Standard Deviation Of Prediction Error Research Articles

The effect of corneal power on the accuracy of 14 IOL power formulas

BackgroundThis study evaluates the impact of corneal power on the accuracy of 14 newer intraocular lens (IOL) calculation formulas in cataract surgery. The aim is to assess how these formulas perform across different corneal curvature ranges, thereby guiding more precise IOL selection.MethodsIn this retrospective case series, 336 eyes from 336 patients who underwent cataract surgery were studied. The cohort was divided into three groups according to preoperative corneal power. Key metrics analyzed included mean prediction error (PE), standard deviation of PE (SD), mean absolute prediction error (MAE), median absolute error (MedAE), and the percentage of eyes with PE within ± 0.25 D, 0.50 D, ± 0.75 D, ± 1.00 D and ± 2.00 D.ResultsIn the flat K group (Km < 43 D), VRF-G, Emmetropia Verifying Optical Version 2.0 (EVO2.0), Kane, and Hoffer QST demonstrated lower SDs (± 0.373D, ± 0.379D, ± 0.380D, ± 0.418D, respectively) compared to the VRF formula (all P < 0.05). EVO2.0 and K6 showed significantly different SDs compared to Barrett Universal II (BUII) (all P < 0.02). In the medium K group (43 D ≤ Km < 46 D), VRF-G, BUII, Karmona, K6, EVO2.0, Kane, and Pearl-DGS recorded lower MAEs (0.307D to 0.320D) than Olsen (OLCR) and Castrop (all P < 0.03), with RBF3.0 having the second lowest MAE (0.309D), significantly lower than VRF and Olsen (OLCR) (all P < 0.05). In the steep K group (Km ≥ 46D), RBF3.0, K6, and Kane achieved significantly lower MAEs (0.279D, 0.290D, 0.291D, respectively) than Castrop (all P < 0.001).ConclusionsThe study highlights the varying accuracy of newer IOL formulas based on corneal power. VRF-G, EVO2.0, Kane, K6, and Hoffer QST are highly accurate for flat corneas, while VRF-G, RBF3.0, BUII, Karmona, K6, EVO2.0, Kane, and Pearl-DGS are recommended for medium K corneas. In steep corneas, RBF3.0, K6, and Kane show superior performance.

A unified prediction approach of fatigue life suitable for diversified engineering materials

Investigation on fatigue life prediction approaches for welded joints of different materials was of great significance for the reliability and safety of engineering structures. A fatigue performance dataset with sufficient characteristics was established via data processing and augmentation. The modification of loss function and the physics-informed influencing factors was used to realize the multi-level physical intervention on the prediction model. The importance of physics-informed influencing factors under mechanical-properties dataset was analyzed and integrated into the deep convolutional neural network (DCNN) framework via attention model. The significance of the intervention using physics-informed influencing factors and the identification using mechanical properties was proved via the comparison of different prediction methods. Further, a mechanical properties-based prediction method for fatigue life of multiple materials was established, and the average prediction error (30.5%) and standard deviation of prediction error (16.1%) of the proposed approach were significantly lower than that of the other prediction methods. By the identification via mechanical properties and the introduction of physics-informed influencing factors, the machine learning method can be used to evaluate the fatigue life of multiple materials in engineering with low consumption.

Intraocular lens power calculation in eyes with a shallow anterior chamber depth and normal axial length.

