and peat bogs) from which fossil pollen records have been produced. Therefore, spatial statistical models have been developed to create continuous maps of past plant cover using the REVEALS-based land cover estimates. In this paper, we present the first continuous time series of spatially complete maps of past plant cover across Europe during the Holocene (25 time windows covering the period from 11.7 k BP to present). We use a spatial-statistical model for compositional data to interpolate REVEALS-based estimates of three major land-cover types (LCTs), i.e., evergreen trees, summer-green trees and open land (grasses, herbs and low shrubs); producing spatially complete maps of the past coverage of these three LCTs. The spatial model uses four auxiliary data sets-latitude, longitude, elevation, and independent scenarios of past anthropogenic land-cover change based on per-capita land-use estimates ("standard" KK10 scenarios)-to improve model performance for areas with complex topography or few observations. We evaluate the resulting reconstructions for selected time windows using present day maps from the European Forest Institute, cross validate, and compare the results with earlier pollen-based spatially-continuous estimates for five selected time windows, i.e., 100 k BP, and 6.2-5.7 k BP. The evaluations suggest that the statistical model provides robust spatial reconstructions. From the maps we observe the broad change in the land-cover Githumbi et al. Continuous European Holocene Land-Cover Maps of Europe from dominance of naturally open land and persisting remnants of continental ice in the Early Holocene to a high fraction of forest cover in the Mid Holocene, and anthropogenic deforestation in the Late Holocene. The temporal and spatial continuity is relevant for land-use, land-cover, and climate research.

In this paper, we construct a hierarchical model for spatial compositional data, which is used to reconstruct past land-cover compositions (in terms of coniferous forest, broadleaved forest, and unforested/open land) for five time periods during the past 6 000 years over Europe. The model consists of a Gaussian Markov Random Field (GMRF) with Dirichlet observations. A block updated Markov chain Monte Carlo (MCMC), including an adaptive Metropolis adjusted Langevin step, is used to estimate model parameters. The sparse precision matrix in the GMRF provides computational advantages leading to a fast MCMC algorithm. Reconstructions are obtained by combining pollen-based estimates of vegetation cover at a limited number of locations with scenarios of past deforestation and output from a dynamic vegetation model. To evaluate uncertainties in the predictions a novel way of constructing joint confidence regions for the entire composition at each prediction location is proposed. The hierarchical model's ability to reconstruct past land cover is evaluated through cross validation for all time periods, and by comparing reconstructions for the recent past to a present day European forest map. The evaluation results are promising and the model is able to capture known structures in past land-cover compositions.

Estimating anthropogenic carbon release in north-western Europe during the Holoceneintegrating pollen-based land use reconstructions with a dynamic vegetation model. Abstract from PAGES Focus 4 Conference / Workshop "Towards a more accurate quantification of human-environment interactions in the past",

Context. One possible way to investigate the nature of the primordial power spectrum fluctuations is by investigating the statistical properties of the local maximum in the density fluctuation fields. Aims. In this work we present a study of the mean correlation function, ξ r , and the correlation function for high amplitude fluctuations (peakpeak correlation) in a slighlty non-Gaussian context. Methods. From the definition of the correlation excess, we compute the Gaussian two-point correlation function and, using an expansion in Generalized Hermite polynomials, we estimate the correlation of high density peaks in a non-Gaussian field with generic distribution and power spectrum. We also apply the results obtained to a scale-mixed distribution model, which correspond to a nearly Gaussian model. Results. The results reveal that, even for a small deviation from Gaussianity, we can expect high density peaks to be much more correlated than in a Gaussian field with the same power spectrum. In addition, the calculations reveal how the amplitude of the peaks in the fluctuations field is related to the existing correlations. Conclusions. Our results may be used as an additional tool to investigate the behavior of the N-point correlation function, to understand how non-Gaussian correlations affect the peak-peak statistics and extract more information about the statistics of the density field.

