Covariance Terms Research Articles

A Stochastic Covariance Shrinkage Approach in Ensemble Transform Kalman Filtering

The Ensemble Kalman Filters (EnKF) employ a Monte-Carlo approach to represent covariance information, and are affected by sampling errors in operational settings where the number of model realizations is much smaller than the model state dimension. To alleviate the effects of these errors EnKF relies on model-specific heuristics such as covariance localization, which takes advantage of the spatial locality of correlations among the model variables. This work proposes an approach to alleviate sampling errors that utilizes a locally averaged-in-time dynamics of the model, described in terms of a climatological covariance of the dynamical system. We use this covariance as the target matrix in covariance shrinkage methods, and develop a stochastic covariance shrinkage approach where synthetic ensemble members are drawn to enrich both the ensemble subspace and the ensemble transformation. We additionally provide for a way in which this methodology can be localized similar to the state-of-the-art LETKF method, and that for a certain model setup, our methodology significantly outperforms it.

A theoretical analysis of one-dimensional discrete generation ensemble Kalman particle filters

Despite the widespread usage of discrete generation Ensemble Kalman particle filtering methodology to solve nonlinear and high dimensional filtering and inverse problems, little is known about their mathematical foundations. As genetic-type particle filters (a.k.a. sequential Monte Carlo), this ensemble-type methodology can also be interpreted as mean-field particle approximations of the Kalman-Bucy filtering equation. In contrast with conventional mean-field type interacting particle methods equipped with a globally Lipschitz interacting drift-type function, Ensemble Kalman filters depend on a nonlinear and quadratic-type interaction function defined in terms of the sample covariance of the particles. Most of the literature in applied mathematics and computer science on these sophisticated interacting particle methods amounts to designing different classes of useable observer-type particle methods. These methods are based on a variety of inconsistent but judicious ensemble auxiliary transformations or include additional inflation/localisationtype algorithmic innovations, in order to avoid the inherent time-degeneracy of an insufficient particle ensemble size when solving a filtering problem with an unstable signal. To the best of our knowledge, the first and the only rigorous mathematical analysis of these sophisticated discrete generation particle filters is developed in the pioneering articles by Le Gland-Monbet-Tran and by Mandel-Cobb-Beezley, which were published in the early 2010s. Nevertheless, besides the fact that these studies prove the asymptotic consistency of the Ensemble Kalman filter, they provide exceedingly pessimistic meanerror estimates that grow exponentially fast with respect to the time horizon, even for linear Gaussian filtering problems with stable one dimensional signals. In the present article we develop a novel self-contained and complete stochastic perturbation analysis of the fluctuations, the stability, and the long-time performance of these discrete generation ensemble Kalman particle filters, including time-uniform and non-asymptotic mean-error estimates that apply to possibly unstable signals. To the best of our knowledge, these are the first results of this type in the literature on discrete generation particle filters, including the class of genetic-type particle filters and discrete generation ensemble Kalman filters. The stochastic Riccati difference equations considered in this work are also of interest in their own right, as a prototype of a new class of stochastic rational difference equation.

Pointillisme à la Signac and Construction of a Quantum Fiber Bundle Over Convex Bodies

We use the notion of polar duality from convex geometry and the theory of Lagrangian planes from symplectic geometry to construct a fiber bundle over ellipsoids that can be viewed as a quantum-mechanical substitute for the classical symplectic phase space. The total space of this fiber bundle consists of geometric quantum states, products of convex bodies carried by Lagrangian planes by their polar duals with respect to a second transversal Lagrangian plane. Using the theory of the John ellipsoid we relate these geometric quantum states to the notion of “quantum blobs” introduced in previous work; quantum blobs are the smallest symplectic invariant regions of the phase space compatible with the uncertainty principle. We show that the set of equivalence classes of unitarily related geometric quantum states is in a one-to-one correspondence with the set of all Gaussian wavepackets. We emphasize that the uncertainty principle appears in this paper as geometric property of the states we define, and is not expressed in terms of variances and covariances, the use of which was criticized by Hilgevoord and Uffink.

