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Research on particle filters has been progressing with the aim of applying them to high-dimensional systems, but alleviation of problems with ensemble Kalman filters (EnKFs) in nonlinear or non-Gaussian data assimilation is also an important issue. It is known that the deterministic EnKF is less robust than the stochastic EnKF in strongly nonlinear regimes. We prove that if the observation operator is linear the analysis ensemble perturbations of the local ensemble transform Kalman filter (LETKF) are uniform contractions of the forecast ensemble perturbations in observation space in each direction of the eigenvectors of a forecast error covariance matrix. This property approximately holds for a weakly nonlinear observation operator. These results imply that if the forecast ensemble is strongly non-Gaussian the analysis ensemble of the LETKF is also strongly non-Gaussian, and that strong non-Gaussianity therefore tends to persist in high-frequency assimilation cycles, leading to the degradation of analysis accuracy in nonlinear data assimilation. A hybrid EnKF that combines the LETKF and the stochastic EnKF is proposed to mitigate non-Gaussianity in nonlinear data assimilation with small additional computational cost. The performance of the hybrid EnKF is investigated through data assimilation experiments using a 40- variable Lorenz-96 model. Results indicate that the hybrid EnKF significantly improves analysis accuracy in high-frequency data assimilation with a nonlinear observation operator. The positive impact of the hybrid EnKF increases with the increase of the ensemble size. [ABSTRACT FROM AUTHOR]

Analysis of the criticality in finance and economics is an important topic for scholars. The crises are conditions in which unpredictable behavior have been emerged. On the other hand, the contagion from one market to another one due to the complex nature of them is a crucial concept. Therefore, we should consider economies and financial markets as entangled systems that interact with each other, and studying one’s behavior without considering its interacting structures will not provide us with adequate information. In this paper, we have considered the critical states of some emerging and mature markets’ indices. S&P500 and Nikkei 225 as representatives of mature markets, and SSE Composite and TEDPIX as representatives of emerging markets have been analyzed. Coupled criticality emerges when two interacting systems reach their critical state due to their interactions. One of the efficient methods to study the coupled criticality is the bi-variate multifractal random walk model. This method is useful to assess the correlation of rare events and coupled criticality in entangled systems such as financial markets. The observations in this paper show that TEDPIX and S&P500 have higher critical states among others in most time lags by assessing criticality parameter explained in the model, and in longer time lags criticality parameter decreases in all indices. Coupled criticality parameter explained in the model is assessed between each index mentioned and TEDPIX. Results show that TEDPIX and S&P500 have the highest level of coupled criticality. To figure out how long-range time correlation between rare events in each index affect its critical behavior, the data of each index are shuffled, and the criticality parameter is calculated for the shuffled data. From the observations, it can be concluded that this matter has more substantial effect on mature markets. As it is known, shuffling removes the effect of the long-range time correlations. Therefore, the coupled criticality parameter is calculated for the shuffled S&P500 data and TEDPIX. Results show that the long-range correlation of S&P500 data has a significant effect on the coupled criticality behavior of S&P500 and TEDPIX. [ABSTRACT FROM AUTHOR]

Features in the inflationary landscape can inject extra energies to inflation models and produce on-shell particles with masses much larger than the Hubble scale of inflation. This possibility extends the energy reach of the program of cosmological collider physics, in which signals associated with these particles are generically Boltzmann-suppressed. We study the mechanisms of this classical cosmological collider in two categories of primordial features. In the first category, the primordial feature is classical oscillation, which includes the case of coherent oscillation of a massive field and the case of oscillatory features in the inflationary potential. The second category includes any sharp feature in the inflation model. All these classical features can excite unsuppressed quantum modes of other heavy fields which leave observational signatures in primordial non-Gaussianities, including the information about the particle spectra of these heavy degrees of freedom.

Gravitational coupling between large- and small-scale density perturbations leads to anisotropic distortions to local small-scale matter fluctuations. Such local anisotropic distortions can be used to reconstruct large-scale matter distribution, known as tidal reconstruction. In this paper, we apply the tidal reconstruction methods to simulated galaxies in redshift space. We find that redshift-space distortions (RSDs) lead to anisotropic reconstruction results. While the reconstructed radial modes are more noisy mainly due to the small-scale velocity dispersion, the transverse modes are still reconstructed with high fidelity, and well correlated with the original large-scale density modes. The bias of the reconstructed field at large scales shows a simple angular dependence, which can be described by a form similar to that of the linear RSD. The noise power spectrum is nearly isotropic and scale independent on large scales. This makes the reconstructed tide fields an ideal tracer for cosmic variance cancellation and multi-tracer analysis and has profound implications for future 21 cm intensity mapping surveys. [ABSTRACT FROM AUTHOR]

This paper introduces a non-Gaussian dynamic currency hedging strategy for globally diversified investors with ambiguity. It provides theoretical and empirical evidence that, under the stylized fact of non-Gaussianity of financial returns and for a given optimal portfolio, the investor-specific ambiguity can be estimated from historical asset returns without the need for additional exogenous information. Acknowledging non-Gaussianity, we compute an optimal ambiguity-adjusted mean-variance (dynamic) currency allocation. Next, we propose an extended filtered historical simulation that combines Monte Carlo simulation based on volatility clustering patterns with the semi-parametric non-normal return distribution from historical data. This simulation allows us to incorporate investor's ambiguity into a dynamic currency hedging strategy algorithm that can numerically optimize an arbitrary risk measure, such as the expected shortfall. The out-of-sample backtest demonstrates that, for globally diversified investors, the derived non-Gaussian dynamic currency hedging strategy is stable, robust, and highly risk reductive. It outperforms the benchmarks of constant hedging as well as static/dynamic hedging approaches with Gaussianity in terms of lower maximum drawdown and higher Sharpe and Sortino ratios, net of transaction costs. [ABSTRACT FROM AUTHOR]

