Assumption Of Stationarity Research Articles

A generalized transition model for grouped longitudinal categorical data.

Transition models are an important framework that can be used to model longitudinal categorical data. They are particularly useful when the primary interest is in prediction. The available methods for this class of models are suitable for the cases in which responses are recorded individually over time. However, in many areas, it is common for categorical data to be recorded as groups, that is, different categories with a number of individuals in each. As motivation we consider a study in insect movement and another in pig behaviou. The first study was developed to understand the movement patterns of female adults of Diaphorina citri, a pest of citrus plantations. The second study investigated how hogs behaved under the influence of environmental enrichment. In both studies, the number of individuals in different response categories was observed over time. We propose a new framework for considering the time dependence in the linear predictor of a generalized logit transition model using a quantitative response, corresponding to the number of individuals in each category. We use maximum likelihood estimation and present the results of the fitted models under stationarity and non-stationarity assumptions, and use recently proposed tests to assess non-stationarity. We evaluated the performance of the proposed model using simulation studies under different scenarios, and concluded that our modeling framework represents a flexible alternative to analyze grouped longitudinal categoricaldata.

"ADAPTIVE PARAMETRIC MODEL FOR NONSTATIONARY SPATIAL COVARIANCE"

In modelling environment processes, multi-disciplinary methods are used to explain, explore and predict how the earth responds to natural human-induced environmental changes over time. Consequently, when analyzing spatial processes in environmental and ecological studies, the spatial parameters of interest are always heterogeneous. This often negates the stationarity assumption. In this article, we propose the adaptive parametric nonstationary covariance structure for spatial processes. The adaptive turning parameter for this model was also proposed for nonstationary processes. The flexibility and efficiency of the propose model was examined through simulation. A real life data was also use to examine the efficiency of the propose model. The results show that the propose model perform competitively with existing models.

Investigating the impact of the time interval selection on autoregressive mediation modeling: Result interpretations, effect reporting, and temporal designs.

This study investigates the impact of the time interval (the time passed between 2 consecutive measurements) selection on autoregressive mediation modeling (AMM). For a widely used autoregressive mediation model, via analytical derivations, we explained why and how the conventionally reported time-specific coefficient estimates (e.g., âb̂ and ĉ' ) and inference results in AMM provide limited information and can arrive in even misleading conclusions about direct and indirect effects over time. Furthermore, under the stationarity assumption, we proposed an approach to calculate the overall direct and indirect effect estimates over time and the time lag lengths at which they reach maxima, using AMM results. The derivation results revealed that the overall direct and indirect effect curves are asymptotically invariant to the time interval selection, under stationarity. With finite samples and thus sampling errors and potential computing problems, however, our simulation results revealed that the overall indirect effect curves were better recovered when the time interval is selected to be closer to half of the time lag length at which the overall indirect effect reaches its maximum. An R function and an R Shiny app were developed to obtain the overall direct and indirect effect curves over time and facilitate the time interval selection using AMM results. Our findings provide another look at the connections between AMM and continuous time mediation modeling and the connections are discussed. (PsycInfo Database Record (c) 2020 APA, all rights reserved).

Complete multivariate flood frequency analysis, applied to northern Algeria

AbstractExtreme hydrologic events are commonly described by several dependent characteristics, such as duration, volume and peak flow for floods. Traditionally in Algeria and North Africa, flood frequency analysis (FFA) is conducted as a univariate approach focusing separately on each single of flood characteristics. On the other hand, elsewhere, multivariate FFA studies have been conducted focusing on some FFA steps (especially modelling). The current study aims to consider complete multivariate FFA at‐site case studies in northern Algeria using 11 hydrometric stations. It is also among the first studies dealing with multivariate FFA in a complete way by considering all the required steps of the analysis (multivariate outliers detection, multivariate assumptions testing and copula fitting) and on datasets from Algeria. Multivariate stationarity, homogeneity and independence assumptions have been well verified before modelling. The Weibull distribution is mostly selected as margin distribution for the duration, volume and peak flow series. Frank, Clayton and Gumbel copulas are commonly selected to describe the dependence structure on the three flood pairs of variables. These findings should be interesting in water management and flood risk assessment in these regions. Combining these flood characteristics enables the design of more efficient hydraulic structures.

