Ridge Estimation's Effectiveness for Multiple Linear Regression with Multicollinearity: An Investigation Using Monte-Carlo Simulations

The goal of this research is to compare multiple linear regression coefficient estimations with multicollinearity. In order to quantify the effectiveness of estimations by the mean of average mean square error, the ordinary least squares technique (OLS), modified ridge regression method (MRR), and generalized Liu-Kejian method (LKM) are compared (AMSE). For this study, the simulation scenarios are 3 and 5 independent variables with zero mean normally distributed random error of variance 1, 5, and 10, three correlation coefficient levels; i.e., low (0.2), medium (0.5), and high (0.8) are determined for independent variables, and all combinations are performed with sample sizes 15, 55, and 95 by Monte Carlo simulation technique for 1,000 times in total. As the sample size rose, the AMSE decreased. The MRR and LKM both outperformed the LSM. At random error of variance 10, the MRR is the most suitable for all circumstances.

Pandemic management by a spatio–temporal mathematical model

Many researchers have tried to predict the impact of the COVID-19 outbreak on morbidity, in order to help policy-makers find optimal isolation policies. However, despite the development and use of many models and sophisticated tools, these forecasting attempts have largely failed. We present a model that considers the severity of the disease and the heterogeneity of contacts between the population in complex space–time dynamics. Using mathematical and computational methods, the applied tool was developed to analyze and manage the COVID-19 pandemic (from an epidemiological point of view), with a particular focus on population heterogeneity in terms of age, susceptibility, and symptom severity. We show improved strategies to prevent an epidemic outbreak. We evaluated the model in three countries, obtaining an average mean square error of 0.067 over a full month of the basic reproduction number (R 0). The goal of this study is to create a theoretical framework for crisis management that integrates accumulated epidemiological considerations. An applied result is an open-source program for predicting the outcome of an isolation strategy for future researchers and developers who can use and extend our model.

Deep Learning Assisted Zonal Adaptive Aberration Correction

Deep learning (DL) has been recently applied to adaptive optics (AO) to correct optical aberrations rapidly in biomedical imaging. Here we propose a DL assisted zonal adaptive correction method to perform corrections of high degrees of freedom while maintaining the fast speed. With a trained DL neural network, the pattern on the correction device which is divided into multiple zone phase elements can be directly inferred from the aberration distorted point-spread function image in this method. The inference can be completed in 12.6 ms with the average mean square error 0.88 when 224 zones are used. The results show a good performance on aberrations of different complexities. Since no extra device is required, this method has potentials in deep tissue imaging and large volume imaging.

Spatiality in small area estimation: A new structure with a simulation study

In numerous practical applications, data from neighbouring small areas present spatial correlation. More recently, an extension of the Fay–Herriot model through the Simultaneously Auto- Rregressive (SAR) process has been considered. The Conditional Auto-Regressive (CAR) structure is also a popular choice. The reasons of using these structures are theoretical properties, computational advantages and relative ease of interpretation. However, the assumption of the non-singularity of matrix (Im-ρW) is a problem. We introduce here a novel structure of the covariance matrix when approaching spatiality in small area estimation (SAE) comparing that with the commonly used SAR process. As an example, we present synthetic data on grape production with spatial correlation for 274 municipalities in the region of Tuscany as base data simulating data at each area and comparing the results. The SAR process had the smallest Root Average Mean Square Error (RAMSE) for all conditions. The RAMSE also generally decreased with increasing sample size. In addition, the RAMSE valuess did not show a specific behaviour but only spatially correlation coefficient changes led to a stronger decrease of RAMSE values than the SAR model when our new structure was applied. The new approach presented here is more flexible than the SAR process without severe increasing RAMSE values.

Detection of Biomedical Images by Using Bio-inspired Artificial Intelligent

Computer vision and image processing are extremely necessary for medical pictures analysis. During this paper, a method of Bio-inspired Artificial Intelligent (AI) optimization supported by an artificial neural network (ANN) has been widely used to detect pictures of skin carcinoma. A Moth Flame Optimization (MFO) is utilized to educate the artificial neural network (ANN). A different feature is an extract to train the classifier. The comparison has been formed with the projected sample and two Artificial Intelligent optimizations, primarily based on classifier especially with, ANN-ACO (ANN training with Ant Colony Optimization (ACO)) and ANN-PSO (training ANN with Particle Swarm Optimization (PSO)). The results were assessed using a variety of overall performance measurements to measure indicators such as Average Rate of Detection (ARD), Average Mean Square error (AMSTR) obtained from training, Average Mean Square error (AMSTE) obtained for testing the trained network, the Average Effective Processing Time (AEPT) in seconds, and the Average Effective Iteration Number (AEIN). Experimental results clearly show the superiority of the proposed (ANN-MFO) model with different features.