An old problem in multivariate statistics is that linear Gaussian models are often unidentifiable. In factor analysis, an orthogonal rotation of the factors is unidentifiable, while in linear regression, the direction of effect cannot be identified. For such linear models, non-Gaussianity of the (latent) variables has been shown to provide identifiability. In the case of factor analysis, this leads to independent component analysis, while in the case of the direction of effect, non-Gaussian versions of structural equation modeling solve the problem. More recently, we have shown how even general nonparametric nonlinear versions of such models can be estimated. Non-Gaussianity is not enough in this case, but assuming we have time series, or that the distributions are suitably modulated by observed auxiliary variables, the models are identifiable. This paper reviews the identifiability theory for the linear and nonlinear cases, considering both factor analytic and structural equation models. [ABSTRACT FROM AUTHOR]

Nonlinear gravitational evolution induces strong nonlinearities in the observed cosmological density fields, leading to positive off-diagonal correlations in the power spectrum covariance. This has caused the information saturation in the power spectrum, e.g., the neutrino mass constraints from the nonlinear power spectra are lower than their linear counterparts by a factor of ∼2 at z = 0. In this paper, we explore how nonlinear reconstruction methods improve the cosmological information from nonlinear cosmic fields. By applying nonlinear reconstruction to cold dark matter fields from the Quijote simulations, we find that nonlinear reconstruction can improve the constraints on cosmological parameters significantly, nearly reaching the linear theory limit. For neutrino mass, the result is only 12% lower than the linear power spectrum, i.e., the theoretical best result. This makes nonlinear reconstruction an efficient and useful method to extract neutrino information from current and upcoming galaxy surveys. [ABSTRACT FROM AUTHOR]

While causes and consequences of uncertainty in the US economy have attracted viable interest, the literature still lacks a consensus on several aspects. To name two matters of debate, it remains unclear whether uncertainty shocks are a source or the result of recessions and whether uncertainty shocks have adverse (or even stimulating) effects on the economy. We find that ambiguous results in these regards can be traced back to the selection of an appropriate identification strategy in structural vector autoregressive models. We find that both macroeconomic and financial uncertainty are exogenous to business cycle fluctuations and cause economic slowdowns. [ABSTRACT FROM AUTHOR]

Multivariate functional data arise in a wide range of applications. One fundamental task is to understand the causal relationships among these functional objects of interest. In this paper, we develop a novel Bayesian network (BN) model for multivariate functional data where conditional independencies and causal structure are encoded by a directed acyclic graph. Specifically, we allow the functional objects to deviate from Gaussian processes, which is the key to unique causal structure identification even when the functions are measured with noises. A fully Bayesian framework is designed to infer the functional BN model with natural uncertainty quantification through posterior summaries. Simulation studies and real data examples demonstrate the practical utility of the proposed model. [ABSTRACT FROM AUTHOR]

We study the non-minimal inflation with both the large field and small field potentials in the context of the new observational data. We analyze the linear and non-linear perturbations to obtain the scalar spectral index, tensor-to-scalar ratio, and nonlinearity parameter. By performing a numerical analysis on the scalar spectral index and tensor-to-scalar ratio, and comparing the results with Planck2018 TT, TE, EE+lowE+lensing+BAO+BK14(18) data, we find that the non-minimal large field inflation is observationally viable if the non-minimal coupling parameter is of the order of 10-3. The same analysis on the non-minimal small field inflation gives the values for the non-minimal coupling parameter as 10-4. We also study the non-Gaussian features in both equilateral and orthogonal configurations for large and small field potentials and find small values for these amplitudes, consistent with Planck2018 TTT, EEE, TTE and EET data. We show that the absolute values of the non-linearity parameter, fNL, is larger in large field inflation than the small field model for both configurations. Also, we obtain more severe constraints on the parameter p in the introduced large field and small field potentials with respect to previously reported constraints. [ABSTRACT FROM AUTHOR]

The complex interplay of magnetohydrodynamics, gravity, and supersonic turbulence in the interstellar medium (ISM) introduces a non-Gaussian structure that can complicate a comparison between theory and observation. In this paper, we show that the wavelet scattering transform (WST), in combination with linear discriminant analysis (LDA), is sensitive to non-Gaussian structure in 2D ISM dust maps. WST-LDA classifies magnetohydrodynamic (MHD) turbulence simulations with up to a 97% true positive rate in our testbed of 8 simulations with varying sonic and Alfvénic Mach numbers. We present a side-by-side comparison with two other methods for non-Gaussian characterization, the reduced wavelet scattering transform (RWST) and the three-point correlation function (3PCF). We also demonstrate the 3D-WST-LDA, and apply it to the classification of density fields in position-position-velocity (PPV) space, where density correlations can be studied using velocity coherence as a proxy. WST-LDA is robust to common observational artifacts, such as striping and missing data, while also being sensitive enough to extract the net magnetic field direction for sub-Alfvénic turbulent density fields. We include a brief analysis of the effect of point-spread functions and image pixelization on 2D-WST-LDA applied to density fields, which informs the future goal of applying WST-LDA to 2D or 3D all-sky dust maps to extract hydrodynamic parameters of interest.