We analyze generalized Gaussian cat states obtained by superposing arbitrary Gaussian states, e.g., a coherent state and a squeezed state. The Wigner functions of such states exhibit the typical pair of Gaussian hills plus an interference term which presents a novel structure, as compared with the standard superposition of coherent states (degenerate case). We prove that, in any dimensions, the structure of the interference term is characterized by a particular quadratic form; in one degree of freedom the phase is hyperbolic. This phase-space structure survives the action of a thermal reservoir. We also discuss certain superpositions of mixed Gaussian states generated by conditional Gaussian operations or Kerr-type dynamics on thermal states.

A unified method is developed for simulating realizations of real-valued stationary Gaussian processes, vector processes, fields, and vector fields. The method has direct applications to earthquake engineering. Realizations of Gaussian processes and vector processes can be used to model seismic ground accelerations at single and multiple sites. Gaussian random fields can provide representations of the spatial variation of soil properties that need to be considered in earthquake engineering when dealing with systems extending over large areas such as pipeline systems. The proposed method involves parametric random models consisting of superpositions of deterministic functions of time or space with random amplitudes. The parametric models are based on the sampling theorem for random processes and generalizations of it for vector processes and random fields. The proposed simulation method is efficient and uses algorithms for generating realizations of random processes and fields that are similar to simulation techniques based on ARMA models.

We study the intersection points of a fixed planar curve Γ with the nodal set of a translationally invariant and isotropic Gaussian random field Ψ(r) and the zeros of its normal derivative across the curve. The intersection points form a discrete random process which is the object of this study. The field probability distribution function is completely specified by the correlation G(|rr ′ |) = Ψ(r)Ψ(r ′ ) . Given an arbitrary G(|rr ′ |), we compute the two point correlation function of the point process on the line, and derive other statistical measures (repulsion, rigidity) which characterize the short and long range correlations of the intersection points. We use these statistical measures to quantitatively characterize the complex patterns displayed by various kinds of nodal networks. We apply these statistics in particular to nodal patterns of random waves and of eigenfunctions of chaotic billiards. Of special interest is the observation that for monochromatic random waves, the number variance of the intersections with long straight segments grows like L ln L, as opposed to the linear growth predicted by the percolation model, which was successfully used to predict other long range nodal properties of that field.

A vector-valued homogeneous random field is said to be semibinary if its single-point marginal distribution is a sum of a singular distribution and a continuous one. In this paper, we present methods of numerical simulation of semibinary fields on the basis of the correlation structure and the marginal distribution. As an example we construct a combined model of cloud top height and optical thickness using satellite observations.

The incompressible smoothed particle hydrodynamics (ISPH) method with projection based pressure correction has been shown to be highly accurate and stable for internal flows. We have proposed a focused effort to optimize an efficient fluid solver using the incompressible smoothed particle hydrodynamics (ISPH) method for violent free-surface flows on offshore and coastal structures. In ISPH, previous benchmarks showed that the simulation costs are dominated by the neighbour searching algorithm and the pressure Poisson equation(PPE) solver. In parallelisation, a Hilbert space filling curve(HSFC) and the Zoltan package have been used to perform domain decomposition where preservation of the spatial locality is critical for the performance of neighbour searching The following list highlights the major developments: • The map kernel which provide the functionality of sending particles and their physical field data blocks to an appropriate partition have been rewritten and optimised with MPI one-sided communications and Zoltan distributed directory utility. The percentage of the map kernel is now reduced to less than 20% for those simulations with particles distributed evenly across the domain. For non-evenly distributed particles, using only non-empty cells will be part of future work.

We study sequential change-point detection when observations form a sequence of independent Gaussian random fields, and the change-point is the time at which a signal of known functional form involving a finite number of unknown parameters appears. Building on , which identifies in a simpler problem a detection procedure of Shiryayev-Roberts type that is asymptotically minimax up to terms that vanish as the false detection rate converges to zero, we compare easily computed approximations to the Shiryayev-Roberts detection procedure with similar approximations to CUSUM type procedures. Although the CUSUM type procedures are suboptimal, our studies indicate that they compare favorably to the asymptotically optimal procedures.

The PAGES LandCover6k working group focused on the reconstruction of the absolute cover of land-use categories and vegetation units over major regions of the globe and over the last 12,000 years, applicable to studies on land use as a climate forcing in the past.

