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We study individual male earnings dynamics over the life cycle using panel data on millions of U.S. workers. Using nonparametric methods, we first show that the distribution of earnings changes exhibits substantial deviations from lognormality, such as negative skewness and very high kurtosis. Further, the extent of these nonnormalities varies significantly with age and earnings level, peaking around age 50 and between the 70th and 90th percentiles of the earnings distribution. Second, we estimate nonparametric impulse response functions and find important asymmetries: Positive changes for high-income individuals are quite transitory, whereas negative ones are very persistent; the opposite is true for low-income individuals. Third, we turn to long-run outcomes and find substantial heterogeneity in the cumulative growth rates of earnings and the total number of years individuals spend nonemployed between ages 25 and 55. Finally, by targeting these rich sets of moments, we estimate stochastic processes for earnings that range from the simple to the complex. Our preferred specification features normal mixture innovations to both persistent and transitory components and includes state-dependent long-term nonemployment shocks with a realization probability that varies with age and earnings.

Identifying highly channelized hydraulic conductivity fields and contaminant source parameters remains a challenging task, primarily due to the non‐Gaussian nature and high dimensionality of the parameter space, as well as the computational burden caused by repeatedly running forward numerical models. This study proposes a novel deep learning parameterization method called AEdiffusion, which combines Diffusion Denoising Probabilistic Model (DDPM) with Variational Autoencoder (VAE) for dimensionality reduction. The method employs a generator‐refiner strategy to generate high‐dimensional aquifer properties from low‐dimensional latent representations. The inversion modeling was performed on a synthetic non‐Gaussian hydraulic conductivity field with line‐source contamination using the Iterative Local Updating Ensemble Smoother (ILUES) algorithm. The results demonstrate that the AEdiffusion‐ILUES framework can accurately identify model parameters. To reduce the computational burden, an AR‐Net‐WL (ARNW) surrogate model was introduced, resulting in an efficient inversion framework (AEdiffusion‐ILUES‐ARNW) with similar prediction accuracy and predictive uncertainty estimation as the AEdiffusion‐ILUES but at a lower computational cost. Plain Language Summary Identifying highly channelized hydraulic conductivity fields and contaminant source parameters is crucial for developing groundwater remediation strategies. However, this remains a challenging task due to the non‐Gaussian nature and high dimensionality of the parameter space, as well as the computational burden caused by repeatedly running numerical models. We propose a novel deep learning‐based inversion framework to identify hydraulic conductivity fields and contaminant sources from sparse and error‐prone observations. Key Points A novel and accurate deep learning parameterization method combining DDPM and VAE is proposed to parameterize non‐Gaussian hydraulic conductivity fields A deep autoregressive neural network is integrated into the inversion framework as a surrogate to alleviate the high computational cost of the forward numerical models The integrated approach is assessed with inverse problems for the identification of a non‐Gaussian conductivity and line contaminant source parameters

In many applications of data assimilation, especially when the size of the problem is large, a substantial assumption is made: all variables are well‐described by Gaussian error statistics. This assumption has the advantage of making calculations considerably simpler, but it is often not valid, leading to biases in forecasts or, even worse, unphysical predictions. We propose a simple, but effective, way of replacing this assumption, by making use of transforming functions, while remaining consistent with Bayes' theorem. This method allows the errors to have any value of the skewness and kurtosis, and permits physical bounds for the variables. As such, the error distribution can conform better to the underlying statistics, reducing biases introduced by the Gaussian assumption. We apply this framework to a 3D variational data assimilation method, and find improved performance in a simple atmospheric toy model (Lorenz‐63), compared to an all‐Gaussian technique. Plain Language Summary Data assimilation is the technique of combining model predictions with observations in the optimal way and is, for example, used in weather forecasting. To simplify the procedure, a crucial assumption is made on the statistics of all components. However, as models are becoming increasingly precise, and computational techniques are improving, it is becoming more and more obvious that this simple assumption is inadequate, resulting in inaccurate forecasts. We provide a very general framework that relaxes this assumption, and that allows for a much broader scope of statistics. This generalization significantly improves prevailing methods, as tested with a simple atmospheric toy model. Key Points A general framework for non‐Gaussian data assimilation is formulated The proposed method allows for skewness and kurtosis and provides a straightforward approach to handling variables with physical bounds Experiments with the Lorenz‐63 model show significant improvements over an all‐Gaussian approach