Separation-based parameterization strategies for estimation of restricted covariance matrices in multivariate model systems

Many multivariate model systems involve the estimation of a covariance matrix that must be positive-definite. A common strategy to ensure positive definiteness of the covariance matrix is through the use of a Cholesky parameterization of the covariance matrix. However, several model systems require imposing restrictions on the elements of the covariance elements. For instance, modelling systems may require fixing some (or all) of the diagonal elements in the covariance matrix to unity due to identification considerations. However, imposing such restrictions using the traditional Cholesky decomposition approach is not feasible and requires the additional parameterization of the Cholesky elements.In this paper, we explore a separation-based strategy with spherical parameterization of the Cholesky matrix to impose restrictions on the covariance matrix. Importantly, using this separation-based parameterization strategy, we also explore the possibility of restricting some covariance (or correlation) terms to zero. The effectiveness of the proposed strategy is assessed through extensive simulation experiments. The results from the simulation experiments highlight better performance of the separation-based strategy in terms of recovery of model parameters – particularly those in the covariance matrix, than the traditional Cholesky parameterization approach. Finally, the proposed strategy is implemented in a joint multivariate binary probit ordered probit model system to analyze the usage (and the extent of use) of non-private modes of transportation in Bengaluru, India. In doing so, the proposed strategy is implemented to restrict several correlations to zero, thus avoiding the estimation of a profligate correlation matrix and substantially easing the estimation process.

Mixed Exponentially Weighted Moving Average—Moving Average Control Chart with Application to Combined Cycle Power Plant

Statistical process control (SPC) consists of various tools for effective monitoring of the production processes and services to ensure their stable and satisfactory performance. A control chart is an important tool of SPC for detecting the process shifts that may undermine the quality of the products or services. In the literature, a mixed exponentially weighted moving average–moving average (EWMA–MA) control chart for monitoring the process location is proposed to enhance the overall shift detection ability of the EWMA control chart. It is noted that the moving averages terms were considered as independent irrespective of their order. Consequently, the covariance terms are ignored while deriving the variance expression of the monitoring statistic. However, the successive moving averages of span w might not be independent since each term includes w − 1 preceding samples’ information. In this study, the variance expression of the mixed EWMA-MA charting statistic is derived by considering the dependency among the sequential moving averages. The control limits of the mixed EWMA-MA control chart are revised and the run-length profile is studied by using Monte Carlo simulations. The performance of the mixed EWMA-MA chart is compared with the existing counterparts and its robustness under various process distributions is studied. In the end, a real-life example is provided to demonstrate its application by using the data from a combined cycle power plant.

Kidney Disease Progression in Membranous Nephropathy among Black Participants with High-Risk APOL1 Genotype.

Disparity in CKD progression among Black individuals persists in glomerular diseases. Genetic variants in the apolipoprotein L1 ( APOL1 ) gene in the Black population contribute to kidney disease, but the influence in membranous nephropathy remains unknown. Longitudinally followed participants enrolled in the Glomerular Disease Collaborative Network or Cure Glomerulonephropathy Network were included if they had DNA or genotyping available for APOL1 (Black participants with membranous nephropathy) or had membranous nephropathy but were not Black. eGFR slopes were estimated using linear mixed-effects models with random effects and adjusting for covariates and interaction terms of covariates. Fisher exact test, Kruskal-Wallis test, and Kaplan-Meier curves with log-rank tests were used to compare groups. Among 118 Black membranous nephropathy participants, 16 (14%) had high-risk APOL1 genotype (two risk alleles) and 102 (86%) had low-risk APOL1 genotype (zero or one risk alleles, n =53 and n =49, respectively). High-risk APOL1 membranous nephropathy participants were notably younger at disease onset than low-risk APOL1 and membranous nephropathy participants that were not Black ( n =572). eGFR at disease onset was not different between groups, although eGFR decline (slope) was steeper in participants with high-risk APOL1 genotype (-16±2 [±SE] ml/min per 1.73 m 2 per year) compared with low-risk APOL1 genotype (-4±0.8 ml/min per 1.73 m 2 per year) or membranous nephropathy participants that did not identify themselves as Black (-2.0±0.4 ml/min per 1.73 m 2 per year) ( P <0.0001). Time to kidney failure was faster in the high-risk APOL1 genotype than low-risk APOL1 genotype or membranous nephropathy participants that were not Black. The prevalence of high-risk APOL1 variant among Black membranous nephropathy participants is comparable with the general Black population (10%-15%), yet the high-risk genotype was associated with worse eGFR decline and faster time to kidney failure compared with low-risk genotype and participants that were not Black.

