Real systems face with uncertainty. Two categories are dened for uncertainty: Aleatoric Uncertainty, and Epistemic uncertainty. The rst one is unbiased, and often dened in a probabilistic framework. The second is biased, and it is less naturally dened in a probabilistic framework. One goal of uncertainty quantication is to convert epistemic uncertainties to aleatorics, to apply probabilistic analysis. One of the activities done, calibrating a model, is statistical adjustment. Statistical adjustment is dened by the process of calculating auxiliary variables. Model calibration is studied to be done through minimal adjustments. Minimal adjustment is an adjustment procedure that brings the computer model closer to the data by making minimal changes to it. The probabilistic quanti cation of predicted experimental and computational outcomes with identied and quantied uncertainty is sometimes termed predictive estimation. To forecast accurately and make decisions, this uncertainty must be modeled. In this research, dierent approaches for modeling and quantifying uncertainty are studied. One approach is engineering approach, which is time consuming and unrealistic, due to its simplifying assumptions. The second is based on data gathering, called statistical approach, which is not correct out of the data range, and lacks physical interpretation. Some researchers compounded these two approaches and de- ned engineering- statistical approach which is more useful, fast, and realistic. Besides, for large scale systems, usual techniques of model solving are inadequate. In such cases, surrogate models are used. Uncertainty quantication consists of four steps: veri- cation, validation, calibration and uncertainty propagation, In this research, a methodology is dened to de- velop an engineering-statistical model. Then, the methodology is used for solving a real problem. As a case study, Laser Assisted Micro-Machining (LAMM) system is chosen. The problem is studied by some researches, before. So, it is proper to compare the proposed methodology by the previous ones in literature. In continue, the compare is done.

Statistical modeling has been used for seasonal rainfall forecasting based on synoptical patterns of the atmospheric upper levels in Khorasan province - northeast of Iran. The data of 37 rainfall stations were obtained from Iranian Meteorological Organization and the first stage was filling the gaps estimating and missing data using statistical methods. At the second stage, the RUN-TEST homogeneity procedure were done to find out if the rainfall data are randomly collected. Mean local time series of rainfall have been calculated by Arc GIS software. In order to forecast the seasonal rainfall in the period of Dec ember to May, the relations between rainfall and atmospheric upper level parameters at the difference time intervals were used as inputs of statistical model. Results show that the statistical modeling can successfully predict amount of the rainfall. Root mean square error obtained by stepwise and backward models were 50.4 and 47.3 millimeter respectively.

Usually, data analysis in a finite mixture of statistical models using some of these distributions is complex. One of the distributions which in practice used a lot, but it has a problem in a finite mixture of statistical models is the Poisson distribution. In this paper, due to non-equality of the mean and variance of Poisson distribution for the real data, finite mixture of generalized linear models for negative binomial distribution as alternative distribution has examined. Finally, as application of the proposal model in negative binomial distribution , the equating of Ph.D. test score between years of 92 and 93 in national organization for educational testing has considered. Also, result of simulation for data, has been shown the advantage of negative distribution to Poisson distribution, also the important variables has been determined.

Salinity as an abiotic stress can cause excessive disturbance for seed germination and plant sustainable production. Salinity with three different mechanisms of osmotic potential reduction, ionic toxicity and disturbance of plant nutritional balance, can reduce performance of the final product. Planning for optimal use of available water and saline water with poor quality in agricultural activities is of great importance. Wheat is one of the eight main food sources including rice, corn, sugar beet, cattle, sorghum, millet and cassava which provide 70-90% of all calories and 66-90% of the protein consumed in developing countries. Durum wheat (Triticum turgidum L.) is an important crop grows in some arid and semi-arid areas of the world such as Middle East and North Africa. In these regions, in addition to soil salinity, sharp decline in rainfall and a sharp drop in groundwater levels in recent years has emphasized on the efficient use of limited soil and water resources. Consequently, in order to use brackish water for agricultural productions, it is required to analyze its quantitative response to salinity stress by simulation models in those regions. The objective of this study is to assess the capability of statistics and macro-simulation models of yield in saline conditions.
In this study, two general approach of simulation includes process-physical models and statistical-experimental models were investigated. For this purpose, in order to quantify the salinity effect on seed relative yield of durum wheat (Behrang Variety) at different levels of soil salinity, process-physical models of Maas & Hoffman, van Genuchten & Hoffman, Dirksen et al. and Homaee et al. models were used. Also, statistical-experimental models of Modified Gompertz Function, Bi-Exponential Function and Modified Weibull Function were used too. In order to get closer to real conditions of growth circumstances in saline soils, a natural saline water was taken from Maharlu Lake, Fars province, Iran. This natural and highly saline water with electrical conductivity of 512 dS/m diluted with fresh water to obtain the designated saline waters required for the experimental treatments. The designed experimental treatments were consisted of a non-saline water and five salinity levels of 2, 4, 6, 8 and 10 dS/m with three replicates. Three statistics of modified coefficient efficiency (E'), modified index of agreement (d') and coefficient of residual mass (CRM) were used to compare the used models and to assess their performances.
Comparing the relative performance of models based on statistical indices of Modified Coefficient Efficiency (E') and Modified Index of agreement (d') indicated that the nonlinear model of Homaee et al. is most accurate between process-physical models and Modified Gompertz Function is most accurate between statistical-experimental models. Comparison assessment of all models based on statistical index indicated that Homaee et al. model was the most accurate model for simulation of durum wheat yield. This is while the parameters of Homaee et al. equation is well-defined concept and is easily measurable, but in statistical-experimental models, parameters of each model have no biophysical concept and the absolute values of each parameter do not express any information about development status of the plant. So, the nonlinear model of Homaee et al. was chosen as the optimal model in this research.
Most of the plants such as wheat, are sensitive to salinity and by increasing the age, their sensitivity to salinity are reduced. Based on the obtained results of this study, by knowing and quantitative assessment of the dominant cultivars sensitivity of each region, as well as using appropriate simulation models, one can use brackish or saline waters to partly compensate fresh water shortage for scientific and extension Agricultural programs.