In this article, on the basis of the Langevin equation applied to velocity fluctuations, we numerically model the partial variance of increments, which is a useful tool to measure time and spatial correlations in space plasmas. We consider a coupled map lattice model to relate the spatial scale of fluctuations, k, to some macro parameters of the systems, such as the Reynolds number, R λ , the κ parameter of Kappa distributions, and a skewness parameter, δ. To do so, we compute the velocity probability density function (pdf) for each spatial scale and different values of Reynolds number in the simulations. We fit the pdf with a Skew–Kappa distribution, and we obtain a numerical relationship between the level of turbulence of the plasma and the skewness of obtained distributions, namely, 〈 δ 〉 ∼ R λ − 1 / 2 . We expect the results exposed in this paper to be useful as a tool to characterize the turbulence in the context of space plasma and other environments. [ABSTRACT FROM AUTHOR]

We analyse the transport of diffusive particles that switch between mobile and immobile states with finite rates. We focus on the effect of advection on the density functions and mean squared displacements (MSDs). At relevant intermediate time scales we find strong anomalous diffusion with cubic scaling in time of the MSD for high Péclet numbers. The cubic scaling exists for short and long mean residence times in the immobile state τ i m . For long τ i m the plateau in the MSD at intermediate times, previously found in the absence of advection, also exists for high Péclet numbers. Initially immobile tracers are subject to the newly observed regime of advection induced subdiffusion for short immobilisations and high Péclet numbers. In the long-time limit the effective advection velocity is reduced compared to advection in the mobile phase. In contrast, the MSD is enhanced by advection. We explore physical mechanisms behind the emerging non-Gaussian density functions and the features of the MSD. [ABSTRACT FROM AUTHOR]

The dynamic and static characteristics of hydrostatic thrust bearings are significantly affected by the bearing surface topography. Previous studies on hydrostatic thrust bearings have focused on Gaussian distribution models of bearing surface topography. However, based on actual measurements, the non-Gaussianity of the distribution characteristics of bearing surface topography is clear. To accurately characterize the non-Gaussian distribution of bearing surface topography, the traditional probability density function of Gaussian distribution was modified by introducing Edgeworth expansion. The non-Gaussian surface was then reflected by two parameters: kurtosis and skewness. This had an effect on the static characteristics of hydrostatic thrust bearings with both circumferential and radial surface topographies. The comparison between the Gaussian distribution results and those of the non-Gaussian model showed that errors between the two models could reach more than 10%. Therefore, it is important to take into account the non-Gaussianity of bearing surface when discussing static characteristics of hydrostatic thrust bearings considering the surface topography. [ABSTRACT FROM AUTHOR]

When searching over a large parameter space for anomalies such as events, peaks, objects, or particles, there is a large probability that spurious signals with seemingly high signi ficance will be found. This is known as the look-elsewhere effect and is prevalent throughout cosmology, (astro)particle physics, and beyond. To avoid making false claims of detection, one must account for this effect when assigning the statistical significance of an anomaly. This is typically accomplished by considering the trials factor, which is generally computed numerically via potentially expensive simulations. In this paper we develop a continuous generalization of the Bonferroni and Sidak corrections by applying the Laplace approximation to evaluate the Bayes factor, and in turn relating the trials factor to the prior-to-posterior volume ratio. We use this to define a test statistic whose frequentist properties have a simple interpretation in terms of the global p-value, or statistical significance. We apply this method to various physics-based examples and show it to work well for the full range of p-values, i.e. in both the asymptotic and non-asymptotic regimes. We also show that this method naturally accounts for other model complexities such as additional degrees of freedom, generalizing Wilks' theorem. This provides a fast way to quantify statistical significance in light of the look-elsewhere effect, without resorting to expensive simulations.

Cosmological Collider Physics gives us the opportunity to probe high-energy physics from observing the space–time fluctuations generated during inflation imprinted on the cosmic microwave background. In other words, it is a method to investigate physics on energy scales that cannot be reached by terrestrial accelerators by means of precise observations of the universe. In this paper, we focus on the case where the GUT scale is close to the energy scale of inflation, and calculate three-point function of inflaton by exchanging the Higgs boson in GUT at tree level. The results are found to be consistent with the current observed restrictions on non-Gaussianity without a drastic fine-tuning of parameters, and it might be possible to detect the signature of the Higgs boson in GUT by 21 cm spectrum, future LSS and future CMB depending on our model parameters. [ABSTRACT FROM AUTHOR]

In the analysis of neural data, measures of non-Gaussianity are generally applied in two ways: as tests of normality for validating model assumptions and as Independent Component Analysis (ICA) contrast functions for separating non-Gaussian signals. Consequently, there is a wide range of methods for both applications, but they all have trade-offs. We propose a new strategy that, in contrast to previousmethods, directly approximates the shape of a distribution via Hermite functions. Applicability as a normality test was evaluated via its sensitivity to non-Gaussianity for three families of distributions that deviate from a Gaussian distribution in different ways (modes, tails, and asymmetry). Applicability as an ICA contrast function was evaluated through its ability to extract non-Gaussian signals in simple multi-dimensional distributions, and to remove artifacts from simulated electroencephalographic datasets. The measure has advantages as a normality test and, for ICA, for heavy-tailed and asymmetric distributions with small sample sizes. For other distributions and large datasets, it performs comparably to existing methods. Compared to standard normality tests, the newmethod performs better for certain types of distributions. Compared to contrast functions of a standard ICA package, the newmethod has advantages but its utility for ICA ismore limited. This highlights that even though both applications--normality tests and ICA--require a measure of deviation from normality, strategies that are advantageous in one application may not be advantageous in the other. Here, the new method has broad merits as a normality test but only limited advantages for ICA. [ABSTRACT FROM AUTHOR]

The relationship between brain microstructure and aging has been the subject of intense study, with diffusion MRI perhaps the most effective modality for elucidating these associations. Here, we used the mean apparent propagator (MAP)-MRI framework, which is suitable to characterize complex microstructure, to investigate age-related cerebral differences in a cohort of cognitively unimpaired participants and compared the results to those derived using diffusion tensor imaging. We studied MAP-MRI metrics, among them the non-Gaussianity (NG) and propagator anisotropy (PA), and established an opposing pattern in white matter of higher NG alongside lower PA among older adults, likely indicative of axonal degradation. In gray matter, however, these two indices were consistent with one another, and exhibited regional pattern heterogeneity compared to other microstructural parameters, which could indicate fewer neuronal projections across cortical layers along with an increased glial concentration. In addition, we report regional variations in the magnitude of age-related microstructural differences consistent with the posterior-anterior shift in aging paradigm. These results encourage further investigations in cognitive impairments and neurodegeneration. [ABSTRACT FROM AUTHOR]