We compared the accuracy of three intraocular lens (IOL) calculation formulas in eyes with a shallow anterior chamber depth (ACD) and normal axial length (AXL) and control eyes. We retrospectively reviewed eyes with a shallow ACD (<2.5 mm from the corneal epithelium) with normal AXL (22.5≤AXL<24.0 mm) and controls (3.0≤ACD<3.5 mm and normal AXL). Prediction error (PE) and median absolute error (MedAE) were evaluated with SRK/T, Barrett Universal II (BUII), and Kane formulas after adjusting the mean PE to zero for all patients. Percentages of eyes achieving a PE within 0.25 to 1.00 D, and correlations between ACD, lens thickness (LT), and PE were analyzed. Thirty-five shallow ACD and 63 control eyes were included. PE in the shallow ACD group showed more hyperopic results with BUII and Kane but not with SRK/T compared to controls. Within the shallow ACD group, PE showed more hyperopic results in BUII and Kane compared to SRK/T. However, the standard deviation (SD) of PE among formulas was not different. In the shallow ACD group, SRK/T showed a higher percentage of PE within 0.25 D than BUII and Kane, but the percentages within 0.50 to 1.00 D were similar. PE was negatively correlated with ACD in BUII and Kane, and positively correlated with LT in all formulas. BUII and Kane may induce slight hyperopic shift in eyes with a shallow ACD and normal AXL. However, the performance of the three formulas was comparable in the shallow ACD group in terms of MedAE, the SD of PE, and the percentage of eyes achieving PE within 0.50 D.

The Zhu-Lu formula: a machine learning-based intraocular lens power calculation formula for highly myopic eyes

BackgroundTo develop a novel machine learning-based intraocular lens (IOL) power calculation formula for highly myopic eyes.MethodsA total of 1828 eyes (from 1828 highly myopic patients) undergoing cataract surgery in our hospital were used as the internal dataset, and 151 eyes from 151 highly myopic patients from two other hospitals were used as external test dataset. The Zhu-Lu formula was developed based on the eXtreme Gradient Boosting and the support vector regression algorithms. Its accuracy was compared in the internal and external test datasets with the Barrett Universal II (BUII), Emmetropia Verifying Optical (EVO) 2.0, Kane, Pearl-DGS and Radial Basis Function (RBF) 3.0 formulas.ResultsIn the internal test dataset, the Zhu-Lu, RBF 3.0 and BUII ranked top three from low to high taking into account standard deviations (SDs) of prediction errors (PEs). The Zhu-Lu and RBF 3.0 showed significantly lower median absolute errors (MedAEs) than the other formulas (all P < 0.05). In the external test dataset, the Zhu-Lu, Kane and EVO 2.0 ranked top three from low to high considering SDs of PEs. The Zhu-Lu formula showed a comparable MedAE with BUII and EVO 2.0 but significantly lower than Kane, Pearl-DGS and RBF 3.0 (all P < 0.05). The Zhu-Lu formula ranked first regarding the percentages of eyes within ± 0.50 D of the PE in both test datasets (internal: 80.61%; external: 72.85%). In the axial length subgroup analysis, the PE of the Zhu-Lu stayed stably close to zero in all subgroups.ConclusionsThe novel IOL power calculation formula for highly myopic eyes demonstrated improved and stable predictive accuracy compared with other artificial intelligence-based formulas.

Comparison of the accuracy of nine intraocular lens power calculation formulas using partial coherence interferometry.

Cataract surgery is the most performed procedure in the world. To achieve the target refraction, several intraocular lens (IOL) power calculation formulas have been developed to improve the accuracy of IOL power predictions. We compared the accuracy of 9 IOL power calculation formulas (SRK/T, Hoffer Q, Holladay 1, Haigis, Barrett Universal II, Kane, EVO 2.0, Ladas Super formula and Hill-RBF 3.0) using partial coherence interferometry (PCI). We collected data from patients who underwent uncomplicated cataract surgery with implantation of 1 of 3 IOL types currently used in our center. All preoperative biometric measurements were performed using PCI. Prediction errors (PE) were deduced from refractive outcomes evaluated 3 months after surgery. The mean prediction error (ME), mean absolute prediction error (MAE), median absolute prediction error (MedAE), and standard deviation of prediction error (SD) were calculated, as well as the percentage of eyes with a PE within ±0.25, ±0.50, ±0.75 and ±1.00D for each formula. We included 126 eyes of 126 patients. Kane achieved the lowest MAE and SD across the entire sample as well as the highest percentage of PE within ±0.50D and was shown to be more accurate than Haigis and Hoffer Q (P<001). For an axial length of more than 26.0mm, EVO 2.0 and Barrett obtained the lowest MAEs, with EVO 2.0 and Kane showing a higher percentage of prediction at ±0.50D compared to old generation formulas except for SRK/T (P=04). All investigated formulas achieved good results; there was a tendency toward better outcomes with new generation formulas, especially in atypical eyes.