Investigating the impacts of climate change and human activities on hydrological drought using non-stationary approaches

Climate variation and human activities are two prime drivers influencing the hydrological cycle and the stationarity of hydrologic systems. Hydrological drought is caused by significant negative variation from normal hydrologic conditions, influenced by climate variation and human activities. Traditional methods employed for quantifying the impacts of climate change and human activities are based on the assumption of stationarity, which is no longer valid under the current changing environment. In this study, a heuristic segmentation method was used to identify the change point in streamflow time series by considering its non-linearity, and trend analysis was performed on hydro-meteorological variables before and after the change point. A non-stationary Standardized Runoff Index (SRINS) was constructed using Generalized Additive Models in Location, Scale, and Shape (GAMLSS). Finally, the influences of climate change and human activities on hydrological drought were quantified at various time scales. The results reveal change points in the streamflow time series after the 1990s. Significant decreases in precipitation and streamflow were also observed after the change points in all study watersheds, whereas the trend of potential evapotranspiration increased at a higher rate after the change points. The impact of climate change on the seasonal (three-month) time scale was greater in the winter and spring seasons, whereas the impact of human activities was significantly higher in the summer and autumn seasons. The influence of climate change on hydrological drought was dominant at longer (6- and 12-month) time scales, whereas human activities accounted for 25.6% and 20% of the changes in watersheds #1018 and #1019 on the 12-month time scale, respectively.

Using Coherence-based spectro-spatial filters for stimulus features prediction from electro-corticographic recordings

The traditional approach in neuroscience relies on encoding models where brain responses are related to different stimuli in order to establish dependencies. In decoding tasks, on the contrary, brain responses are used to predict the stimuli, and traditionally, the signals are assumed stationary within trials, which is rarely the case for natural stimuli. We hypothesize that a decoding model assuming each experimental trial as a realization of a random process more likely reflects the statistical properties of the undergoing process compared to the assumption of stationarity. Here, we propose a Coherence-based spectro-spatial filter that allows for reconstructing stimulus features from brain signal’s features. The proposed method extracts common patterns between features of the brain signals and the stimuli that produced them. These patterns, originating from different recording electrodes are combined, forming a spatial filter that produces a unified prediction of the presented stimulus. This approach takes into account frequency, phase, and spatial distribution of brain features, hence avoiding the need to predefine specific frequency bands of interest or phase relationships between stimulus and brain responses manually. Furthermore, the model does not require the tuning of hyper-parameters, reducing significantly the computational load attached to it. Using three different cognitive tasks (motor movements, speech perception, and speech production), we show that the proposed method consistently improves stimulus feature predictions in terms of correlation (group averages of 0.74 for motor movements, 0.84 for speech perception, and 0.74 for speech production) in comparison with other methods based on regularized multivariate regression, probabilistic graphical models and artificial neural networks. Furthermore, the model parameters revealed those anatomical regions and spectral components that were discriminant in the different cognitive tasks. This novel method does not only provide a useful tool to address fundamental neuroscience questions, but could also be applied to neuroprosthetics.

The Variability of Star Formation Rate in Galaxies. II. Power Spectrum Distribution on the Main Sequence

Abstract We constrain the temporal power spectrum of the specific star formation rate of star-forming galaxies, using a well-defined sample of main sequence galaxies from MaNGA and our earlier measurements of the ratio of the star formation rate averaged within the last 5 Myr to that averaged over the last 800 Myr. We explore the assumptions of stationarity and ergodicity that are implicit in this approach. We assume a single power-law form of the power spectrum distribution (PSD) but introduce an additional free parameter, the “intrinsic scatter”, to try to account for any non-ergodicity introduced from various sources. We analyze both an “integrated” sample consisting of global measurements of all of the galaxies, as well as 25 subsamples obtained by considering five radial regions and five bins of integrated stellar mass. Assuming that any intrinsic scatter is not the dominant contribution to the main sequence dispersion of galaxies, we find that the PSDs have slopes between 1.0 and 2.0, indicating that the power (per log interval of frequency) is mostly contributed by longer-timescale variations. We find a correlation between the returned PSDs and the inferred gas depletion times ( ) obtained from application of the extended Schmidt Law, such that regions with shorter gas depletion times show larger integrated power and flatter PSD. Intriguingly, it is found that shifting the PSDs by the inferred causes all 25 PSDs to closely overlap, at least in the region where the PSD is best constrained and least affected by uncertainties about any intrinsic scatter. A possible explanation for these results is the dynamical response of the gas-regulator system of Lilly et al. to a uniform time-varying inflow, as previously proposed in Wang et al.

