A tutorial on reproducing a predefined autocovariance function through AR models: application to stationary homogeneous isotropic turbulence

Sequential methods for synthetic realisation of random processes have a number of advantages compared with spectral methods. In this article, the determination of optimal autoregressive (AR) models for reproducing a predefined target autocovariance function of a random process is addressed. To this end, a novel formulation of the problem is developed. This formulation is linear and generalises the well-known Yule-Walker (Y-W) equations and a recent approach based on restricted AR models (Krenk-Møller approach, K-M). Two main features characterise the introduced formulation: (i) flexibility in the choice for the autocovariance equations employed in the model determination, and (ii) flexibility in the definition of the AR model scheme. Both features were exploited by a genetic algorithm to obtain optimal AR models for the particular case of synthetic generation of homogeneous stationary isotropic turbulence time series. The obtained models improved those obtained with the Y-W and K-M approaches for the same model parsimony in terms of the global fitting of the target autocovariance function. Implications for the reproduced spectra are also discussed. The formulation for the multivariate case is also presented, highlighting the causes behind some computational bottlenecks.

Moving beyond the classic difference-in-differences model: a simulation study comparing statistical methods for estimating effectiveness of state-level policies

Background Reliable evaluations of state-level policies are essential for identifying effective policies and informing policymakers’ decisions. State-level policy evaluations commonly use a difference-in-differences (DID) study design; yet within this framework, statistical model specification varies notably across studies. More guidance is needed about which set of statistical models perform best when estimating how state-level policies affect outcomes. Methods Motivated by applied state-level opioid policy evaluations, we implemented an extensive simulation study to compare the statistical performance of multiple variations of the two-way fixed effect models traditionally used for DID under a range of simulation conditions. We also explored the performance of autoregressive (AR) and GEE models. We simulated policy effects on annual state-level opioid mortality rates and assessed statistical performance using various metrics, including directional bias, magnitude bias, and root mean squared error. We also reported Type I error rates and the rate of correctly rejecting the null hypothesis (e.g., power), given the prevalence of frequentist null hypothesis significance testing in the applied literature. Results Most linear models resulted in minimal bias. However, non-linear models and population-weighted versions of classic linear two-way fixed effect and linear GEE models yielded considerable bias (60 to 160%). Further, root mean square error was minimized by linear AR models when we examined crude mortality rates and by negative binomial models when we examined raw death counts. In the context of frequentist hypothesis testing, many models yielded high Type I error rates and very low rates of correctly rejecting the null hypothesis (< 10%), raising concerns of spurious conclusions about policy effectiveness in the opioid literature. When considering performance across models, the linear AR models were optimal in terms of directional bias, root mean squared error, Type I error, and correct rejection rates. Conclusions The findings highlight notable limitations of commonly used statistical models for DID designs, which are widely used in opioid policy studies and in state policy evaluations more broadly. In contrast, the optimal model we identified--the AR model--is rarely used in state policy evaluation. We urge applied researchers to move beyond the classic DID paradigm and adopt use of AR models.

Brain Connectivity Estimation Pitfall in Multiple Trials of EEG Data

The electroencephalography signal is well suited to calculate brain connectivity due to its high temporal resolution. When the purpose is to compute connectivity from multi-trial EEG data, confusion arises about how these trials involved in calculating the connectivity. The purpose of this paper is to study this confusing issue using simulated and experimental data. To this end, Granger causality-based connectivity measures were considered. Using simulations, two signals were generated with known AR (Auto-Regressive) coefficients and then simple MVAR (Multivariate AR) models based on different numbers of trials were extracted. For accurate estimation of the MVAR model, the data samples should be sufficient. Two Granger causality-based connectivity, GC and PDC were estimated. Estimating connectivity corresponding to small trial numbers (5 and 10 trials) resulted in an average value of connectivity that is significantly higher and also more variable over different estimates. By increasing the number of trials, the MVAR model has fitted more appropriately to the data and the connectivity values were converged. This procedure was implemented on real EEG data. The obtained results agreed well with the findings of simulated data. The results showed that the brain connectivity should calculate for each trial, and then average the connectivity values on all trials. Also, the larger the trial numbers, the MVAR model has fitted more appropriately to the data, and connectivity estimations are more reliable.

Using Three-Dimensional Augmented Reality to Enhance General Aviation Weather Training

This work evaluates augmented reality (AR) training materials for general aviation (GA) weather training. Reviews of GA weather training identify gaps where students lack opportunities to experience weather patterns and lack the ability to correlate weather knowledge in weather-related situations. Three-dimensional (3D) visual models may help close the gaps by visualizing information about weather processes, hazards, and visual cues. A 3D AR thunderstorm model visualizes a single-cell thunderstorm clouds, winds, precipitation, lightning, and advective movement. Preliminary evaluation of the model was conducted through a subject matter expert (SME) review and a usability study. The SME review identified improvements to the model and areas for future content design. The usability study identified usability issues with the model. Insights about the design of weather visualizations are developed into recommendations. The approach will integrate 3D AR models into the weather training curriculum to create interactive print training.