Deep Learning-Based Path Loss Model in Urban Environments Using Image-to-Image Translation

Ray-tracing techniques offer accurate predictions on path loss but suffer from high computational complexity. To have a fast and accurate path loss prediction, this article applies a deep learning-based image-to-image translation technique to construct a path loss model in urban environments. The proposed method combines a variational autoencoder with a generative adversarial network to translate images from the domain of street maps to the domain of path loss. It is trained in a supervised manner using paired samples, where the input is the street map with 3-D building information and the output is the path loss in the area obtained from the ray-tracing model. Based on a realistic digital map of urban Taipei city, simulation results show that the proposed model outperforms conventional ones when operating at the 3.5 GHz frequency band. The standard deviation of prediction error is reduced by over 62%. Besides prediction accuracy, the proposed model has the advantage of low computational complexity over ray-tracing techniques. Hence, it has great potential for the deployment of unmanned aerial vehicle-mounted base stations (UAV-BSs) for future communication systems. In this future work, the optimal UAV mobility can be determined upon the rapid evaluation of the UAV-BS coverage using the proposed model.

Application of total keratometry in ten intraocular lens power calculation formulas in highly myopic eyes.

BackgroundThe accuracy of using total keratometry (TK) value in recent IOL power calculation formulas in highly myopic eyes remained unknown.MethodsHighly myopic patients who underwent uneventful cataract surgery were prospectively enrolled in this prospective comparative study. At one month postoperatively, standard deviation (SD) of the prediction errors (PEs), mean and median absolute error (MedAE) of 103 highly myopic eyes were back-calculated and compared among ten formulas, including XGboost, RBF 3.0, Kane, Barrett Universal II, Emmetropia Verifying Optical 2.0, Cooke K6, Haigis, SRK/T, and Wang-Koch modifications of Haigis and SRK/T formulas, using either TK or standard keratometry (K) value.ResultsIn highly myopic eyes, despite good agreement between TK and K (P > 0.05), larger differences between the two were associated with smaller central corneal thickness (P < 0.05). As to the refractive errors, TK method showed no differences compared to K method. The XGBoost, RBF 3.0 and Kane ranked top three when considering SDs of PEs. Using TK value, the XGboost calculator was comparable with the RBF 3.0 formula (P > 0.05), which both presented smaller MedAEs than others (all P < 0.05). As for the percentage of eyes within ± 0.50 D or ± 0.75 D of PE, the XGBoost TK showed comparable percentages with the RBF 3.0 TK formula (74.76% vs. 66.99%, or 90.29% vs. 87.38%, P > 0.05), and statistically larger percentages than the other eight formulas (P < 0.05).ConclusionsHighly myopic eyes with thinner corneas tend to have larger differences between TK and K. The XGboost enhancement calculator and RBF 3.0 formula using TK showed the most promising outcomes in highly myopic eyes.Supplementary InformationThe online version contains supplementary material available at 10.1186/s40662-022-00293-3.