Seawater intrusion (SI) poses a substantial threat to water security in coastal regions, where numerical models play a pivotal role in supporting groundwater management and protection. However, the inherent heterogeneity of coastal aquifers introduces significant uncertainties into SI predictions, potentially diminishing their effectiveness in management decisions. Data assimilation (DA) offers a solution by integrating various types of observational data with the model to characterize heterogeneous coastal aquifers. Traditional DA techniques, like ensemble smoother using the Kalman formula (ESK) and Markov chain Monte Carlo, face challenges when confronted with the non‐linearity, non‐Gaussianity, and high‐dimensionality issues commonly encountered in aquifer characterization. In this study, we introduce a novel DA approach rooted in deep learning (DL), referred to as ESDL, aimed at effectively characterizing coastal aquifers with varying levels of heterogeneity. We systematically investigate a range of factors that impact the performance of ESDL, including the number and types of observations, the degree of aquifer heterogeneity, the structure and training options of the DL models. Our findings reveal that ESDL excels in characterizing heterogeneous aquifers under non‐linear and non‐Gaussian conditions. Comparison between ESDL and ESK under different experimentation settings underscores the robustness of ESDL. Conversely, in certain scenarios, ESK displays noticeable biases in the characterization results, especially when measurement data from non‐linear and discontinuous processes are used. To optimize the efficacy of ESDL, attention must be given to the design of the DL model and the selection of observational data, which are crucial to ensure the universal applicability of this DA method. Key Points Non‐linearity and non‐Gaussianity in coastal aquifer characterization problems pose challenges to traditional data assimilation (DA) methods We propose to address these issues with a deep learning‐based DA method called ESDL Various factors influencing the performance of ESDL are systematically investigated

We develop results for the use of Lasso and post-Lasso methods to form first-stage predictions and estimate optimal instruments in linear instrumental variables (IV) models with many instruments, p. Our results apply even when p is much larger than the sample size, n. We show that the IV estimator based on using Lasso or post-Lasso in the first stage is root-n consistent and asymptotically normal when the first stage is approximately sparse, that is, when the conditional expectation of the endogenous variables given the instruments can be well-approximated by a relatively small set of variables whose identities may be unknown. We also show that the estimator is semiparametrically efficient when the structural error is homoscedastic. Notably, our results allow for imperfect model selection, and do not rely upon the unrealistic \"beta-min\" conditions that are widely used to establish validity of inference following model selection (see also Belloni, Chernozhukov, and Hansen (2011b)). In simulation experiments, the Lasso-based IV estimator with a data-driven penalty performs well compared to recently advocated many-instrument robust procedures. In an empirical example dealing with the effect of judicial eminent domain decisions on economic outcomes, the Lasso-based IV estimator outperforms an intuitive benchmark. Optimal instruments are conditional expectations. In developing the IV results, we establish a series of new results for Lasso and post-Lasso estimators of nonparametric conditional expectation functions which are of independent theoretical and practical interest. We construct a modification of Lasso designed to deal with non-Gaussian, heteroscedastic disturbances that uses a data-weighted 𝓁₁-penalty function. By innovatively using moderate deviation theory for self-normalized sums, we provide convergence rates for the resulting Lasso and post-Lasso estimators that are as sharp as the corresponding rates in the homoscedastic Gaussian case under the condition that log p = o(n 1/3 ). We also provide a data-driven method for choosing the penalty level that must be specified in obtaining Lasso and post-Lasso estimates and establish its asymptotic validity under non-Gaussian, heteroscedastic disturbances.

