دکتر امید کریمی

Spatial regression models are used to analyze quantitative spatial responses based on linear and non-linear relationships with explanatory variables. Usually, the spatial correlation of responses is modeled with a Gaussian random field based on a multivariate normal distribution. However, in practice, we encounter skewed responses, which are analyzed using skew-normal distributions. Closed skew-normal distribution is one of the extended families of skew-normal distributions, which has similar properties to normal distributions. This article presents a hierarchical Bayesian analysis based on a flexible subclass of closed skew-normal distributions. Given the time-consuming nature of Monte Carlo methods in hierarchical Bayes analysis, we have opted to use the variational Bayes approach to approximate the posterior distribution. This decision was made to expedite the analysis process without compromising the accuracy of our results. Then, the proposed model is implemented and analyzed based on the real earthquake data of Iran.

Investors typically seek to strike the optimal balance between potential returns and associated risks in their trades. Various models have been presented to choose the optimal portfolio using different approaches. one of these methods is based on the statistical distribution of asset return. In these methods, the type of distribution of returns is first identified, and a suitable portfolio selection method is then applied based on this identified distribution type. This study compares the effectiveness of the mean-absolute deviation-entropy model utilizing both Skew-Normal Distribution and Skew-Laplace-Normal Distribution for constructing an optimal portfolio in the Tehran Stock Exchange over 36 months from April 2018 to March 2020.

The data used in this study comprises the monthly returns of 181 companies listed on the Tehran Stock Exchange. These returns were gathered from a statistical population of 338 members utilizing Morgan's table and Cochran’s formula. After fitting density functions for Skew-Normal and Skew-Laplace-Normal distributions to the returns, maximum likelihood estimates were obtained using the Stats package and the optim Function in R software. The reliability of these estimates was then checked using bootstrap sampling with 1,000 repetitions. Subsequently, relationships corresponding to the mathematical expectation of return distribution and the objective function representing the risk of absolute deviation were estimated using numerical methods. Therefore, this paper aimed to propose a multi-objective optimization model, namely a mean-absolute deviation-entropy model for portfolio optimization by using a goal-programming approach based on Skew-Normal Distribution and Skew-Laplace-Normal Distribution. The objective functions of the model were to maximize the mean return, minimize the absolute deviation, and maximize the entropy of the portfolio.

It can be inferred from the observed values ​​of the descriptive statistics of the monthly stock returns corresponding to the stock exchange symbols that some stocks have different skewness and kurtosis values ​​compared to the normal distribution. For example, The symbol "Shepna" exhibits negative skewness, indicating a left-skewed distribution. Similarly, the distribution of the "Basama" symbol exceeds the normal distribution. These instances suggest that the normal distribution is inadequate for describing monthly return distributions. Instead, distributions with parameters should be employed to account for skewness and kurtosis. According to the obtained results, the model utilizing the Skew- Laplace- Normal distribution has a higher performance ratio than the model based on the Skew-Normal distribution.

The reason for this superiority, where the model utilizing the Skew-Laplace-Normal distribution outperforms the model based on the Skew-Normal distribution, is the incorporation of both skewness and kurtosis criteria within the former. Additionally, upon analyzing the descriptive statistics of the symbols, it's evident that the kurtosis of most stock symbols is substantial. Therefore, integrating a combination of higher-order moments (skewness and kurtosis) along with entropy leads to enhanced performance.

The spatial generalized linear mixed models are often used, where the latent variables representing spatial correlations are modeled through a Gaussian random field to model the categorical spatial data. The violation of the Gaussian assumption affects the accuracy of predictions and parameter estimates in these models. In this paper, the spatial generalized linear mixed models are fitted and analyzed by utilizing a stationary skew Gaussian random field and employing an approximate Bayesian approach. The performance of the model and the approximate Bayesian approach is examined through a simulation example, and implementation on an actual data set is presented.