Strategies for formula constant optimisation for intraocular lens power calculation

BackgroundTo investigate modern nonlinear iterative strategies for formula constant optimisation and show the application and results from a large dataset using a set of disclosed theoretical-optical lens power calculation concepts.MethodsNonlinear iterative optimisation algorithms were implemented for optimising the root mean squared (SoSPE), the mean absolute (SoAPE), the mean (MPE), the standard deviation (SDPE), the median (MEDPE), as well as the 90% confidence interval (CLPE) of the prediction error (PE), defined as the difference between postoperative achieved and formula predicted spherical equivalent power of refraction. Optimisation was performed using the Levenberg-Marquardt algorithm (SoSPE and SoAPE) or the interior point method (MPE, SDPE, MEDPE, CLPE) for the SRKT, Hoffer Q, Holladay 1, Haigis, and Castrop formulae. The results were based on a dataset of measurements made on 888 eyes after implantation of an aspherical hydrophobic monofocal intraocular lens (Vivinex, Hoya).ResultsFor all formulae and all optimisation metrics, the iterative algorithms showed a fast and stable convergence after a couple of iterations. The results prove that with optimisation for SoSPE, SoAPE, MPE, SDPE, MEDPE, and CLPE the root mean squared PE, mean absolute PE, mean PE, standard deviation of PE, median PE, and confidence interval of PE could be minimised in all situations. The results in terms of cumulative distribution function are quite coherent with optimisation for SoSPE, SoAPE, MPE and MEDPE, whereas with optimisation for SDPE and CLPE the standard deviation and confidence interval of the PE distribution could only be minimised at the cost of a systematic offset in mean and median PE.ConclusionNonlinear iterative techniques are capable of minimising any statistical metrics (e.g. root mean squared or mean absolute error) of any target parameter (e.g. PE). These optimisation strategies are an important step towards optimising for the target parameters which are used for evaluating the performance of lens power calculation formulae.

Path loss modelling based on path profile in urban propagation environments

This paper presents a path loss model based on path profile in urban propagation environments for 5G systems. Although deep learning approaches are indeed powerful in tasks involving prediction or classification, they often lack transparency and suffer from high computational complexity. The proposed model combines the log-distance path loss model for line-of-sight propagation scenarios and a machine-learning-based model for non-line-of-sight (NLOS) cases. This paper uses the principal component analysis algorithm to extract relevant features out of some selected attributes of the path profile for NLOS cases. Then, the path loss model can be constructed based on the approach of polynomial regression. Simulation results show that the proposed model outperforms the conventional models when operating in the 3.5 GHz frequency band. The standard deviation of prediction error was reduced by about 22.2–37.2% dB when compared to the conventional models. Furthermore, the prediction performance was also evaluated in a non-standalone 5G New Radio network in the urban environment of Taipei city. The real-world measurements show that the standard deviation of prediction error can be reduced by 3.33–6.13 dB when compared to the conventional models.

Explainable Deep-Learning-Based Path Loss Prediction from Path Profiles in Urban Environments

This paper applies a deep learning approach to model the mechanism of path loss based on the path profile in urban propagation environments for 5G cellular communication systems. The proposed method combines the log-distance path loss model for line-of-sight propagation scenarios and a deep-learning-based model for non-line-of-sight cases. Simulation results show that the proposed path loss model outperforms the conventional models when operating in the 3.5 GHz frequency band. The standard deviation of prediction error was reduced by 34% when compared to the conventional models. To explain the internal behavior of the proposed deep-learning-based model, which is a black box in nature, eight relevant features were selected to model the path loss based on a linear regression approach. Simulation results show that the accuracy of the explanatory model reached 72% when it was used to explain the proposed deep learning model. Furthermore, the proposed deep learning model was also evaluated in a non-standalone 5G New Radio network in the urban environment of Taipei City. The real-world measurements show that the standard deviation of prediction error can be reduced by 30–43% when compared to the conventional models. In addition, the transparency of the proposed deep learning model reached 63% in the realistic 5G network.