Recent works show that glass-forming liquids display Fickian non-Gaussian Diffusion, with non-Gaussian displacement distributions persisting even at very long times, when linearity in the mean square displacement (Fickianity) has already been attained. Such non-Gaussian deviations temporarily exhibit distinctive exponential tails, with a decay length λ growing in time as a power-law. We herein carefully examine data from four different glass-forming systems with isotropic interactions, both in two and three dimensions, namely, three numerical models of molecular liquids and one experimentally investigated colloidal suspension. Drawing on the identification of a proper time range for reliable exponential fits, we find that a scaling law λ(t)∝tα, with α≃1/3, holds for all considered systems, independently from dimensionality. We further show that, for each system, data at different temperatures/concentration can be collapsed onto a master-curve, identifying a characteristic time for the disappearance of exponential tails and the recovery of Gaussianity. We find that such characteristic time is always related through a power-law to the onset time of Fickianity. The present findings suggest that FnGD in glass-formers may be characterized by a “universal” evolution of the distribution tails, independent from system dimensionality, at least for liquids with isotropic potential.

Entanglement is the key quantum resource for improving measurement sensitivity beyond classical limits. However, the production of entanglement in mesoscopic atomic systems has been limited to squeezed states, described by Gaussian statistics. Here, we report on the creation and characterization of non-Gaussian many-body entangled states. We develop a general method to extract the Fisher information, which reveals that the quantum dynamics of a classically unstable system creates quantum states that are not spin squeezed but nevertheless entangled. The extracted Fisher information quantifies metrologically useful entanglement, which we confirm by Bayesian phase estimation with sub–shot-noise sensitivity. These methods are scalable to large particle numbers and applicable directly to other quantum systems.

We study the effect of randomly distributed diffusivities and speeds in two models for active particle dynamics with active and passive fluctuations. We demonstrate how non-Gaussian displacement distributions emerge in these models in the long time limit, including Cauchy-type and exponential (Laplace) shapes. Notably the asymptotic behaviours of such Cauchy shapes are universal and do not depend on the precise diffusivity distributions. Moreover, the resulting shapes of the displacement distributions with distributed diffusivities for the active models considered here are in striking contrast to passive diffusion models. For the active motion models our discussion points out the differences between active- and passive-noise. Specifically, we demonstrate that the case with active-noise is in nice agreement with measured data for the displacement distribution of social amoeba.

Continuous-variable quantum-computing is the most scalable implementation of QC to date but requires non-Gaussian resources to allow exponential speedup and quantum correction, using error encoding such as Gottesman-Kitaev-Preskill (GKP) states. However, GKP state generation is still an experimental challenge. We show theoretically that photon catalysis, the interference of coherent states with single-photon states followed by photon-number-resolved detection, is a powerful enabler for non-Gaussian quantum state engineering such as exactly displaced single-photon states and M-symmetric superpositions of squeezed vacuum (SSV), including squeezed cat states (M = 2). By including photon-counting based state breeding, we demonstrate the potential to enlarge SSV states and produce GKP states.

A considerable number of systems have recently been reported in which Brownian yet non-Gaussian dynamics was observed. These are processes characterised by a linear growth in time of the mean squared displacement, yet the probability density function of the particle displacement is distinctly non-Gaussian, and often of exponential (Laplace) shape. This apparently ubiquitous behaviour observed in very different physical systems has been interpreted as resulting from diffusion in inhomogeneous environments and mathematically represented through a variable, stochastic diffusion coefficient. Indeed different models describing a fluctuating diffusivity have been studied. Here we present a new view of the stochastic basis describing time-dependent random diffusivities within a broad spectrum of distributions. Concretely, our study is based on the very generic class of the generalised Gamma distribution. Two models for the particle spreading in such random diffusivity settings are studied. The first belongs to the class of generalised grey Brownian motion while the second follows from the idea of diffusing diffusivities. The two processes exhibit significant characteristics which reproduce experimental results from different biological and physical systems. We promote these two physical models for the description of stochastic particle motion in complex environments.