Presently, we are faced with a demographic crisis to the extent that within the next forty years, we will witness a demographic catastrophe, transforming our young country into an elderly one. One of the strategies to increase society's inclination towards childbearing is establishing legal frameworks and incentives, which have been demonstrated in recent years through a proposal presented to the Islamic Consultative Assembly under the title "Population and Youth Plan." This plan contains 15 incentives for increasing childbirth and is currently under review in the parliament. One crucial aspect of evaluating this plan is the lawmakers' confidence in its success in achieving the desired objectives, namely increasing the desire for childbearing in society. The present study aims to investigate this matter through conducting a social survey. The target population comprises all adults aged 18 to 45, approximately 35 million individuals, according to the population pyramid announced by the Statistical Center of Iran in the 2016 census. The sampling method was stratified proportional, and the sample size was determined to be 384 individuals based on Cochran's formula with a 5% error margin. The research findings indicate that the most significant motivating factor for increasing childbirth, from society's perspective, is adequate support for mothers and children and ensuring a promising future for themselves and their children. The 15 incentives devised in this regard are expected to be more successful

Gaussian random field is usually used to model Gaussian spatial data. In practice, we may encounter non-Gaussian data that are skewed. One solution to model skew spatial data is to use a skew random field. Recently, many skew random fields have been proposed to model this type of data, some of which have problems such as complexity, non-identifiability, and non-stationarity. In this article, a flexible class of closed skew-normal distribution is introduced to construct valid stationary random fields, and some important properties of this class such as identifiability and closedness under marginalization and conditioning are examined. The reasons for developing valid spatial models based on these skew random fields are also explained. Additionally, the identifiability of the spatial correlation model based on empirical variogram is investigated in a simulation study with the stationary skew random field as a competing model. Furthermore, spatial predictions using a likelihood approach are presented on these skew random fields and a simulation study is performed to evaluate the likelihood estimation of their parameters.

Spatial generalized linear mixed model is commonly used to model Non-Gaussian data and the spatial correlation of the data is modelled by latent variables. In this paper, latent variables are modeled using a stationary skew Gaussian random field and a new algorithm based on composite marginal likelihood is presented. The performance of this stationary random field in the model and the proposed algorithm is implemented in a simulation example.

 Count data over time are observed in many application areas. Many researchers use time series patterns to analyze this data. In this paper, the poisson count time series linear models and negative binomials on this type of data with the explanatory variables are studied. The Likelihood analysis and the evaluation of count time series model based on generalized linear models are presented and investigated. Also, the data of the number of addicts referred to the addiction treatment centers in Semnan county are analyzed based on the proposed models and methods. According to the results of the model selection criteria, the negative binomial count time series model is a good fit for this data and based on it, a monthly forecast for the year 2019 was made.

Spatial generalized linear mixed models are used commonly for modeling discrete spatial responses. In this models the spatial correlation of the data is considered as spatial latent variables. For simplicity, it is usually assumed in these models that spatial latent variables are normally distributed. An incorrect normality assumption may leads to inaccurate results and is therefore erroneous. In this paper we model the spaial latent variables in a general random field, namely the closed skew Gaussian random field which is more flexible and includes the Gaussian random field. We propose a new algorithm for maximum likelihood estimates of the parameters. A key ingredient in our algorithm is using a Hamiltonian Monte Carlo version of the EM algorithm. The performance of the proposed model and algorithm is presented through a simulation study.

The Gaussian random field is commonly used to analyze spatial data. One of the important features of this random field is having essential properties of the normal distribution family, such as closure under linear transformations, marginalization and conditioning, which makes the marginal consistency condition of the Kolmogorov extension theorem. Similarly, the skew-Gaussian random field is used to model skewed spatial data. Although the skew-normal distribution has many of the properties of the normal distribution, in some definitions of the skew-Gaussian random field, the marginal consistency property is not satisfied. This paper introduces a stationery skew-Gaussian random field, and its marginal consistency property is investigated. Then, the spatial correlation model of this skew random field is analyzed using an empirical variogram. Also, the likelihood analysis of the introduced random field parameters is expressed with a simulation study, and at the end, a discussion and conclusion are presented.