Developing variable moving window PLS models: Using case of NOx emission prediction of coal-fired power plants

The efficiency of selective catalytic reduction denitrification heavily depends on the amount of ammonia injection, which is determined by the emission of nitrogen oxides (NOx) in flue gas. To accurately predict NOx emission of the coal-fired boiler with strong variable correlations, nonlinear and time-varying characteristics for determining the amount of injected ammonia, a soft sensor modeling method based on the moving window partial least squares (MWPLS) and locally weighted regression, referred to as variable exponentially weighted MWPLS (VEW-MWPLS), is proposed. It adjusts the window size in disguised form by automatically strengthen or weaken the information in the selected window according to the prediction errors of the current model. In this work, with the added new sample and the removed old sample, a series of rank-1 modification formulations are used to calculate both, the means and standard deviations among the input and output variables and the covariance and cross-covariance matrices so that a quick and adaptive update can be done for the PLS model. The numerical results have demonstrated that VEW-MWPLS algorithm can reduce the mean and standard deviation of prediction errors by one order of magnitude, and reduce the computational complexity by two orders of magnitude when being compared with other algorithms. Thus the proposed VEW-MWPLS is more suitable for predicting NOx emission online.

Towards vendor-agnostic real-time optical network design with extended Kalman state estimation and recurrent neural network machine learning [Invited

The network operator’s call for open, disaggregated optical networks to accelerate innovation and reduce cost, make progress in the standardization of interfaces, and raise telemetry capabilities in optical network systems has created an opportunity to adopt a new paradigm for optical network design. This new paradigm is driven by direct measurement and continuous learning from the actual optical hardware deployed in the field. We report an approach towards practical, vendor-agnostic, real-time optical network design and network management using a combination of two learning models. We generalize our physics-based optical model parameter estimation algorithm using the extended Kalman state estimation theory and, for the first time, to the best of our knowledge, present results using real optical network field data. An observed 0.3 dB standard deviation of the difference between typical predicted and measured signal quality appears mostly attributable to transponder performance variance. We further propose using the physics-based optical model parameter values as inputs to a second learning model with a recurrent neural network such as a gated recurrent unit (GRU) to allocate the appropriate required optical margin relative to the typical signal quality predicted by the physics-based optical model. A proof of concept shows that for a dataset of 3000 optical connections with a wide variety of amplified spontaneous emission noise and nonlinear noise limited conditions, a 10-hidden-unit 2-layer GRU was sufficient to realize a margin prediction error standard deviation below 0.2 dB. This approach of measurement data-driven automated network design will simplify deployment and enable efficient operation of open optical networks.

A machine learning-based framework for delivery error prediction in proton pencil beam scanning using irradiation log-files.

This study aims to investigate the use of machine learning models for delivery error prediction in proton pencil beam scanning (PBS) delivery. A dataset of planned and delivered PBS spot parameters was generated from a set of 20 prostate patient treatments. Planned spot parameters (spot position, MU and energy) were extracted from the treatment planning system (TPS) for each beam. Delivered spot parameters were extracted from irradiation log-files for each beam delivery following treatment. The dataset was used as a training dataset for three machine learning models which were trained to predict delivered spot parameters based on planned parameters. K-fold cross validation was employed for hyper-parameter tuning and model selection where the mean absolute error (MAE) was used as the model evaluation metric. The model with lowest MAE was then selected to generate a predicted dose distribution for a test prostate patient within a commercial TPS. Analysis of the spot position delivery error between planned and delivered values resulted in standard deviations of 0.39mm and 0.44mm forxand y spot positions respectively. Prediction error standard deviation values of spot positions using the selected model were 0.22mm and 0.11mm forxand y spot positions respectively. Finally, a three-way comparison of dose distributions and DVH values for select OARs indicates that the random-forest-predicted dose distribution within the test prostate patient was in closer agreement to the delivered dose distribution than the planned distribution. PBS delivery error can be accurately predicted using machine learning techniques.