Assessment of the changing role of lower tropospheric temperature advection under arctic amplification using a large ensemble climate simulation dataset

The role of temperature advection in the Arctic lower troposphere under changing level of global warming is investigated using a large-ensemble climate simulation dataset. Taking the 30-year climatology of the non-warming simulation (HPB-NAT) as a reference, we examined the difference in temperature advection under changing basic states of the historical experiment (HPB) and 2 K and 4 K warming experiments (HFB-2K and HFB-4K) and decomposed them into terms related to dynamical changes, thermodynamical changes and the eddy term which is a covariance term related to the effect of sub-monthly transient eddies. Under the HPB experiment, it was found that the total change in advection hangs in a balance between the positive signal located along the sea-ice boundary in the North Atlantic and along the Eurasian continent driven by a stronger dynamical term and a negative signal in the thermodynamical term and eddy term. It is found that with the progression of global warming the dynamical term of advection increases due to changes in the large-scale atmospheric circulation, but the thermodynamical term and eddy term decrease due to weaker temperature gradient and increased sensible heat flux from the newly opened ice-free ocean, respectively. Atmospheric temperature advection terms related to large-scale atmospheric circulation partially cancels one another, and the relative importance of the eddy term diverging locally induced sensible heat from the newly opened ice-free ocean dominates as global warming progresses.

Quantifying the Inspection Paradox with Random Time

The well-known inspection paradox of renewal theory states that, in expectation, the inspection interval is larger than a common renewal interval, in general. For a random inspection time, which includes the deterministic case, and a delayed renewal process, representations of the expected length of an inspection interval and related inequalities in terms of covariances are shown. Datasets of eruption times of Beehive Geyser and Riverside Geyser in Yellowstone National Park, as well as several distributional examples, illustrate the findings.

Corrigendum: Food restriction reveals individual differences in insulin-like growth factor-1 reaction norms

Corrigendum on: Tóth Z, Mahr K, Ölveczki G, Őri L and Lendvai ÁZ (2022) Food Restriction Reveals Individual Differences in Insulin-Like Growth Factor-1 Reaction Norms. Front. Ecol. Evol. 10:826968. doi: 10.3389/fevo.2022.826968In the published article, there was an error in Table 2 as published. In the original version of the manuscript, the values indicating 95% credible intervals were separated by hyphens, which were replaced by semicolons during the revision, but the hyphens were accidentally not deleted, suggesting wrongly as if the second values were negative. The corrected TABLE 2 Variancecovariance matrix from the multivariate MCMCglmm model including IGF-1 and body mass under each treatment (control, "C" or food-restricted, "FR") and its caption The diagonal shows the variances, while off-diagonal elements correspond to the covariance between the variables. Significant covariance terms are highlighted in bold font appear below.The authors apologize for this error and state that this does not change the scientific conclusions of the article in any way. The original article has been updated.