Flood hazard mapping incorporating multiple probability models

Hazard mapping is essential for risk assessment and mitigation measurement design in flood prone areas. In Europe, long-term fluvial stage data, acquired since the 18th century, represent a resource of fundamental importance in this perspective, especially where rivers monitoring is completed by multiple stations distributed along the course. In these conditions, a major challenge is represented by the possibility of incorporating multiple probability models, representative of river dynamics at different distance from the mouth, in flood hazard estimation over so large areas. In this paper, we propose a new procedure of hazard estimation based on LiDAR derived flood inundation model and multiple hydrometric time series that, using a specifically developed algorithm/code of interpolation/assignation of multiple probability models, has the potential to work at local to national scale providing reliable estimation also in presence of urban areas. We applied the developed procedure and associated algorithm/code to a selected study area in southern Italy, recently hit by a destructive flood event, and quantitatively evaluate model performance. Confidence interval computation provides an overview of uncertainty related to flood magnitude estimation by extreme value analysis, indicating a substantial uncertainty related to 500 years flood magnitude estimation. Sensitivity analysis indicates a high degree of robustness of the developed procedure. Result validation through comparison against the observed 2015 flood event indicates that the method has the potential to support flood hazard analysis at regional to national scale. Limits of method application are related to the basic assumption of stationarity of hydrologic time series that might be considered too “simplicistic” in a changing climate also related to the limited length of some time series that only in few cases have no discontinuities. The absence of propagation modelling as part of the estimation procedure might be considered as an additional limit since in complex topographic and hydrological conditions it might provide a better evaluation of flood hazard. However, comparison of the 500 years flood derived from our procedure and 500 years flood scenarios derived by 2D hydraulic simulations indicate the capabilities of our procedure in identifying area floodable by specific events with only local overestimation that generally increase safety in human life protection perspective. This confirms the potential of considering multiple probability models distributed along the river course in flood hazard estimation perspective and indicate that our procedure can be a valid alternative to simulation based flood hazard estimation procedures.

Web-Based Tool for the Development of Intensity Duration Frequency Curves under Changing Climate at Gauged and Ungauged Locations

Rainfall Intensity–Duration–Frequency (IDF) curves are among the most essential datasets used in water resources management across the globe. Traditionally, they are derived from observations of historical rainfall, under the assumption of stationarity. Change of climatic conditions makes use of historical data for development of IDFs for the future unreliable, and in some cases, may lead to underestimated infrastructure designs. The IDF_CC tool is designed to assist water professionals and engineers in producing IDF estimates under changing climatic conditions. The latest version of the tool (Version 4) provides updated IDF curve estimates for gauged locations (rainfall monitoring stations) and ungauged sites using a new gridded dataset of IDF curves for the land mass of Canada. The tool has been developed using web-based technologies and takes the form of a decision support system (DSS). The main modifications and improvements between version 1 and the latest version of the IDF_CC tool include: (i) introduction of the Generalized Extreme value (GEV) distribution; (ii) updated equidistant matching algorithm (QM); (iii) gridded IDF curves dataset for ungauged location and (iv) updated Climate Models.