The image intensity of high-resolution synthetic aperture radar (SAR) is closely related to the facet scattering distribution. In this paper, the effects of wind wave spectra, non-Gaussianity of the sea surface, and swell on the distribution of the facet normalized radar cross section (NRCS) simulated by the facet two-scale model (TSM) are analyzed by comparing the simulated results with the Sentinel-1 SAR data, the Advanced Scatterometer (ASCAT) data, and the geophysical model function (GMF) at the wind speed range of 3–16 m/s, the wind direction range of 0°–360°, and the incidence angle range of 30°–50° under VV and HH polarizations. The results show that the Apel spectrum achieves a more consistent mean NRCS and NRCS distribution with the reference data at low incidence angles, while the composite spectra perform better at high incidence angles under VV polarization. Under HH polarization, the Apel spectrum always has a better performance. The upwind–downwind asymmetry of backscattering can be predicted well by the modified TSM, which is constructed by incorporating bispectrum correction into the conventional TSM. The distribution of the scattering simulated by the modified TSM deviates from the Gaussian distribution significantly, which is in good agreement with the Sentinel-1 data. Additionally, the introduction of swell widens the spread of the NRCS distribution, and the fluctuation range of the NRCS profile considering swell is larger than that without swell. All these changes caused by the introduction of swell make the distribution of the facet scattering more consistent with the Sentinel-1 data. Moreover, the scattering image patterns and scattering image spectrum of the Sentinel-1 data can be successfully simulated at various sea states with the consideration of swell. [ABSTRACT FROM AUTHOR]

Gravitational coupling between large- and small-scale density perturbations leads to anisotropic distortions to local small-scale matter fluctuations. Such local anisotropic distortions can be used to reconstruct large-scale matter distribution, known as tidal reconstruction. In this paper, we apply the tidal reconstruction methods to simulated galaxies in redshift space. We find that redshift-space distortions (RSDs) lead to anisotropic reconstruction results. While the reconstructed radial modes are more noisy mainly due to the small-scale velocity dispersion, the transverse modes are still reconstructed with high fidelity, and well correlated with the original large-scale density modes. The bias of the reconstructed field at large scales shows a simple angular dependence, which can be described by a form similar to that of the linear RSD. The noise power spectrum is nearly isotropic and scale independent on large scales. This makes the reconstructed tide fields an ideal tracer for cosmic variance cancellation and multi-tracer analysis and has profound implications for future 21 cm intensity mapping surveys.

Nonlinear gravitational evolution induces strong nonlinearities in the observed cosmological density fields, leading to positive off-diagonal correlations in the power spectrum covariance. This has caused the information saturation in the power spectrum, e.g., the neutrino mass constraints from the nonlinear power spectra are lower than their linear counterparts by a factor of ∼2 at z = 0. In this paper, we explore how nonlinear reconstruction methods improve the cosmological information from nonlinear cosmic fields. By applying nonlinear reconstruction to cold dark matter fields from the Quijote simulations, we find that nonlinear reconstruction can improve the constraints on cosmological parameters significantly, nearly reaching the linear theory limit. For neutrino mass, the result is only 12% lower than the linear power spectrum, i.e., the theoretical best result. This makes nonlinear reconstruction an efficient and useful method to extract neutrino information from current and upcoming galaxy surveys.

In the analysis of neural data, measures of non-Gaussianity are generally applied in two ways: as tests of normality for validating model assumptions and as Independent Component Analysis (ICA) contrast functions for separating non-Gaussian signals. Consequently, there is a wide range of methods for both applications, but they all have trade-offs. We propose a new strategy that, in contrast to previous methods, directly approximates the shape of a distribution via Hermite functions. Applicability as a normality test was evaluated via its sensitivity to non-Gaussianity for three families of distributions that deviate from a Gaussian distribution in different ways (modes, tails, and asymmetry). Applicability as an ICA contrast function was evaluated through its ability to extract non-Gaussian signals in simple multi-dimensional distributions, and to remove artifacts from simulated electroencephalographic datasets. The measure has advantages as a normality test and, for ICA, for heavy-tailed and asymmetric distributions with small sample sizes. For other distributions and large datasets, it performs comparably to existing methods. Compared to standard normality tests, the new method performs better for certain types of distributions. Compared to contrast functions of a standard ICA package, the new method has advantages but its utility for ICA is more limited. This highlights that even though both applications—normality tests and ICA—require a measure of deviation from normality, strategies that are advantageous in one application may not be advantageous in the other. Here, the new method has broad merits as a normality test but only limited advantages for ICA.

Purpose: We seek to reformulate the so‐called Propagator Anisotropy (PA) and Non‐Gaussianity (NG), originally conceived for the Mean Apparent Propagator diffusion MRI (MAP‐MRI), to the Micro‐Structure adaptive convolution kernels and dual Fourier Integral Transforms (MiSFIT). These measures describe relevant normalized features of the Ensemble Average Propagator (EAP). Theory and Methods: First, the indices, which are defined as the EAP's dissimilarity from an isotropic (PA) or a Gaussian (NG) one, are analytically reformulated within the MiSFIT framework. Then a comparison between the resulting maps is drawn by means of a visual analysis, a quantitative assessment via numerical simulations, a test‐retest study across the MICRA dataset (6 subjects scanned five times) and, finally, a computational time evaluation. Results: Findings illustrate the visual similarity between the indices computed with either technique. Evaluation against synthetic ground truth data, however, demonstrates MiSFIT's improved accuracy. In addition, the test–retest study reveals MiSFIT's higher degree of reliability in most of white matter regions. Finally, the computational time evaluation shows MiSFIT's time reduction up to two orders of magnitude. Conclusions: Despite being a direct development on the MAP‐MRI representation, the PA and the NG can be reliably and efficiently computed within MiSFIT's framework. This, together with the previous findings in the original MiSFIT's article, could mean the difference that definitely qualifies diffusion MRI to be incorporated into regular clinical settings. [ABSTRACT FROM AUTHOR]