Spatial regression models are often used for modeling spatial economic data. The main purpose of studying these models is to obtain parameter estimates and then predict at new locations. For this purpose, the maximum likelihood approach is first investigated and in order to increase the accuracy of parameter estimation and reduce the computation time, the conventional Bayesian approach and an approximate Bayesian approach are examined for three regression models, spatial Lag model, spatial Durbin model and spatial error model. Finally, in a simulation study and a real example of housing data in Tehran, the performance of models and approaches are compared. The existence of a spatial effect and a direct relationship between housing price and area in the data is accepted. Using the Relative Root Mean Square Error for these two data sets, it was concluded that the approximate Bayesian approach for spatial econometric models has a better performance than the maximum likelihood and the conventional Bayesian approaches. In addition, it was found that the computational time of the Bayesian approach is about twice as long as the approximate Bayesian approach.

In spatial generalized linear mixed models, spatial correlation is assumed by adding normal latent variables to the model. In these models because of the non-Gaussian spatial response and the presence of latent variables the likelihood function cannot usually be given in a closed form, thus the maximum likelihood approach is very challenging. The main purpose of this paper is to introduce two new algorithms for the maximum likelihood estimations of parameters and to compare them in terms of speed and accuracy with existing algorithms. The presented algorithms are applied to a simulation study and their performance are compared.

Spatial count data is usually found in most sciences such as environmental science, meteorology, geology and medicine. Spatial generalized linear models based on poisson (poisson-lognormal spatial model) and binomial (binomial-logitnormal spatial model) distributions are often used to analyze discrete count data in which spatial correlation is observed. The likelihood function of these models is complex as analytic and so computation.  The Bayesian approach using Monte Carlo Markov chain algorithms can be a solution to fit these models, although there are usually problems with low sample acceptance rates and long runtime to implement the algorithms. An appropriate solution is to use the Hamilton (hybrid) Monte Carlo algorithm  in The Bayesian approach. In this paper, the new Hamilton (hybrid) Monte Carlo method for Bayesian analysis of spatial count models on air pollution data in Tehran is studied. Also, the two common Monte Carlo algorithms such as the Markov chain (Gibbs and Metropolis-Hastings) and Langevin-Hastings are used to apply  the complete Bayesian approach on the data modeling.  Finally, an appropriate approach to data analysis and forecasting in all points of the city is introduced with the diagnostic criteria.

‎Tree models represent a new and innovative way of analyzing large data sets by dividing predictor space into simpler areas‎. ‎Bayesian Additive Regression Trees model‎, ‎a model that we explain in this article‎, ‎uses a totality of trees in its structure‎, ‎since the combination of several trees from a tree only has a higher accuracy‎.
‎Then‎, ‎this model is a tree-based model and a nonparametric model that uses general aggregation methods‎, ‎and boosting algorithms in particular and in fact is extension of the classification and Regression Tree methods in which the decision tree exists in the structure of these methods‎.

‎In this method‎, ‎on the parameters of the model sum of tree and put regular prior then use the boosting algorithms for analysis‎. ‎In this paper‎, ‎first the Bayesian Additive Regression Trees model is introduced and then applied in survival analysis of lung cancer patients‎.

Sometimes, in econometrics problems the observations are not independent, so that their dependence is due to the location of observations in the studied space. To analyze these data are used the spatial regression models. Due to the large number of parameters in these models are used the iteration algorithms to obtain the maximum likelihood estimations, so that it encounters problems such as the complexity of the calculation. In addition in economic studies, the number of observation is large and it seems useful to use the Bayesian approach. The main purpose is using the Bayesian and the Likelihood approaches to estimate the parameters of the three spatial econometric models. Then, comparing the performance of these two approaches, as well as comparing the performance of these three spatial regression models and finally the three models are implemented on two real data. It is observed that the results of the Bayesian approach are more credible than the likelihood approach in these type of econometric models.

Often in practice the data on the mortality of a living unit with a correlation of location of the observations in space are studied. One of the most important issues in this type of analysis of survival data with spatial dependence is estimation of the parameters and prediction of the unknown values in known sites based on observations vector. In this paper to analyze this type of survival data, Cox regression model with piecewise exponential function is used as a hazard and spatial dependence as a Gaussian random eld and as a latent variable is added to the model. Because there is no closed form for the posterior distribution and the full conditional distributions, also long computing for Markov Chain Monte Carlo of algorithms, to analyze the model is used the approximate Bayesian approach. In a practical example is presented how to implement an approximate Bayesian approach.