Identification of Visual Imagery by Electroencephalography Based on Empirical Mode Decomposition and an Auto-Regressive Model

The traditional imagery task for brain−computer interfaces (BCIs) consists of motor imagery (MI) in which subjects are instructed to imagine moving a certain part of their body. This kind of imagery task is difficult for subjects. In this study, we used a less studied yet more easily performed type of mental imagery—visual imagery (VI)—in which subjects are instructed to visualize a picture in their brain to implement a BCI. In this study, 18 subjects were recruited and instructed to observe one of two visual-cued pictures (one was static, while the other was moving), and then imagine the cued picture in each trial. Simultaneously, electroencephalography (EEG) signals were collected. Hilbert-Huang Transform (HHT), auto-regressive (AR) models and the combination of empirical mode decomposition (EMD) and AR were used to extract features, respectively. A support vector machine (SVM) was used to classify the two kinds of VI tasks. The average, highest, and lowest classification accuracies of HHT were 68.143.06%, 78.33%, and 53.3%, respectively. The values of the AR model were 56.292.73%, 71.67%, and 30%, respectively. The values obtained by the combination of EMD and the AR model were 78.402.07%, 87%, and 48.33%, respectively. The results indicate that multiple VI tasks were separable based on EEG, and that the combination of EMD and an AR model used in VI feature extraction was better than that of an HHT or AR model alone. Our work may provide ideas for the construction of a new online VI-BCI.

Limit Theory for Stationary Autoregression with Heavy-Tailed Augmented GARCH Innovations

This paper considers stationary autoregressive (AR) models with heavy-tailed, general GARCH (G-GARCH) or augmented GARCH noises. Limit theory for the least squares estimator (LSE) of autoregression coefficient ρ=ρn is derived uniformly over stationary values in [0,1), focusing on ρn→1 as sample size n tends to infinity. For tail index α∈(0,4) of G-GARCH innovations, asymptotic distributions of the LSEs are established, which are involved with the stable distribution. The convergence rate of the LSE depends on 1−ρn2, but no condition on the rate of ρn is required. It is shown that, for the tail index α∈(0,2), the LSE is inconsistent, for α=2, logn/(1−ρn2)-consistent, and for α∈(2,4), n1−2/α/(1−ρn2)-consistent. Proofs are based on the point process and the asymptotic properties in AR models with G-GARCH errors. However, this present work provides a bridge between pure stationary and unit-root processes. This paper extends the existing uniform limit theory with three issues: the errors have conditional heteroscedastic variance; the errors are heavy-tailed with tail index α∈(0,4); and no restriction on the rate of ρn is necessary.

An integrated deterministic–stochastic approach for forecasting the long-term trajectories of COVID-19

The ongoing coronavirus disease 2019 (COVID-19) pandemic is one of the major health emergencies in decades that affected almost every country in the world. As of June 30, 2020, it has caused an outbreak with more than 10 million confirmed infections, and more than 500,000 reported deaths globally. Due to the unavailability of an effective treatment (or vaccine) and insufficient evidence regarding the transmission mechanism of the epidemic, the world population is currently in a vulnerable position. The daily cases data sets of COVID-19 for profoundly affected countries represent a stochastic process comprised of deterministic and stochastic components. This study proposes an integrated deterministic–stochastic approach to forecast the long-term trajectories of the COVID-19 cases for Italy and Spain. The deterministic component of the daily-cases univariate time series is assessed by an extended version of the SIR [Susceptible–Infected–Recovered–Protected–Isolated (SIRCX)] model, whereas its stochastic component is modeled using an autoregressive (AR) time series model. The proposed integrated SIRCX-AR (ISA) approach based on two operationally distinct modeling paradigms utilizes the superiority of both the deterministic SIRCX and stochastic AR models to find the long-term trajectories of the epidemic curves. Experimental analysis based on the proposed ISA model shows significant improvement in the long-term forecasting of COVID-19 cases for Italy and Spain in comparison to the ODE-based SIRCX model. The estimated Basic reproduction numbers for Italy and Spain based on SIRCX model are found to be [Formula: see text] and [Formula: see text], respectively. ISA model-based results reveal that the number of cases in Italy and Spain between 11 May, 2020–9 June, 2020 will be 10,982 (6383–15,582) and 13,731 (3395–29,013), respectively. Additionally, the expected number of daily cases on 9 July, 2020 for Italy and Spain is estimated to be 30 (0–183) and 92 (0–602), respectively.

Assessing the Value of a Novel Augmented Reality Application for Presurgical Planning in Adolescent Elbow Fractures

Objectives: We retrospectively assess the potential impact of a novel, investigational Augmented Reality (AR) software application, Radiology with Holographic Augmentation (RadHA), on pediatric orthopedic surgeon's confidence in surgical planning, hardware selection, hardware fit, and estimated potential intraoperative time savings in the setting of complex adolescent elbow fractures.Methods: After study selection, 12 individual cases of complex elbow fractures in adolescent pediatric patients were identified for review. AR models were generated for each case derived from the patient's CT. Five fellowship-trained pediatric orthopedic surgeons reviewed each case for a total of 60 separate observations. Surgeons reviewed clinical data, radiologic imaging, and AR models and then answered Likert Scale questions on measures of confidence in presurgical planning and projected potential time savings. These data were reviewed and analyzed using various statistical tools.Results: Surgeons reported high confidence in the quality of the AR models created. Additionally, surgeons reported increased confidence in their surgical plan, increased confidence in hardware selection, and increased confidence in hardware fit. Within the sub-analysis of complex (comminuted) fractures, surgeons reported greater expected increases in confidence of their surgical plan and hardware fit. Overall, surgeons estimated potential intraoperative time savings, averaging 17.3 min for all fracture types and 17.6 min for complex fractures.Conclusions: Preoperative planning using AR-based models can increase surgeon confidence in preoperative planning, hardware selection, and confidence in hardware fit.