This paper develops two techniques of oriented texture analysis: the modified Gabor filters (MGF) and the Gaussian Markov random field model with circular neighborhoods (CGMRF). The neighborhood-oscillating tabu search algorithm (NOTS) is proposed to solve the MGF/CGMRP feature fusion problem, and compared with classical algorithms, such as sequential forward selection and sequential forward floating selection methods. Based on the experimental results, NOTS is shown to be a promising tool for feature fusion, and the MGF/CGMRF fused features achieved by NOTS perform better than either MGF or CGMRP alone according to the Fisher criterion and classification accuracy.

This paper reports our findings on the return dynamics of Bitcoin and Ethereum using high-frequency data (minute-by-minute observations) from 2015 to 2022 for Bitcoin and from 2016 to 2022 for Ethereum. The main objective of modeling these two series was to obtain a dynamic estimation of risk premium with the intention of characterizing its behavior. To this end, we estimated the Generalized Autoregressive Conditional Heteroskedasticity in Mean with Normal-Inverse Gaussian distribution (GARCH-M-NIG) model for the residuals. We also estimated the other parameters of the model and discussed their evolution over time, including the skewness and kurtosis of the Normal-Inverse Gaussian distribution. Similarly, we determined the parameters that define the evolution of the estimated variance, i.e., the parameters related to the fitted past variance, square error and long-term average value. We found that, despite the market uncertainty during the COVID-19 emergency period (2020 and 2021), ...

We consider the contribution of 3rd and 4th order terms to the power spectrum of 21 cm brightness temperature fluctuations during the epoch of reionization (EoR), which arise because the 21 cm brightness temperature involves a product of the hydrogenic neutral fraction and the gas density. The 3rd order terms vanish for Gaussian random fields, and have been previously neglected or ignored. We measure these higher order terms from radiative transfer simulations and estimate them using cosmological perturbation theory. In our simulated models, the higher order terms are significant: neglecting them leads to a 100% error in 21 cm power spectrum predictions on scales of k 1 h Mpc -1 when the neutral fraction is x H ∼ 0.5. At later stages of reionization, when the ionized regions are bigger, the higher order terms impact 21 cm power spectrum predictions on still larger scales, while they are less important earlier during reionization. The higher order terms have a simple physical interpretation. On small scales they are produced by gravitational mode coupling. Small scale structure grows more readily in large-scale overdense regions, but the same regions tend to be ionized and hence do not contribute to the 21 cm signal. This acts to suppress the influence of non-linear density fluctuations and the small-scale amplitude of the 21 cm power spectrum. In alternate models, where the voids are reionized before over-dense regions ('outside-in' reionization), the effect should have the opposite sign, and lead to an enhancement in the 21 cm power spectrum. These results modify earlier intuition that the 21 cm power spectrum simply traces the density power spectrum on scales smaller than that of a typical bubble, and imply that small scale measurements contain more information about the nature of the ionizing sources than previously believed. On large scales, higher order moments are not directly related to gravity. They are non-zero because over-dense regions tend to ionize first and are important in magnitude at late times owing to the large fluctuations in the neutral fraction. Finally, we show that 2nd order Lagrangian perturbation theory approximately reproduces the statistics of the density field from full numerical simulations for all redshifts and scales of interest, including the mode-coupling effects mentioned above. It can, therefore, be used in conjunction with semi-analytic models to accurately, and rapidly, explore the broad regions of parameter space relevant for future 21 cm surveys.

When a random field (X t , t ∈ R 2 ) is thresholded on a given level u, the excursion set is given by its indicator 1 [u,∞) (X t ). The purpose of this work is to study functionals (as established in stochastic geometry) of these random excursion sets, as e.g. the capacity functional as well as the second moment measure of the boundary length. It extends results obtained for the one-dimensional case to the two-dimensional case, with tools borrowed from crossings theory, in particular Rice methods, and from integral and stochastic geometry.

This paper presents a new approach to the estimation of the deformation of an isotropic Gaussian random field on R 2 based on dense observations of a single realization of the deformed random field. Under this framework we investigate the identification and estimation of deformations. We then present a complete methodological package-from model assumptions to algorithmic recovery of the deformation-for the class of nonstationary processes obtained by deforming isotropic Gaussian random fields.