Application of Markovian models for non-ergodic and non-stationary earthquake times series for the identification of seismic patterns and future projections*

The current earthquake forecast algorithms are not free of shortcomings due to inherent limitations. Especially, the requirement of stationarity in the evaluation of earthquake time series as a prerequisite, significantly limits the use of forecast algorithms to areas where stationary data is not available. Another shortcoming of forecast algorithms is the ergodicity assumption, which states that certain characteristics of seismicity are spatially invariant. In this study, a new earthquake forecast approach is introduced for the locations where stationary data are not available. For this purpose, the spatial activity rate density for each spatial unit is evaluated as a parameter of a Markov chain. The temporal pattern is identified by setting the states at certain spatial activity rate densities. By using the transition patterns between the states, 1- and 5-year forecasts were computed. The method is suggested as an alternative and complementary to the existing methods by proposing a solution to the issues of ergodicity and stationarity assumptions at the same time.

Posterior inference for sparse hierarchical non-stationary models

Gaussian processes are valuable tools for non-parametric modelling, where typically an assumption of stationarity is employed. While removing this assumption can improve prediction, fitting such models is challenging. Hierarchical models are constructed based on Gaussian Markov random fields with stochastic spatially varying parameters. Importantly, this allows for non-stationarity while also addressing the computational burden through a sparse banded representation of the precision matrix. In this setting, efficient Markov chain Monte Carlo (MCMC) sampling is challenging due to the strong coupling a posteriori of the parameters and hyperparameters. Three adaptive MCMC schemes are developed and compared making use of banded matrix operations for faster inference. Furthermore, a novel extension to higher dimensional input spaces is proposed through an additive structure that retains the flexibility and scalability of the model, while also inheriting interpretability from the additive approach. A thorough assessment of the efficiency and accuracy of the methods in nonstationary settings is presented for both simulated experiments and a computer emulation problem.

Evaluating quantitative pollen representation of vegetation in the tropics: A case study on the Hainan Island, tropical China

Complex pollen-vegetation relationships in tropical environments have long been a challenge for the interpretation of pollen spectra in terms of vegetation cover. Here, we test the application of the widely-used Extended R-Value (ERV) model in the tropical secondary and planted woodlands of the Hainan Island (China) to estimate relative pollen productivities (RPPs) for common plant taxa occurring as pollen in surface and fossil samples of the region. We collected pollen (soil samples) and related vegetation data within 1500 m radius at 23 random distributed sites within an area of 50 km × 100 km. We found a large difference between the modern pollen assemblages and the related vegetation composition in terms of number and dominance of taxa. We tested the three existing ERV sub-models and three methods to distance-weight vegetation cover, i.e. 1/d, the Prentice’s model (using a Gaussian Plume dispersal model, GPM), and the Lagrangian stochastic dispersal model (LSM). The LSM appears to be inappropriate for our dataset. The combination of ERV sub-model 2 and Prentice’s model using nine anemophilous and zoophilous (or with “messy” pollination syndrome) taxa was found to provide the best results. The relevant source area of pollen (RSAP) of the soil samples was estimated to ca. 1000–1500 m. The ranking of RPPs is as follows: Castanopsis-Lithocarpus (19.44 ± 0.17) > Asteraceae (8.74 ± 0.05) > Moraceae (6.52 ± 0.08) > Euphorbiaceae (5.22 ± 0.1) > Papilionaceae (2.66 ± 0.05) > Mallotus-Macaranga (2.21 ± 0.08) > Anacardiaceae (1.77 ± 0.04) > Rubiaceae (1.29 ± 0.02) > Poaceae (=1). Violation of the ERV model assumptions of anemophily and stationarity of vegetation composition influenced the performance of the ERV analysis in this study and implied careful evaluation of the results. Nevertheless, the obtained RPPs are considered reliable and will allow to quantify the relative cover of the nine plant taxa in the past. Further studies of this kind will be worthwhile to obtain additional RPP values for a larger number of tropical taxa, even though quantification of past plant cover in the tropics will remain a challenge. The numerous zoophilous taxa may either be absent of the pollen record, or exhibit pollen-vegetation relationships for which the ERV-model is not successful in estimating RPPs. These plant taxa will require other approaches for their quantification in the past.