Euro adoption obliged countries viewed by Melitz Optimum Currency Area model

Empirically applied alternative Optimum Currency Area theory model proposed by J. Mélitz. We calculated trade-weighted terms of trade covariance of several European countries bound to become Eurozone members. The higher the covariance, the higher the cost of joining the Eurozone. Considering the openness index and nominal rigidities, we ordered the countries by the (dis)advantage of joining the Eurozone. According to the model, the highest cost of joining the currency block is attributed to Croatia as its trade partners have high covariance of terms of trade. Croatia is also not as open as other countries like the Czech Republic or Hungary, showing relatively higher nominal rigidity. On the other hand, Bulgaria appears to profit from adopting the Euro the most.

Validation of the information processing theory of consumer choice: evidence from travel search engine clickstream data

PurposeThis paper aims to demonstrate how consumer clickstream data from a leading hotel search engine can be used to validate two hidden information processing stages – first eliminate alternatives, then choose – proposed by the revered information processing theory of consumer choice.Design/methodology/approachThis study models the two hidden information processing stages as hidden states in a hidden Markov model, estimated on consumer search behavior, product attributes and diversity of alternatives in the consideration set.FindingsFirst, the stage of information processing can be statistically characterized in terms of consumer search covariates, including trip characteristics, use of search tools and the diversity of the consideration set, operationalized in terms of: number of brands, dispersion of price and dispersion of quality. Second, users are more sensitive to price and quality in the first rather than the second stage, which is closer to purchase.Research limitations/implicationsThe results suggest practical implications for how search engine managers can target consumers with appropriate marketing-mix actions, based on which information processing stage consumers might be in.Originality/valueMost previous studies on validating the information processing theory of consumer choice have used laboratory experiments, subjects and information display boards comprising hypothetical product alternatives and attributes. Only a few studies use observational data. In contrast, this study uniquely uses point-of-purchase clickstream data on actual visitors at a leading hotel search engine and tests the theory based on real products, attributes and diversity of the consideration set.

CoCoA: conditional correlation models with association size.

Many scientific questions can be formulated as hypotheses about conditional correlations. For instance, in tests of cognitive and physical performance, the trade-off between speed and accuracy motivates study of the two variables together. A natural question is whether speed-accuracy coupling depends on other variables, such as sustained attention. Classical regression techniques, which posit models in terms of covariates and outcomes, are insufficient to investigate the effect of a third variable on the symmetric relationship between speed and accuracy. In response, we propose a conditional correlation model with association size, a likelihood-based statistical framework to estimate the conditional correlation between speed and accuracy as a function of additional variables. We propose novel measures of the association size, which are analogous to effect sizes on the correlation scale while adjusting for confound variables. In simulation studies, we compare likelihood-based estimators of conditional correlation to semiparametric estimators adapted from genomic studies and find that the former achieves lower bias and variance under both ideal settings and model assumption misspecification. Using neurocognitive data from the Philadelphia Neurodevelopmental Cohort, we demonstrate that greater sustained attention is associated with stronger speed-accuracy coupling in a complex reasoning task while controlling for age. By highlighting conditional correlations as the outcome of interest, our model provides complementary insights to traditional regression modeling and partitioned correlation analyses.

Low-budget CubeSat star tracker calibration using Earth’s rotation

A low-budget calibration method for a star tracker using Earth’s rotation is presented. The rotating Earth is one of the most accurate turntables in nature, as its rotation rate and axis are known precisely, thanks to astronomers. Using a precise model of the Earth’s rotation and time tags, it is possible to set the attitude of a star tracker fixed on the ground so that all star measurements can be used in a full-state estimation with only one attitude state. The proposed method needs only a GPS receiver that outputs pulse-per second signals for time synchronization, which is useful for low-budget star-tracker development in university-level CubeSat projects. The simulation results show that the proposed method outperforms the previous calibration method, which does not use the Earth’s rotation, in terms of estimate covariance. An outdoor experiment demonstrated the accuracy of the star tracker calibration with low-cost hardware.

Bayesian estimation for heterogeneous spatial autoregressive models with variance modelling

In this paper, we introduce a new class of heterogeneous spatial autoregressive models (heterogeneous SAR models) where the variance parameters are modeled in terms of covariates. In order to estimate the model parameters, as well as their corresponding standard error estimates, we proposed a computational efficient MCMC method which combines the Gibbs sampler with Metropolis-Hastings algorithm. The proposed estimate method is illustrated through numerous simulations and is applied to the Boston housing data.