The nowcasting performance of autoregressive models for GDP growth are analysed in a setting where the error term is allowed to be characterized both by conditional heteroscedasticity and non-Gaussianity. Standard, publicly available, quarterly data on GDP growth from 1979 to 2019 for six countries are employed: Australia, Canada, France, Japan, the United Kingdom and the United States. In-sample analysis suggests that when homoscedasticity is assumed, support is provided for non-Gaussian error terms; the estimated degrees of freedom of the t-distribution lie between two and seven for all countries. However, allowing for both conditional heteroscedasticity and t-distributed innovations, results indicate that conditional heteroscedasticity captures the fat-tailed behaviour of the data to a large extent. Results from out-of-sample analysis show that point nowcasts are hardly affected by taking conditional heteroscedasticity and/or non-Gaussianity into account. For the density nowcasts, it is found that accounting for conditional heteroscedasticity leads to improvements for Australia, Canada, Japan, the United Kingdom and the United States; allowing for non-Gaussianity seems less important though. This result is robust to which measure is used for assessing density nowcasting performance. [ABSTRACT FROM AUTHOR]

• A novel model can capture hydrological heteroscedasticity and non-Gaussianity. • Our model generates conditional mixture distributions with time-varying parameters. • Number of mixture components is identified with Akaike information criterion. Improving probabilistic streamflow prediction requires proper characterization of residual errors in hydrological models. Previous studies often adopt data transformation techniques to stabilize the variability of residual errors to make them more Gaussian. Here, we introduce a novel residual error model that directly captures the intrinsic properties of residual errors, thereby avoiding potential pitfalls such as misinterpretation and conflict assumptions during data transformation. The proposed model, based on a Mixture Density Network (MDN), combines a neural network with a mixture density model to generate time-varying mixture distributions conditioned on the magnitude of streamflow and other variables. The model was examined using both synthetic data as well as data from a real catchment in the source of the Yellow River. Two model selection criteria, the Akaike information criterion (AIC) and the Bayesian information criterion (BIC), were adopted to choose the optimal number of mixture components. Compared to the benchmark model, which assumes homoscedastic Gaussian residual errors, our proposed model yields uncertainty intervals over 20% narrower and provides more accurate uncertainty coverage, particularly enhancing the capture of low and high flows. Besides, it effectively characterized heteroscedasticity and non-Gaussianity in residual errors following model assumptions checking. Further, we discovered that the optimal number of mixture components was better identified using AIC rather than BIC as the criterion. [ABSTRACT FROM AUTHOR]

Likelihood analysis is typically limited to normally distributed noise due to the difficulty of determining the probability density function of complex, high-dimensional, non-Gaussian, and anisotropic noise. This is a major limitation for precision measurements in many domains of science, including astrophysics, for example, for the analysis of the cosmic microwave background, gravitational waves, gravitational lensing, and exoplanets. This work presents Score-based LIkelihood Characterization, a framework that resolves this issue by building a data-driven noise model using a set of noise realizations from observations. We show that the approach produces unbiased and precise likelihoods even in the presence of highly non-Gaussian correlated and spatially varying noise. We use diffusion generative models to estimate the gradient of the probability density of noise with respect to data elements. In combination with the Jacobian of the physical model of the signal, we use Langevin sampling to produce independent samples from the unbiased likelihood. We demonstrate the effectiveness of the method using real data from the Hubble Space Telescope and James Webb Space Telescope.

During the actual machining process of journal surface, such as milling and fine turning, the surface roughness has strong non-Gaussianity. Thus, the effect of non-Gaussian longitudinal roughness on threshold speed of short journal bearings is investigated in this study. Introducing the parameters of kurtosis and skewness, the model of non-Gaussian surface roughness is established by modifying the Gaussian distribution. It is found that the non-Gaussianity of surface roughness cannot be neglected especially for the journal rotating with a larger eccentricity ratio, the error of Gaussian distribution surface reaches 19.33% when the eccentricity ratio equal 0.7. The increasing of kurtosis would reduce the threshold speed, while the increasing of skewness would enhance the threshold speed. For a larger eccentricity ratio, the effect of kurtosis and skewness on threshold speed is more distinctly. [ABSTRACT FROM AUTHOR]

The dynamic and static characteristics of hydrostatic thrust bearings are significantly affected by the bearing surface topography. Previous studies on hydrostatic thrust bearings have focused on Gaussian distribution models of bearing surface topography. However, based on actual measurements, the non-Gaussianity of the distribution characteristics of bearing surface topography is clear. To accurately characterize the non-Gaussian distribution of bearing surface topography, the traditional probability density function of Gaussian distribution was modified by introducing Edgeworth expansion. The non-Gaussian surface was then reflected by two parameters: kurtosis and skewness. This had an effect on the static characteristics of hydrostatic thrust bearings with both circumferential and radial surface topographies. The comparison between the Gaussian distribution results and those of the non-Gaussian model showed that errors between the two models could reach more than 10%. Therefore, it is important to take into account the non-Gaussianity of bearing surface when discussing static characteristics of hydrostatic thrust bearings considering the surface topography.