Choice of clear-sky model in solar forecasting

This paper is concerned with the choice of clear-sky model in solar forecasting. This issue is discussed from three perspectives: (1) accessibility, (2) forecast performance, and (3) statistical properties. Accessibility refers to the time and effort involved in obtaining clear-sky irradiance through a clear-sky model. Forecast performance is analyzed through a new concept called “mean square error (MSE) scaling,” which allows one to decompose the MSE of reference irradiance forecasts into three terms, each carrying a notion of predictability. The decomposition, however, resides on the assumption that the clear-sky index time series is stationary. In this regard, the stationarity assumption is investigated using statistical hypotheses. It is found that even the best clear-sky models, such as the REST2 model, are not able to produce a stationary clear-sky index time series. Instead, the time series is only local stationary, which, in the present context, means that its statistical properties change slowly with the value of clear-sky irradiance. Contrary to the common belief that a better clear-sky model leads to better forecasts, no evidence suggests that the more intricate REST2 has an advantage over the simpler Ineichen–Perez model, in terms of forecast performance. In that, accessibility becomes the primary concern when opting a clear-sky model for forecasting purposes. At this point, the McClear model, available as a web service for worldwide locations at 1-, 15-, and 60-min resolutions, is highly recommended.

Psychometric network models from time-series and panel data

Researchers in the field of network psychometrics often focus on the estimation of Gaussian graphical models (GGMs)—an undirected network model of partial correlations—between observed variables of cross-sectional data or single-subject time-series data. This assumes that all variables are measured without measurement error, which may be implausible. In addition, cross-sectional data cannot distinguish between within-subject and between-subject effects. This paper provides a general framework that extends GGM modeling with latent variables, including relationships over time. These relationships can be estimated from time-series data or panel data featuring at least three waves of measurement. The model takes the form of a graphical vector-autoregression model between latent variables and is termed the ts-lvgvar when estimated from time-series data and the panel-lvgvar when estimated from panel data. These methods have been implemented in the software package psychonetrics, which is exemplified in two empirical examples, one using time-series data and one using panel data, and evaluated in two large-scale simulation studies. The paper concludes with a discussion on ergodicity and generalizability. Although within-subject effects may in principle be separated from between-subject effects, the interpretation of these results rests on the intensity and the time interval of measurement and on the plausibility of the assumption of stationarity.

Paleo-hydrologic reconstruction of 400 years of past flows at a weekly time step for major rivers of Western Canada

Abstract. The assumption of stationarity in water resources no longer holds, particularly within the context of future climate change. Plausible scenarios of flows that fluctuate outside the envelope of variability of the gauging data are required to assess the robustness of water resource systems to future conditions. This study presents a novel method of generating weekly time step flows based on tree-ring chronology data. Specifically, this method addresses two long-standing challenges with paleo-reconstruction: (i) the typically limited predictive power of tree-ring data at the annual and sub-annual scale and (ii) the inflated short-term persistence in tree-ring time series and improper use of pre-whitening. Unlike the conventional approach, this method establishes relationships between tree-ring chronologies and naturalized flow at a biennial scale to preserve persistence properties and variability of hydrological time series. Biennial flow reconstructions are further disaggregated to weekly flow reconstructions, according to the weekly flow distribution of reference 2-year instrumental periods, identified as periods with broadly similar tree-ring properties to those of every 2-year paleo-period. The Saskatchewan River basin (SaskRB) in Western Canada is selected as a study area, and weekly flows in its four major tributaries are extended back to the year 1600. The study shows that the reconstructed flows properly preserve the statistical properties of the reference flows, particularly in terms of short- to long-term persistence and the structure of variability across timescales. An ensemble approach is presented to represent the uncertainty inherent in the statistical relationships and disaggregation method. The ensemble of reconstructed weekly flows are publicly available for download from https://doi.org/10.20383/101.0139 (Slaughter and Razavi, 2019).