The cross-section of expected stock returns and components of idiosyncratic volatility

PurposeThe purpose of this paper is to contribute to the existing stock return predictability and idiosyncratic risk literature by examining the relationship between stock returns and components derived from the decomposition of stock returns variance at the portfolio and firm levels.Design/methodology/approachA theoretical model is used to decompose the variance of stock returns into two volatility and two covariance terms by using a conditional Fama-French three-factor model. This study adopts portfolio analysis and Fama-MacBeth cross-sectional regression to examine the relationship between components of idiosyncratic risk and expected stock returns.FindingsThe portfolio analysis results show that volatility terms are negatively related to expected stock returns, and alpha risk has the most significant relationship with stock returns. On the contrary, covariance terms have positive relationships with expected stock returns at the portfolio level. Furthermore, the results of the Fama-MacBeth cross-sectional regression show that only alpha risk can explain variations in stock returns at the firm level. Another finding is that when volatility and covariance terms are excluded from idiosyncratic volatility, the relation between idiosyncratic volatility and stock returns becomes weak at the portfolio level and disappears at the firm level.Originality/valueThis is the first study that examines the relations between all the components of idiosyncratic risk and expected stock returns in equal-weighted and value-weighted portfolios. This research also suggests covariance terms of idiosyncratic volatility as new predictors of stock returns at the portfolio level. Moreover, this paper contributes to the idiosyncratic risk literature by examining whether all the four additional components explain all the systematic patterns included in the unconditional idiosyncratic risk.

Copula miss-specification in REML multivariate genetic animal model estimation

BackgroundIn animal genetics, linear mixed models are used to deal with genetic and environmental effects. The variance and covariance terms of these models are usually estimated by restricted maximum likelihood (REML), which provides unbiased estimators. A strong hypothesis of REML estimation is the multi-normality of the response variables. However, in practice, even if the marginal distributions of each phenotype are normal, the multi-normality assumption may be violated by non-normality of the cross-sectional dependence structure, that is to say when the copula of the multivariate distribution is not Gaussian. This study uses simulations to evaluate the impact of copula miss-specification in a bivariate animal model on REML estimations of variance components.ResultBivariate phenotypes were simulated for populations undergoing selection, considering different copulas for the dependence structure between the error components. Two multi-trait situations were considered: two phenotypes were measured on the selection candidates, or only one phenotype was measured on the selection candidates. Three generations with random selection and five generations with truncation selection based on estimated breeding values were simulated. When selection was performed at random, no significant differences were observed between the REML estimations of variance components and the true parameters even for the non-Gaussian distributions. For the truncation selections, when two phenotypes were measured on candidates, biases were systematically observed in the variance components for high residual dependence in the case of non-Gaussian distributions, especially in the case of a heavy-tailed or asymmetric distribution when the two traits were measured. Conversely, when only one phenotype was measured on candidates, no difference was observed between the Gaussian and non-Gaussian distributions in REML estimations.ConclusionsThis study confirms that REML can be used by geneticists to evaluate breeding values in the multivariate case even if the multivariate phenotypes deviate from normality in the situation of random selection or if one trait is not measured for the candidate under selection. Nevertheless, when the two traits are measured, the violation of the normality assumption may lead to non-negligible biases in the REML estimations of the variance-covariance components.