Pseudogap physics in strongly correlated systems is essentially scale dependent. We generalize the dynamical-mean field theory (DMFT) by including into the DMFT equations dependence on correlation length of pseudogap fluctuations via additional (momentum dependent) self-energy Σ k . This self -energy describes non-local dynamical correlations induced by short-ranged collective SDW-like antiferromagnetic spin (or CDW-like charge) fluctuations. At high enough temperatures these fluctuations can be viewed as a quenched Gaussian random field with finite correlation length. This generalized DMFT+Σ k approach is used for the numerical solution of the weakly doped oneband Hubbard model with repulsive Coulomb interaction on a square lattice with nearest and next nearest neighbour hopping. The effective single impurity problem is solved by numerical renormalization group (NRG). Both types of strongly correlated metals, namely (i) doped Mott insulator and (ii) the case of bandwidth W U (U -value of local Coulomb interaction) are considered. Densities of states, spectral functions and ARPES spectra calculated within DMFT+Σ k show a pseudogap formation near the Fermi level of the quasiparticle band. We also briefly discuss effects of random impurity scattering. Finally we demonstrate the qualitative picture of Fermi surface "destruction" due to pseudogap fluctuations and formation of "Fermi arcs" which agrees well with ARPES observations.

Motivated by the problem of testing for the existence of a signal of known parametric structure and unknown "location" (as explained below) against a noisy background, we obtain for the maximum of a centered, smooth random field an approximation for the tail of the distribution. For the motivating class of problems this gives approximately the significance level of the maximum score test. The method is based on an application of a likelihood-ratio-identity followed by approximations of local fields. Numerical examples illustrate the accuracy of the approximations.

The skeleton formalism, which aims at extracting and quantifying the filamentary structure of our Universe, is generalized to 3D density fields. A numerical method for computing a local approximation of the skeleton is presented and validated here on Gaussian random fields. It involves solving equation (H∇ρ × ∇ρ) = 0, where ∇ρ and H are the gradient and Hessian matrix of the field. This method traces well the filamentary structure in 3D fields such as those produced by numerical simulations of the dark matter distribution on large scales, and is insensitive to monotonic biasing. Two of its characteristics, namely its length and differential length, are analysed for Gaussian random fields. Its differential length per unit normalized density contrast scales like the probability distribution function of the underlying density contrast times the total length times a quadratic Edgeworth correction involving the square of the spectral parameter. The total length-scales like the inverse square smoothing length, with a scaling factor given by 0.21 (5.28 + n) where n is the power index of the underlying field. This dependency implies that the total length can be used to constrain the shape of the underlying power spectrum, hence the cosmology. Possible applications of the skeleton to galaxy formation and cosmology are discussed. As an illustration, the orientation of the spin of dark haloes and the orientation of the flow near the skeleton is computed for cosmological dark matter simulations. The flow is laminar along the filaments, while spins of dark haloes within 500 kpc of the skeleton are preferentially orthogonal to the direction of the flow at a level of 25 per cent.

Estimating anthropogenic carbon release in north-western Europe during the Holoceneintegrating pollen-based land use reconstructions with a dynamic vegetation model. Abstract from PAGES Focus 4 Conference / Workshop "Towards a more accurate quantification of human-environment interactions in the past",