Micromechanical model for rapid prediction of plain weave fabric composite strengths under biaxial tension

The biaxial properties of plain weave fabric composites are important as they are more representative of the performance under complex loading conditions. Experimental determination of these properties is difficult and Finite Element Analysis provides accurate prediction but is computationally expensive and requires skilled users. To provide a simple and rapid prediction of the strength of plain weave fabric composites under biaxial tension a novel micromechanical model is proposed in this paper. To predict the biaxial tensile strengths the minimum total complementary potential energy principle is used on a micromechanical unit cell where the orthogonally interlaced yarns are idealised as curved beams. The new model is verified with a finite element method model on three warp/weft biaxial loading ratios: 1:1, 2:1 (1:2) and 3:1 (1:3) and uniaxial experimental data. The model is verified on four types of material, ranging in mechanical properties from carbon to glass fibres, and 11 yarn specifications, including five cases compared to experimental results and six cases compared to the FE model, giving a mean error of 9.85% and a maximum error of 16.74% compared to experimental results and a mean error of 10.71% and a maximum error of 14.67% compared to the FE model, which demonstrates the effectiveness of the model. The standard deviation of prediction errors among the 11 cases is 2.66%, which demonstrates the robustness of the model for a range of applications. The proposed model is able to predict the uniaxial and biaxial tensile strengths without experimental investigations at the fabric and laminate level and only requires the yarn mechanical properties and specifications.

Impact of baseline coronary flow and its distribution on fractional flow reserve prediction.

Model-based prediction of fractional flow reserve (FFR) in the context of stable coronary artery disease (CAD) diagnosis requires a number of modelling assumptions. One of these assumptions is the definition of a baseline coronary flow, ie, total coronary flow at rest prior to the administration of drugs needed to perform invasive measurements. Here we explore the impact of several methods available in the literature to estimate and distribute baseline coronary flow on FFR predictions obtained with a reduced-order model. We consider 63 patients with suspected stable CAD, for a total of 105 invasive FFR measurements. First, we improve a reduced-order model with respect to previous results and validate its performance versus results obtained with a 3D model. Next, we assess the impact of a wide range of methods to impose and distribute baseline coronary flow on FFR prediction, which proved to have a significant impact on diagnostic performance. However, none of the proposed methods resulted in a significant improvement of prediction error standard deviation. Finally, we show that intrinsic uncertainties related to stenosis geometry and the effect of hyperemic inducing drugs have to be addressed in order to improve FFR prediction accuracy.

Assessment of the various soft computing techniques to predict sodium absorption ratio (SAR)

ABSTRACT In this investigation, the performance of the four soft computing techniques, that is M5P model tree, random forest (RF), bagging M5P model tree and group method for data handling (GMDH) were compared to estimate the sodium absorption ratio (SAR). Total data set consists of water quality of three (Alsthar, Biranshahr and Khoramabad in Iran) watershed out of which 70% data used to train the model and 30% data were used to test the model. The models’ accuracy were assessed using three performance evaluation parameters, which were correlation coefficient (C.C.), root mean square error (RMSE) and maximum absolute error (MAE). The obtained results suggest that the bagging M5P model tree regression technique (with C.C. = 0.9993, RMSE = 0.0097 and MAE = 0.006) is more accurate to estimate the SAR as compare to the M5P model tree, RF and GMDH for the given study area. Uncertainty analysis also suggested the same trends with minimum mean prediction error, standard deviation of prediction error and width of uncertainty band. Further, a comparison was also done with the previous study which also shows bagging M5P model tree predicts the SAR accurately.

A probabilistic approach for the quantification of prediction error in deterministic phase-resolved wave forecasting

This paper presents a semi-analytical methodology for the determination of prediction error statistics in deterministic sea wave predictions (DSWP), based on linear wave models. The underlying wave elevation is modelled as a Gaussian stochastic process and the coefficients of the wave propagation model are assumed to be determined by linear fitting on available measurements in time and/or space. The possible data contamination due to measurement error is also explicitly considered. The resulting approach eventually provides a Linear Estimator of Prediction Error (LEPrE) in time and space, in terms of prediction error standard deviation, given the fitting procedure and the sea spectrum. The presented approach allows supplementing deterministic predictions based on phase-resolved linear wave models with a sound prediction error measure, and allows defining the concept of “Predictability Region” in a consistent probabilistic framework. Example applications are reported, both for long-crested and short-crested waves, with verification through Monte Carlo simulations. Single point wave gauge/wave buoy measurements as well as wave radar measurements have been considered as simulated examples. The developed methodology is also compared with existing approaches highlighting and discussing both the differences and the interesting qualitative commonalities.