Propensity score-integrated approach to survival analysis: leveraging external evidence in single-arm studies

ABSTRACT External data, referred to as data external to the traditional clinical study being planned, include but are not limited to real-world data (RWD) and data collected from clinical studies being conducted in the past or in other countries. The external data are sometimes leveraged to augment a single-arm, prospectively designed study when appropriate. In such an application, recently developed propensity score-integrated approaches including PSPP and PSCL can be used for study design and data analysis when the clinical outcomes are binary or continuous. In this paper, the propensity score-integrated Kaplan–Meier (PSKM) method is proposed for a similar situation but the outcome of interest is time-to-event. The propensity score methodology is used to select external subjects that are similar to those in the current study in terms of baseline covariates and to stratify the selected subjects from both data sources into more homogeneous strata. The stratum-specific PSKM estimators are obtained based on all subjects in the stratum with the external data being down-weighted, and then these estimators are combined to obtain an overall PSKM estimator. A simulation study is conducted to assess the performance of the PSKM method, and an illustrative example is presented to demonstrate how to implement the proposed method.

Cosmology in the non-linear regime: the small scale miracle

Interest is rising in exploiting the full shape information of the galaxy power spectrum, and in pushing analyses to smaller non-linear scales. Here I use the halo model to quantify the information content in the tomographic angular power spectrum of galaxies Cℓgal(iz) for the future high-resolution surveys Euclid and SKA2. I study how this information varies as a function of the scale cut applied, either with angular cut ℓmax or physical cut kmax. For this, I use analytical covariances with the most complete census of non-Gaussian terms, which proves to be critical. I find that the Fisher information on most cosmological and astrophysical parameters shows a striking behaviour. Beyond the perturbative regime, we first get decreasing returns: the information continues to rise but the slope slows down until reaching saturation. The location of this plateau, at k ∼ 2 Mpc−1, is slightly beyond the reach of current modelling methods and depends to some extent on the parameter and redshift bin considered. I explain the origin of this plateau, which is due to non-linear effects both on the power spectrum, and more importantly on non-Gaussian covariance terms. Then, pushing further, we see the information rising again in the highly non-linear regime, with a steep slope. This is the small-scale miracle, for which I give my interpretation and discuss the properties. There are suggestions that it may be possible to disentangle this information from the astrophysical content, and improve dark energy constraints. Finally, more hints are shown that high-order statistics may yield significant improvements over the power spectrum in this regime, with the improvements increasing with kmax.

Lepton phenomenology of Stueckelberg portal to dark sector

We propose an extension of the Standard Model (SM) with a $U_{A'}(1)$ gauge invariant dark dector connected to the SM via a new portal -- the Stueckelberg portal, arising in the framework of dark photon $A'$ mass generation via Stueckelberg mechanism. This portal opens through the effective dim=5 operators constructed from the covariant term of the auxiliary Stueckelberg scalar field $\sigma$ providing flavor non-diagonal renormalizable couplings of both $\sigma$ and $A'$ to the SM fermions $\psi$. The Stueckelberg scalar plays a role of Goldstone boson in the generation of mass of the Dark Photon. Contrary to the conventional kinetic mixing portal, in our scenario flavor diagonal $A'$-$\psi$ couplings are not proportional to the fermion charges and are, in general, flavor nondiagonal. These features drastically change the phenomenology of dark photon $A'$ relaxing or avoiding some previously established experimental constraints. We focus on the phenomenology of the described scenario of the Stueckelberg portal in the lepton sector and analyze the contribution of the dark sector fields $A'$ to the anomalous magnetic moment of muon $(g-2)_{\mu}$, lepton flavor violating decays $l_{i}\to l_{k}\gamma$ and $\mu-e$ conversion in nuclei. We obtain limits on the model parameters from the existing data on the corresponding observables.

Fitting mixture models for feeling and uncertainty for rating data analysis

In this article, we present the command cub, which fits ordinal rating data using combination of uniform and binomial (CUB) models, a class of finite mixture distributions accounting for both feeling and uncertainty of the response process. CUB identifies the components that define the mixture in the baseline model specification. We apply maximum likelihood methods to estimate feeling and uncertainty parameters, which are possibly explained in terms of covariates. An extension to inflated CUB models is discussed. We also present a subcommand, scattercub, for visualization of results. We then illustrate the use of cub using a case study on students’ satisfaction for the orientation services provided by the University of Naples Federico II in Italy.