Context. The imprint of baryonic acoustic oscillations (BAO) on the matter power spectrum can be constrained using the neutral hydrogen density in the intergalactic medium (IGM) as a tracer of the matter density. One of the goals of the baryon oscillation spectroscopic survey (BOSS) of the Sloan Digital Sky Survey (SDSS-III) is to derive the Hubble expansion rate and the angular scale from the BAO signal in the IGM. To this aim, the Lyman-α forest about 150 000 quasars will be observed in the redshift range 2.2 < z < 3.5 and over ∼10 000 deg 2 . Aims. We simulated the BOSS QSO survey to estimate the statistical accuracy on the BAO scale determination provided by such a large-scale survey. In particular, we discuss the effect of the poorly constrained estimate of the quasar's unabsorbed intrinsic spectrum. Methods. The volume of current N-body simulations being too small for such studies, we resorted to Gaussian random field (GRF) simulations. We validated the use of GRFs by comparing the output of GRF simulations with that of the Horizon-4Π N-body darkmatter-only simulation with the same initial conditions. Realistic mock samples of QSO Lyman-α forest were generated and their power spectrum computed and fitted to obtain the BAO scale. The rms of the results for 100 different simulations provides an estimate of the statistical error expected from the BOSS survey. Results. We confirm the results from the Fisher matrix estimate. In the absence of error on the quasar's unabsorbed spectrum, our simulations give an expected uncertainty of 2.3% for the BOSS quasar survey measurement of the BAO scale. The expected uncertainties for the transverse and radial BAO scales are 6.8% and 3.9%, respectively. The significance of the BAO detection is assessed by an average Δχ 2 = 17 but Δχ 2 ranges from 2 to 35 for individual realizations. The error on the quasar's unabsorbed spectrum increases the error on the BAO scale by 10 to 20% and results in a subpercent bias.

Aucunhis thesis is a contribution to the statistical modeling of the index of extreme values ​​in the univariate framework. It aims to propose a generalization of Hill&#39;s estimator (1975). For this, we are interested in the study of a new functional statistics.This stochastic process Tn (f, s) is such that each of its margins is an estimator of the extremal index (PSMEI). It allows to study the consecutive spacings of the order statistics of the random variable Y = logX.The asymptotic theory of this PSMEI process reveals Gaussian and non-Gaussian boundary laws. The study of the optimal variance of the family of Gaussian estimators allowed us to discover an efficient and very stable estimator of the extremal index when the two parameters f and s are equal, with a sufficiently weak bias.To this doubly indexed stochastic process Tn (f, s) is added a complete study of the mathematical theory of extreme values ​​in the framework of the theory of vague convergence.Cette thèse est une c...

This paper studies the problem of equivalence of Gaussian measures induced by Gaussian random fields (GRFs) with stationary increments and proves a sufficient condition for the equivalence in terms of the behavior of the spectral measures at infinity. The main results extend those of and are applicable to a rich family of nonstationary space-time models with possible anisotropy behavior.

Let {X(t) = (X1(t), X2(t)) T , t ∈ R N } be an R 2 -valued continuous locally stationary Gaussian random field with E[X(t)] = 0. For any compact sets A1, A2 ⊂ R N , precise asymptotic behavior of the excursion probability is investigated by applying the double sum method. The explicit results depend not only on the smoothness parameters of the coordinate fields X1 and X2, but also on their maximum correlation ρ.

We confirm Flandrin's prediction for the expected average of local maxima of spectrograms of complex white noise with Gaussian windows (Gaussian spectrograms or, equivalently, modulus of weighted Gaussian Entire Functions), a consequence of the conjectured double honeycomb mean model for the network of zeros and local maxima, where the area of local maxima centered hexagons is three times larger than the area of zero centered hexagons. More precisely, we show that Gaussian spectrograms, normalized such that their expected density of zeros is 1, have an expected density of 5/3 critical points, among those 1/3 are local maxima, and 4/3 saddle points, and compute the distributions of ordinate values (heights) for spectrogram local extrema. This is done by first writing the spectrograms in terms of Gaussian Entire Functions (GEFs). The extrema are considered under the translation invariant derivative of the Fock space (which in this case coincides with the Chern connection from complex differential geometry). We also observe that the critical points of a GEF are precisely the zeros of a Gaussian random function in the first higher Landau level. We discuss natural extensions of these Gaussian random functions: Gaussian Weyl-Heisenberg functions and Gaussian bi-entire functions. The paper also reviews recent results on the applications of white noise spectrograms, connections between several developments, and is partially intended as a pedestrian introduction to the topic.

In this paper, we determine the upper and lower bounds for the norm of lower triangular matrix operators on Cesàro weighted (p, v)-fractional difference sequence spaces of modulus functions. We consider the matrix operators acting between ℓp(w) and Cp(v, ω, ∆ (η,ℓ) , F) and identify their bounds and vice-versa. We also investigate the same characteristics for Nörlund and weighted mean matrix operators.