Animal models are used to model the observations of animal performance that are genetically dependent.These models are considered as generalized linear mixed models and the genetic correlation structure of data is considered through random effects of breeding values. One goal of the mentioned models is to estimate variance components. In this research, an approximate Bayesian approach presented to estimate variance components in animal model and compared with the conventional Bayesian approach. A generated data set for hypothetical animal population with 1084 records was used. The observations are the animal's birth weight and the data includes dam ID, sire ID, sex and birth year. The effect of gender was considered as fixed effect and the effects of dam, animal and year of birth were used as random effect. Four different models were fitted by the conventional Bayesian approach and the appropriate model was selected by deviance information criteria. The approximate Bayesian approach was applied on it. Time consuming with a PC with configuration (Intel Core i7, 4GB, 2.7 GHz) was about 120 second for the conventional Bayesian approach and little than 10 second for the approximate Bayesian approach. Goodness of fit was computed by relative root mean squared error of prediction that was respectively 0.1568 and 0.1499 for conventional Bayesian and the approximate Bayesian approaches. T-test was used to illustrate lack of significant different to fit weight of animals between two approaches. The null hypothesis was accepted with p-value 0.98 that it shows mean of fitted animal weights for two approaches are equal.

Skew spatial data often are modeled by using skew Gaussian random field. The main problem is that simulations from this random field are very time consuming for some parameter values and large dimensions. Also it is impossible in some cases and requires using of an approximation methods. One a spatial statistics branch often used to determine the natural resources such as oil and gas, is analysis of seismic data by inverse model. Bayesian Gaussian inversion model commonly is used in seismic inversion that the analytical and computational can easily be done for large dimensions. But in practice, we are encountered with the variables that are asymmetric and skewed. They are modeled using skew distributions. In Bayesian Analysis of closed skew Gaussian inversion model, there is an important problem to generate samples from closed skew normal distributions. In this paper, an efficient algorithm for the realization of the Closed Skew Normal Distribution is provided with higher dimensions. Also the Closed Skew T Distribution is offered that include heavy tails in the density function and the simulation algorithm for generating samples from the Closed Skew T Distribution is provided. Finally, the discussion and conclusions are presented.

Spatial generalized linear mixed models are used for modeling geostatistical discrete spatial responses and spatial correlation of the data is considered via latent variables. The most important interest in these models is estimation of the model parameters and the prediction of the latent variables. In this paper، first a prediction method is presented and then، Bayesian approach and MCMC algorithms are intrpretation. Since these models are complex and in the Bayes inference of these models، are used Monte Carlo sampling، computation time is long. The Approximatin Baysian methods are considered for solving this problem. Finally، the proposed methods are applied to a case study on rainfall data observed in the weather stations of Semnan in 1391.

Non-Gaussian spatial responses are usually modeled using spatial generalized linear mixed models، such that the spatial correlation of the data can be introduced via normal latent variables. The model parameters and the prediction of the latent variables at unsampled locations are of the most important interest in SGLMM by estimating of the latent variables at sampled locations. In these models، since there are the latent variables and non-Gaussian spatial response variables، likelihood function cannot usually be given in a closed form and maximum likelihood estimations may be computationally prohibitive. In this paper، a new algorithm is introduced for maximum likelihood estimation of the model parameters and predictions، that is faster than the former method. This algorithm obtains to combine the pseudo maximum likelihood method، the Expectation maximization Gradient algorithm and an approximate method. The performance and accuracy of the proposed model are illustrated through a simulation study. Finally، the model and the algorithm are applied to a case study on rainfall data observed in the weather stations of Semnan in 2012.

In regression analysis, it is usually assumed that the error terms are independent, but in practice we occasionally deal with many cases such as spatial data that the error terms in regression models are correlated and their correlation structure is a function of the observation locations. This type of models, namely spatial regression, are used for surface determination in geology, archaeology, epidemiology and image processing. In this paper, the Bayesian approach is used for spatial regression analysis with first order spatially autocorrelated errors. Because of computation difficulties of posterior distribution, MCMC methods are used for estimation of the posterior parameters. Then the efficiency of introduced method is considered in a simulation study for different sample and lattice sizes