The output response of any intact oscillatory system subjected to a Gaussian excitation is also Gaussian in nature. On the contrary, when the system contains any type of underlying nonlinearity, the output signal is definitely non-Gaussian. In beam structures, the presence of fatigue-breathing cracks significantly influences the dynamic response characteristics under Gaussian excitation. The presence of such cracks alters the response to be nonlinear, and the non-Gaussianity of the system will arise. In order to examine the non-Gaussianity features and ability for the detection and localization of fatigue cracks, several breathing crack identification scenarios in beam-like structures are presented in this paper. The effects of single and multiple breathing cracks corresponding to different boundary conditions on the responses of beams are studied. The results are analyzed based on the higher-order time-domain transformations. Higher-order transformations, namely the skewness and kurtosis coefficients in addition to the Shannon entropy, are exploited to provide dynamic details about the response, which the conventional second-order statistics cannot show. The results exhibit that the proposed methods are robust and immune to noise and can detect and localize breathing cracks with different sensitivities. [ABSTRACT FROM AUTHOR]

The image intensity of high-resolution synthetic aperture radar (SAR) is closely related to the facet scattering distribution. In this paper, the effects of wind wave spectra, non-Gaussianity of the sea surface, and swell on the distribution of the facet normalized radar cross section (NRCS) simulated by the facet two-scale model (TSM) are analyzed by comparing the simulated results with the Sentinel-1 SAR data, the Advanced Scatterometer (ASCAT) data, and the geophysical model function (GMF) at the wind speed range of 3–16 m/s, the wind direction range of 0°–360°, and the incidence angle range of 30°–50° under VV and HH polarizations. The results show that the Apel spectrum achieves a more consistent mean NRCS and NRCS distribution with the reference data at low incidence angles, while the composite spectra perform better at high incidence angles under VV polarization. Under HH polarization, the Apel spectrum always has a better performance. The upwind–downwind asymmetry of backscattering can be predicted well by the modified TSM, which is constructed by incorporating bispectrum correction into the conventional TSM. The distribution of the scattering simulated by the modified TSM deviates from the Gaussian distribution significantly, which is in good agreement with the Sentinel-1 data. Additionally, the introduction of swell widens the spread of the NRCS distribution, and the fluctuation range of the NRCS profile considering swell is larger than that without swell. All these changes caused by the introduction of swell make the distribution of the facet scattering more consistent with the Sentinel-1 data. Moreover, the scattering image patterns and scattering image spectrum of the Sentinel-1 data can be successfully simulated at various sea states with the consideration of swell.

A computational finite-element (FE)-based technique is proposed for developing a stochastic reduced order model for rotating bladed disc with spatial random inhomogeneities. The spatial inhomogeneities imply the system to be randomly mistuned. The formulation assumes the availability of a high fidelity FE model for the tuned system. The corresponding FE matrices are antisymmetric on account of the Coriolis forces due to rotation. The spatial inhomogeneities, available from limited point measurements on the blades, are modelled as non-Gaussian random fields with arbitrary distributions. A low order stochastic computational model is developed by projecting the FE model onto a reduced dimensional state space defined in terms of specified observable nodal points and expressing the stochasticity through an arbitrary polynomial chaos (aPC) basis. This model enables probabilistic quantification of the variabilities in the system response and estimating failure probabilities. The methodology enables drastic reduction in the state space and stochastic dimensions, addresses the practical difficulties with having limited measurable data points, antisymmetric FE matrices, aPC representation in complex irregular geometries and carrying out probabilistic analyses on industrial systems, at significantly reduced computational costs. The methodology is illustrated through an academic rotor and an industrial rotor blade. [ABSTRACT FROM AUTHOR]

In most data assimilation and numerical weather prediction systems, the Gaussian assumption is prevalent for the behavior of the random variables/errors that are involved. At the Cooperative Institute for Research in the Atmosphere theory has been developed for different forms of variational data assimilation schemes that enables the Gaussian assumption to be relaxed. For certain variable types, a lognormally distributed random variable can be combined in a mixed Gaussian‐lognormal distribution to better capture the interactions of the errors of different distributions. However, assuming that a distribution can change in time, then developing techniques to know when to switch between different versions of the data assimilation schemes becomes very important. By dynamically changing the formulation of the data assimilation system we are able to assimilate observations in a way that reflects the flow‐dependent variability of their distribution. In this paper, we present results with a machine learning technique (the support vector machine) to switch between data assimilation methods based on the detection of a change in the Lorenz 1963 model's z component's probability distribution. Given the machine learning technique's detection/prediction of a change in the distribution, then either a Gaussian or a mixed Gaussian‐lognormal 3DVar based cost function is used to minimize the errors in this period of time. It is shown that switching from a Gaussian 3DVar to a lognormal 3DVar at lognormally distributed parts of the attractor improves the data assimilation analysis error compared to using one distribution type for the entire attractor. Key Points: Machine learning can be used to detect non‐Gaussian distributionsGiven the machine learning detection, we can switch between optimal data assimilation schemesData assimilation can be improved using machine learning techniques [ABSTRACT FROM AUTHOR]

Structural vector autoregressive analysis aims to trace the contemporaneous linkages among multiple economic time series back to underlying orthogonal structural shocks. Traditionally, researchers rely on economically motivated restrictions to identify these shocks. However, in the presence of heteroskedasticity or non‐Gaussian independent components, only these statistical properties allow a locally unique identification. In this paper, we compare alternative statistical identification procedures under distinct covariance changes and distributional frameworks. We find that statistical identification schemes are robust under distinct data structures to some extent and support researchers in detecting shocks that feature an economic underpinning. The detection of independent components appears most flexible. [ABSTRACT FROM AUTHOR]

Inflationary model driven by a scalar field whose potential has a step in the second derivative with respect to the field is considered. For the best-fit potential parameter values, the 3-point function and the non-Gaussianity associated with the featured model is calculated. We study the shape and scale dependence of the 3-point function. The distinctive feature of this model is its characteristic ringing behaviour of f NL . We can see that the oscillations in f NL in this model last for a much longer range of k values, than the previously studied models. In that sense, this model is potentially distinguishable from models with other features in the potential. [ABSTRACT FROM AUTHOR]