Economic theories seek a scientific explanation or prediction of economic phenomena using a set of axiom, defined expressions, and theorems. Mathematically explicit economic models are one of these theories. Due to the unknown structure of each model, the existence of measurement error in economic committees and failure of Ceteris Paribus; the Synthetic of any economic theory requires probabilistic and statistical modeling. Therefore, understanding the current method of modeling and the importance of its proper use in economics requires economists to have an accurate knowledge of statistical modeling. The present study seeks to correct the view that although the purpose of providing statistical models is to experimentally test the claims of theories, statistical methods do not play a secondary role in economic theories, but the appropriate method of economic modeling depends on the correct use of statistical methods and probability models in the situation. of make a theory.

The purpose of this study was to compare the efficiency of machine learning models (32 models) and statistical models (14 models) in predicting the financial risk of listed 145 companies in Tehran Stock Exchange during the period 2010 to 2020 and selecting the best model using advanced optimization techniques. Findings of the research using the test of comparing the accuracy of prediction coefficients, indicates that with 99 percent confidence, the prediction accuracy of machine learning models is higher than statistical models. Also, the best machine learning model after optimization was the evolutionary support vector machine model with 99.86 percent prediction accuracy and the value of the area under the curve was 0.998. In addition, accrual financial ratios with 99.45 percent predictive accuracy and operating financial ratios with 98.62 percent predictive accuracy were able to perform better than other financial ratios in using the evolutionary support vector to predict financial risk. on the other side, the projected financial risk varied according to different industries. Therefore, it was found that machine learning models can be used as an important tool in predicting corporate financial risk due to the lack of limitations that statistical models face.

Pipes failure events in the water distribution networks provide leakage of water. Failures cause the loss of significant fresh water and investments losses. The most important parameters are: material, age, length, diameter and hydraulic pressure. In this paper four statistical methods have used for analyzing pipe incidents, with the goal of estimation of failure probability in future, with finding the most influences parameters in the incidents. The statistical regression models using in this research are linear regression model, exponential regression model, Poisson regression model , and Logistic regression model . For evaluation of the models, the data of a pilot in the first district of the Tehran’s Water and Wastewater Company with more than 48500 consumers, total pipe length of 582702 meter, different materials and diameters were used. The results demonstrated that the logistic model has a better performance than others to predict the future events with a higher probability.

In this study, Artificial Neural Network (ANN) as a black box model was used in order to evaluate the temperature and water discharge effects on suspended sediment load of Ligvanchay River. For this purpose, the hydrological data such as mean river flow discharge, mean daily temperature and mean daily suspended sediment load of Ligvanchay at the outlet hydromerey station were collected and divided to seven categories. These data were then entered to the ANN and the model with Levenberg-Marquardt (LM) of back propagation training algorithm was executed about 2000 times to determine the optimum structure of ANN model includes numbers of hidden layers and neurons in each layer. After determine the optimum structure, other back propagation training algorithms were tested for doing more comparison among the algorithms; in this manner the results of training and verifying as graphs and tables were presented. Furthermore, the results of the ANN model were compared with the results of some other classical black box models such as multi and single linear regression, auto regressive (AR) time series models. The obtained results of the study showed better performanceof the ANN model in comparison of the others when only one neuron was considered as model input. However when more than one neuron was used as input data, MLR and AR (2) showed a hit better results. This may be because of noise propagation in ANN non-linear model in comparison with other linear models. According the results, it can be obviously seen that the suspended sediment load of Ligvanchay has only a little sensitivity to the environment temperature.

Statistical analysis of the data on the Earth's surface was a popular subject among many researchers. Such data can be related to animal's migration from a region to another position. Then, statistical modeling of their paths helps biological researchers to predict their movements and estimate the regions that are most likely to constitute the presence of the animals. To study such typical phenomena, statistical modeling of the objects’ movement path on the earth is considered through non-parametric and least square methods in this paper. The modeling is based on two separated angles on the sphere. The proposed models will be evaluated using simulated and real life data.