---

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.

---

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.

---

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. 

---

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.