The Madden–Julian oscillation (MJO) is the dominant component of tropical intraseasonal variability, with wide-reaching impacts even on extratropical weather and climate patterns. However, predicting the MJO is challenging. One reason is the suboptimal state estimates obtained with standard data assimilation (DA) approaches. These are typically based on filtering methods with Gaussian approximations and do not take into account physical properties that are important specifically for the MJO. In this article, a constrained ensemble DA method is applied to study the impact of different physical constraints on the state estimation and prediction of the MJO. The quadratic programming ensemble (QPEns) algorithm utilized extends the standard stochastic ensemble Kalman filter (EnKF) with specifiable constraints on the updates of all ensemble members. This allows us to recover physically more consistent states and to respect possible associated non-Gaussian statistics. The study is based on identical twin experiments with an adopted nonlinear model for tropical intraseasonal variability. This so-called skeleton model succeeds in reproducing the main large-scale features of the MJO and closely related tropical waves, while keeping adequate simplicity for fast experiments on intraseasonal time-scales. Conservation laws and other crucial physical properties from the model are examined as constraints in the QPEns. Our results demonstrate an overall improvement in the filtering and forecast skill when the model’s total energy is conserved in the initial conditions. The degree of benefit is found to be dependent on the observational setup and the strength of the model’s nonlinear dynamics. It is also shown that, even in cases where the statistical error in some waves remains comparable with the stochastic EnKF during the DA stage, their prediction is improved remarkably when using the initial state resulting from the QPEns. [ABSTRACT FROM AUTHOR]

We study signatures of primordial non-Gaussianity (PNG) in the redshift-space halo field on nonlinear scales using a combination of three summary statistics, namely, the halo mass function (HMF), power spectrum, and bispectrum. The choice of adding the HMF to our previous joint analysis of the power spectrum and bispectrum is driven by a preliminary field-level analysis, in which we train graph neural networks on halo catalogs to infer the PNG f _NL parameter. The covariance matrix and the responses of our summaries to changes in model parameters are extracted from a suite of halo catalogs constructed from the Quijote-png N -body simulations. We consider the three main types of PNG: local, equilateral, and orthogonal. Adding the HMF to our previous joint analysis of the power spectrum and bispectrum produces two main effects. First, it reduces the equilateral f _NL predicted errors by roughly a factor of 2 while also producing notable, although smaller, improvements for orthogonal PNG. Second, it helps break the degeneracy between the local PNG amplitude, ${f}_{\mathrm{NL}}^{\mathrm{local}}$ , and assembly bias, b _ϕ , without relying on any external prior assumption. Our final forecasts for the PNG parameters are ${\rm{\Delta }}{f}_{\mathrm{NL}}^{\mathrm{local}}=40$ , ${\rm{\Delta }}{f}_{\mathrm{NL}}^{\mathrm{equil}}=200$ , ${\rm{\Delta }}{f}_{\mathrm{NL}}^{\mathrm{ortho}}=85$ , on a cubic volume of $1{\left(\mathrm{Gpc}/{\rm{h}}\right)}^{3}$ , with a halo number density of $\bar{n}\sim 5.1\,\times \,{10}^{-5}\,{h}^{3}\,{\mathrm{Mpc}}^{-3}$ , at z = 1, and considering scales up to ${k}_{\max }=0.5\,h\,{\mathrm{Mpc}}^{-1}$ .

In this article, on the basis of the Langevin equation applied to velocity fluctuations, we numerically model the partial variance of increments, which is a useful tool to measure time and spatial correlations in space plasmas. We consider a coupled map lattice model to relate the spatial scale of fluctuations, k , to some macro parameters of the systems, such as the Reynolds number, R _λ , the κ parameter of Kappa distributions, and a skewness parameter, δ . To do so, we compute the velocity probability density function (pdf) for each spatial scale and different values of Reynolds number in the simulations. We fit the pdf with a Skew–Kappa distribution, and we obtain a numerical relationship between the level of turbulence of the plasma and the skewness of obtained distributions, namely, $\langle \delta \rangle \sim {R}_{\lambda }^{-1/2}$ . We expect the results exposed in this paper to be useful as a tool to characterize the turbulence in the context of space plasma and other environments.

We analyse the transport of diffusive particles that switch between mobile and immobile states with finite rates. We focus on the effect of advection on the density functions and mean squared displacements (MSDs). At relevant intermediate time scales we find strong anomalous diffusion with cubic scaling in time of the MSD for high Péclet numbers. The cubic scaling exists for short and long mean residence times in the immobile state $\tau_\mathrm{im}$ . For long $\tau_\mathrm{im}$ the plateau in the MSD at intermediate times, previously found in the absence of advection, also exists for high Péclet numbers. Initially immobile tracers are subject to the newly observed regime of advection induced subdiffusion for short immobilisations and high Péclet numbers. In the long-time limit the effective advection velocity is reduced compared to advection in the mobile phase. In contrast, the MSD is enhanced by advection. We explore physical mechanisms behind the emerging non-Gaussian density functions and the features of the MSD.