We consider a class of stochastic processes X defined by X (t) = T 0 G (t, s) dM (s) for t ∈ [0, T ], where M is a square-integrable continuous martingale and G is a deterministic kernel. Let m be an odd integer. Under the assumption that the quadratic variation m exists and is zero when a quantity δ 2 (r) related to the variance of an increment of M over a small interval of length r satisfies δ (r) = o r 1/(2m) . When M is the Wiener process, X is Gaussian; the class then includes fractional Brownian motion and other Gaussian processes with or without stationary increments. When X is Gaussian and has stationary increments, δ is X's univariate canonical metric, and the condition on δ is proved to be necessary. In the non-stationary Gaussian case, when m = 3, the symmetric (generalized Stratonovich) integral is defined, proved to exist, and its Itô formula is established for all functions of class C 6 .

In this paper, we present an algorithm for the problem of multi-channel blind deconvolution which can adapt to un-known sources with both sub-Gaussian and super-Gaussian probability density distributions using a generalized gaussian source model. We use a state space representation to model the mixer and demixer respectively, and show how the parameters of the demixer can be adapted using a gradient descent algorithm incorporating the natural gradient extension. We also present a learning method for the unknown parameters of the generalized Gaussian source model. The performance of the proposed generalized Gaussian source model on a typical example is compared with those of other algorithm, viz the switching nonlinearity algorithm proposed by Lee et al. [8].

We study the local times of a large class of Gaussian random fields satisfying strong local nondeterminism with respect to an anisotropic metric. We establish moment estimates and Hölder conditions for the local times of the Gaussian random fields. Our key estimates rely on geometric properties of Voronoi partitions with respect to an anisotropic metric and the use of Besicovitch's covering theorem. As a consequence, we deduce sample path properties of the Gaussian random fields that are related to Chung's law of the iterated logarithm and modulus of non-differentiability. Moreover, we apply our results to systems of stochastic heat equations with additive Gaussian noise and determine the exact Hausdorff measure function with respect to the parabolic metric for the level sets of the solutions.

This paper is concerned with the existence of multiple points of Gaussian random fields. Under the framework of , we prove that, for a wide class of Gaussian random fields, multiple points do not exist in critical dimensions. The result is applicable to fractional Brownian sheets and the solutions of systems of stochastic heat and wave equations.

This paper is concerned with the existence of multiple points of Gaussian random fields. Under the framework of , we prove that, for a wide class of Gaussian random fields, multiple points do not exist in critical dimensions. The result is applicable to fractional Brownian sheets and the solutions of systems of stochastic heat and wave equations.

The intensity statistics of signals in the presence of Gaussian noise is obtained by studying the model of a random signal plus a random phasor sum. The additive Gaussian noise is shown to result in a Bessel transform of the probability density of the signal intensity. The transformation of the intensity statistics can generally be applied to a mixture of independent random signals, one of which being a complex-valued Gaussian random process. It is used to retrieve intensity statistics of microwave pulsed transmission from Gaussian noise at long time delays.

O foco deste trabalho esta na aplicacao de modelos inovadores para a analise espacotemporal da biomassa de anchova em um grande banco de dados e no desenvolvimento de um novo campo aleatorio Gaussiano adequado para a analise de grandes conjuntos de dados. O primeiro artigo apresenta uma aplicacao avancada da modelagem espaco-temporal atraves da Equacao Diferencial Parcial Estocastica (SPDE) para estimar e prever a biomassa de anchova na costa do Peru. Foi introduzido um modelo espaco-temporal hierarquico Bayesiano completo, levando em consideracao as possiveis dependencias espaciais ou espaco-temporais dos dados. Estes modelos, computacionalmente eficientes e flexiveis, sao tambem capazes de realizar previsoes tanto da presenca quanto da abundância de anchovas, em particular, quando o conjunto de locais e grande (&gt; 500) e diferente ao longo do tempo. Eles sao baseados em que os campos Gaussianos Matern podem ser vistos como solucoes de uma determinada SPDE que, em combinacao com ...