SSC and pH for sweet assessment and maturity classification of harvested cherry fruit based on NIR hyperspectral imaging technology

The relationships between soluble solids content (SSC) and pH cherry fruit of different maturity stages has been investigated using near-infrared (NIR) hyperspectral imaging technology. Using 550 fruit, 11 hyperspectral images in the 874–1734 nm region were captured and compared with SSC and pH measured by standard methods. Two types of models based on full bands, namely principal components regression model and partial least squares regression model, showed similar predictive ability. To reduce the modeling complexity based on full bands, a genetic algorithm (GA) and a successive projections algorithm were employed to select feature bands; both algorithms were tested by multiple linear regression (MLR). By comparing the results of different modeling methods, GA-MLR was selected as the final modeling method with a ratio of standard deviation of prediction set to standard deviation of prediction error of 2.7 for SSC and 2.4 for pH. SSC and pH distribution maps were generated by inputting the feature bands of each pixel into GA-MLR models. Classification of fruit maturity stages was studied, and a linear discrimination analysis method produced a correct classification ratio of 96.4%. We conclude that it is feasible to detect the quality of cherry fruit by NIR hyperspectral imaging technology.

Regional eco-efficiency prediction with Support Vector Spatial Dynamic MIDAS

To obtain good eco-efficiency prediction with factors accompanied by spatial relationship, mixed frequency data and nonlinearity, based on the existing spatial panel data forecasting models and MIxed DAta Sampling (MIDAS), we established Support Vector Spatial Dynamic MIDAS to incorporate the spatial interaction, different frequencies of sampling data, and non-linear relationship between the eco-efficiency and various factors. Further to testify the effectiveness, we applied the new model to regional eco-efficiency prediction in China. Prediction Error of the Last Year, Mean Percentage Error, Mean Square of Prediction Error and Standard Deviation of Prediction Error were utilized to measure prediction accuracy. Results showed SVSD-MIDAS effectively considered the mixed frequency factors--Financial Development Level, Foreign Direct Investment, Urbanization Level, Price Index, Fixed Asset Investment and their spatial interaction. Prediction performances of 30 regions are very good, with low prediction error below 1% or smaller. And regional prediction characteristics in the eastern, central, western and northeast regions were compared. The different spatial weights impacted the prediction no matter in individual province or the whole 4 areas. Accurate prediction by SVSD-MIDAS can save costs of collecting and calculating indicators, and guide the formulation of regional sustainable development strategies of residents, business managers, government departments in advance.

Comparison of prediction performances between Box–Jenkins and Kalman filter models––Case of annual and monthly sreamflows in Algeria

The present study aims to investigate and to compare Box–Jenkins (BJ) and Kalman filter (KF) models to predict stream flows in northern Algeria. For this purpose, annual and monthly data of 10 hydrometric stations have been considered for application. The results with BJ models led to five Autoregressive and integrated moving average (ARIMA) models for the annual streamflows, with an overall mean explained variance at 63% level, whereas for the monthly flows they led to 10 Seasonal Autoregressive and integrated moving average (SARIMA) models, with an overall mean explained variance around 75%. On the other hand, KF methodology led to two on-line operations, where multisite optimal annual and monthly predictions are obtained. The KF and BJ predictive performances are then compared via some statistical parameters of their prediction error. For both of annual and monthly scales, it is found that KF model performs better in predictions. For example, the mean prediction error for KF is 16 times smaller than the BJ models, the corresponding standard deviation, minimum and maximum values are respectively, 5, 6, and 3 times smaller than the BJ alternatives. This denotes the superiority of KF for the prediction of stream flows in northern Algeria. In addition, an eventual tendency of KF to the underestimation has also been noticed from the prediction error standard deviation illustration.