We study primordial non-Gaussian signatures in the redshift-space halo field on nonlinear scales, using a quasi-maximum likelihood estimator based on optimally compressed power spectrum and modal bispectrum statistics. We train and validate the estimator on a suite of halo catalogs constructed from the Quijote-png N -body simulations, which we release to accompany this paper. We verify its unbiasedness and near-optimality for the three main types of primordial non-Gaussianity (PNG): local, equilateral, and orthogonal. We compare the modal bispectrum expansion with a k -binning approach, showing that the former allows for faster convergence of numerical derivatives in the computation of the score function, thus leading to better final constraints. We find, in agreement with previous studies, that the local PNG signal in the halo field is dominated by the scale-dependent bias signature on large scales and saturates at k ∼ 0.2 h Mpc ^−1 , whereas the small-scale bispectrum is the main source of information for equilateral and orthogonal PNG. Combining the power spectrum and bispectrum on nonlinear scales plays an important role in breaking degeneracies between cosmological and PNG parameters; such degeneracies, however, remain strong for equilateral PNG. We forecast that PNG parameters can be constrained with ${\rm{\Delta }}{f}_{\mathrm{NL}}^{\mathrm{local}}=45$ , ${\rm{\Delta }}{f}_{\mathrm{NL}}^{\mathrm{equil}}=570$ , and ${\rm{\Delta }}{f}_{\mathrm{NL}}^{\mathrm{ortho}}=110$ on a cubic volume of $1{\left(\mathrm{Gpc}\,{h}^{-1}\right)}^{3}$ at z = 1, considering scales up to ${k}_{\max }=0.5\,h\,{\mathrm{Mpc}}^{-1}$ .

We investigate how much can be learnt about four types of primordial non-Gaussianity (PNG) from small-scale measurements of the halo field. Using the quijote-png simulations, we quantify the information content accessible with measurements of the halo power spectrum monopole and quadrupole, the matter power spectrum, the halo–matter cross spectrum, and the halo bispectrum monopole. This analysis is the first to include small, nonlinear scales, up to ${k}_{\max }=0.5\,{\rm{h}}\,{\mathrm{Mpc}}^{-1}$ , and to explore whether these scales can break degeneracies with cosmological and nuisance parameters making use of thousands of N -body simulations. We perform all the halo measurements in redshift space with a single sample comprised of all halos with mass >3.2 × 10 ^13 h ^−1 M _⊙ . For local PNG, measurements of the scale-dependent bias effect from the power spectrum using sample variance cancellation provide significantly tighter constraints than measurements of the halo bispectrum. In this case measurements of the small scales add minimal additional constraining power. In contrast, the information on equilateral and orthogonal PNG is primarily accessible through the bispectrum. For these shapes, small-scale measurements increase the constraining power of the halo bispectrum by up to 4×, though the addition of scales beyond k ≈ 0.3 h Mpc ^−1 improves constraints largely through reducing degeneracies between PNG and the other parameters. These degeneracies are even more powerfully mitigated through combining power spectrum and bispectrum measurements. However, even with combined measurements and small-scale information, equilateral non-Gaussianity remains highly degenerate with σ _8 and our bias model.

Primordial non-Gaussianity (PNG) is one of the most powerful probes of the early universe, and measurements of the large-scale structure of the universe have the potential to transform our understanding of this area. However, relating measurements of the late-time universe to the primordial perturbations is challenging due to the nonlinear processes that govern the evolution of the universe. To help address this issue, we release a large suite of N -body simulations containing four types of PNG: quijote-png . These simulations were designed to augment the quijote suite of simulations that explored the impact of various cosmological parameters on large-scale structure observables. Using these simulations, we investigate how much information on PNG can be extracted by extending power spectrum and bispectrum measurements beyond the perturbative regime at z = 0.0. This is the first joint analysis of the PNG and cosmological information content accessible with power spectrum and bispectrum measurements of the nonlinear scales. We find that the constraining power improves significantly up to ${k}_{\max }\approx 0.3h\,{\mathrm{Mpc}}^{-1}$ , with diminishing returns beyond as the statistical probes signal-to-noise ratios saturate. This saturation emphasizes the importance of accurately modeling all the contributions to the covariance matrix. Further, we find that combining the two probes is a powerful method of breaking the degeneracies with the ΛCDM parameters.

In this paper, we analysed the heavy-tailed behaviour in the dynamics of housing-price returns in the United States. We investigated the sources of heavy tails by estimating autoregressive models in which innovations can be subject to GARCH effects and/or non-Gaussianity. Using monthly data from January 1954 to September 2019, the properties of the models were assessed both within- and out-of-sample. We found strong evidence in favour of modelling both GARCH effects and non-Gaussianity. Accounting for these properties improves within-sample performance as well as point and density forecasts. [ABSTRACT FROM AUTHOR]

The separate universe conjecture states that in General Relativity a density perturbation behaves locally (i.e. on scales much smaller than the wavelength of the mode) as a separate universe with different background density and curvature. We prove this conjecture for a spherical compensated tophat density perturbation of arbitrary amplitude and radius in ΛCDM. We then use Conformal Fermi Coordinates to generalize this result to scalar perturbations of arbitrary configuration and scale in a general cosmology with a mixture of fluids, but to linear order in perturbations. In this case, the separate universe conjecture holds for the isotropic part of the perturbations. The anisotropic part on the other hand is exactly captured by a tidal field in the Newtonian form. We show that the separate universe picture is restricted to scales larger than the sound horizons of all fluid components. We then derive an expression for the locally measured matter bispectrum induced by a long-wavelength mode of arbitrary wavelength, a new result which in standard perturbation theory is equivalent to a relativistic second-order calculation. We show that nonlinear gravitational dynamics does not generate observable contributions that scale like local-type non-Gaussianity flocNL, and hence does not contribute to a scale-dependent galaxy bias Δ b k-2 on large scales; rather, the locally measurable long-short mode coupling assumes a form essentially identical to subhorizon perturbation theory results, once the long-mode density perturbation is replaced by the synchronous-comoving gauge density perturbation. Apparent flocNL-type contributions arise through projection effects on photon propagation, which depend on the specific large-scale structure tracer and observable considered, and are in principle distinguishable from the local mode coupling induced by gravity. We conclude that any observation of flocNL beyond these projection effects signals a departure from standard single-clock inflation.