Theoretical framework to surpass the Betz limit using unsteady fluid mechanics

The Betz limit expresses the maximum proportion of the kinetic energy flux incident on an energy conversion device that can be extracted from an unbounded flow. The derivation of the Betz limit requires an assumption of steady flow through a notional actuator disk that is stationary in the streamwise direction. The present derivation relaxes the assumptions of steady flow and streamwise actuator disk stationarity, which expands the physically realizable parameter space of flow conditions upstream and downstream of the actuator disk. A key consequence of this generalization is the existence of unsteady motions that can, in principle, lead to energy conversion efficiencies that exceed the Betz limit not only transiently but also in time-averaged performance. Potential physical implementations of those unsteady motions are speculated.

Flexible spatial covariance functions

We focus on the discussion of modeling processes that are observed at fixed locations of a region (geostatistics). A standard approach is to assume that the process of interest follows a Gaussian Process with some mean and (valid) covariance functions. It is common to model the covariance function as the product between a variance parameter, and a correlation function which is a function of the Euclidean distance between locations. This implies that the distribution of the process is unchanged when the origin of the index set is translated, and the process is invariant under rotation about the origin; that is the process is stationary and isotropic or homogeneous. However, the assumption of stationarity and isotropy (homogeneity) rarely holds in practice. Commonly, the correlation structures of such processes are influenced by local characteristics resulting in different behaviors in neighborhoods of different spatial locations. We review models that allow for heterogeneous covariance structures and point to some avenues of future research.

Water rights, river compacts, and legal-policy stationarity in the American West**Data sharing is not applicable to this article as no new data were created or analysed in this study.

This article examines static-data assumptions trapped in water rights and, separately, in larger interstate river compacts in the American West. These reflect assumptions of scalar stationarity embedded in water codes in western states. State water adjudications sort how much water is being used, but the resulting data are often publicly unavailable and unchanged. Interstate river compacts often divide fixed, erroneous river flow data. River compact data, based on early 20th century optimistic estimates of river flow, have not changed in policy language. At both the micro- and the macro-scale, these separate data remain fixed, complicating water management in the American West.

Pitching single-focus confocal data analysis one photon at a time with Bayesian nonparametrics.

Fluorescence time traces are used to report on dynamical properties of molecules. The basic unit of information in these traces is the arrival time of individual photons, which carry instantaneous information from the molecule, from which they are emitted, to the detector on timescales as fast as microseconds. Thus, it is theoretically possible to monitor molecular dynamics at such timescales from traces containing only a sufficient number of photon arrivals. In practice, however, traces are stochastic and in order to deduce dynamical information through traditional means-such as fluorescence correlation spectroscopy (FCS) and related techniques-they are collected and temporally autocorrelated over several minutes. So far, it has been impossible to analyze dynamical properties of molecules on timescales approaching data acquisition without collecting long traces under the strong assumption of stationarity of the process under observation or assumptions required for the analytic derivation of a correlation function. To avoid these assumptions, we would otherwise need to estimate the instantaneous number of molecules emitting photons and their positions within the confocal volume. As the number of molecules in a typical experiment is unknown, this problem demands that we abandon the conventional analysis paradigm. Here, we exploit Bayesian nonparametrics that allow us to obtain, in a principled fashion, estimates of the same quantities as FCS but from the direct analysis of traces of photon arrivals that are significantly smaller in size, or total duration, than those required by FCS.

Modeling power loss during blackouts in China using non-stationary generalized extreme value distribution

Power loss during blackouts shows an increasing complexity with the increase in the size of power grids. Traditional statistical methods based on the assumption of stationarity can lead to inappropriate assessments of blackouts. This study builds on the generalized extreme value (GEV) distribution by introducing time as a covariate to account for possible non-stationarities. The location, scale, and shape parameters of GEV are modeled step-by-step through the one-factor-at-a-time experiment. The results indicate that the GEV model of the annual maximum power loss in China exhibits a significant change of the scale parameter. By contrast, changes in location and shape parameters are not significant. Overall, the power loss during blackouts is tested to change with time, which reflects the sustained increase in the variability of power loss due to the growing size of power grids. The mean tends to be stable and the distribution type remains the same, which can be related to technological advances that improve the reliability of power grids. The non-stationary GEV model with time as a covariate can effectively analyze power loss during blackouts in China. It has the potential to be extended to describe non-stationary high-dimensional characteristics of power grids.