Comparing Parameter Estimation of Random Coefficient Autoregressive Model by Frequentist Method

This paper compares the frequentist method that consisted of the least-squares method and the maximum likelihood method for estimating an unknown parameter on the Random Coefficient Autoregressive (RCA) model. The frequentist methods depend on the likelihood function that draws a conclusion from observed data by emphasizing the frequency or proportion of the data namely least squares and maximum likelihood methods. The method of least squares is often used to estimate the parameter of the frequentist method. The minimum of the sum of squared residuals is found by setting the gradient to zero. The maximum likelihood method carries out the observed data to estimate the parameter of a probability distribution by maximizing a likelihood function under the statistical model, while this estimator is obtained by a differential parameter of the likelihood function. The efficiency of two methods is considered by average mean square error for simulation data, and mean square error for actual data. For simulation data, the data are generated at only the first-order models of the RCA model. The results have shown that the least-squares method performs better than the maximum likelihood. The average mean square error of the least-squares method shows the minimum values in all cases that indicated their performance. Finally, these methods are applied to the actual data. The series of monthly averages of the Stock Exchange of Thailand (SET) index and daily volume of the exchange rate of Baht/Dollar are considered to estimate and forecast based on the RCA model. The result shows that the least-squares method outperforms the maximum likelihood method.

Handling Critical Multicollinearity Using Parametric Approach

In regression analysis, it is relatively necessary to have a correlation between the response and explanatory variables, but having correlations amongst explanatory variables is something undesired. This paper focuses on five methodologies for handling critical multicollinearity, they include: Partial Least Square Regression (PLSR), Ridge Regression (RR), Ordinary Least Square Regression (OLS), Least Absolute Shrinkage and Selector Operator (LASSO) Regression, and the Principal Component Analysis (PCA). Monte Carlo Simulations comparing the methods was carried out with the sample size greater than or equal to the levels (n>p) considered in most cases, the Average Mean Square Error (AMSE) and Akaike Information Criterion (AIC) values were computed. The result shows that PCR is the most superior and more efficient in handling critical multicollinearity problems, having the lowest AMSE and AIC values for all the sample sizes and different levels considered.

Quantification of Hydrocarbon Abundance in Soils Using Deep Learning with Dropout and Hyperspectral Data

Terrestrial hydrocarbon spills have the potential to cause significant soil degradation across large areas. Identification and remedial measures taken at an early stage are therefore important. Reflectance spectroscopy is a rapid remote sensing method that has proven capable of characterizing hydrocarbon-contaminated soils. In this paper, we develop a deep learning approach to estimate the amount of Hydrocarbon (HC) mixed with different soil samples using a three-term backpropagation algorithm with dropout. The dropout was used to avoid overfitting and reduce computational complexity. A Hyspex SWIR 384 m camera measured the reflectance of the samples obtained by mixing and homogenizing four different soil types with four different HC substances, respectively. The datasets were fed into the proposed deep learning neural network to quantify the amount of HCs in each dataset. Individual validation of all the dataset shows excellent prediction estimation of the HC content with an average mean square error of ~ 2 . 2 × 10 - 4 . The results with remote sensed data captured by an airborne system validate the approach. This demonstrates that a deep learning approach coupled with hyperspectral imaging techniques can be used for rapid identification and estimation of HCs in soils, which could be useful in estimating the quantity of HC spills at an early stage.

Performance Analysis of ANN Model for Estimation of Trophic Status Index of Lakes

The health of water bodies across the globe is of high concern as the pollution is accelerating rigorously. With the interventions of simple technology, some significant changes could be bought up. Lakes are dying because of high Trophic Index Status which shows the eutrophication level of water bodies. Taking this into account, feed forward back propagation neural network model is used to estimate the Trophic Status Index (TSI) of lakes which could compute the value of TSI with the given parameters; pH, temperature, dissolved oxygen, Secchi disk transparency, chlorophyll and total phosphate. Two learning algorithms; Levenberg Marquardt (LM) and Broyden–Fletcher–Goldfarb–Shanno (BFGS) Quasi Newton were used to train the network, which belongs to different classes. The results were analyzed using mean square error function and further checked for the deviation from actual data. Among both the training algorithm; LM demonstrated better performance with 0.0007 average mean square error for best validation performance and BFGS Quasi Newton shows the average mean square error of 1.07.

Methods for Parameter Estimation of the Negative Binomial-Generalized Exponential Distribution

We proposed several estimation methods for the parameters of the negative binomial-generalized exponential (NB-GE) distribution. In the simulation study, the maximum likelihood estimation (MLE) with nlm function seems to have the most efficiency to estimate the parameters and of the NB-GE distribution when it compares with method of the moments (MM) and MLE with optim function by using the average mean square error (AMSE) for a criteria. The AMSE values of each parameter estimation methods are decreasing when the sample size increasing. Moreover, the example dataset is illustrated. Based on the chi-square values for the fitting distribution via the MLE with nlm function is better than other estimation methods.