Uncertainty is an inherent characteristic of biological and geospatial data which is almost made by measurement error in the observed values of the quantity of interest. Ignoring measurement error can lead to biased estimates and inflated variances and so an inappropriate inference. In this paper, the Gaussian spatial model is fitted based on covariate measurement error. For this purpose, we adopt the Bayesian approach and utilize the Markov chain Monte Carlo algorithms and data augmentations to carry out calculations. The methodology is illustrated using simulated data.

Generalized Linear mixed models (GLMMs) are common methods for the analysis of clustered data. In many longitudinal and hierarchical epidemiological frameworks, accurate measurements of variables are invalid or expensive to be obtained and there might be situations that both the response and covariate variables are likely to be mismeasured. Insensitivity of errors in either covariate or response variable is, not always plausible. With nonLinear regression models for the outcome process, classification errors for binary responses and measurement error in covariates basically needs to be accounted for in order to make conclusive inferences. In this article, we provide an approach to simultaneously adjust for non-differential misclassification in the correlated binary response and classical measurement error in the covariates, using the multivariate Gauss-Hermite quadrature technique for the approximation of the likelihood function. Simulation studies are then conducted to inform the effects of correcting for measurement error and misclassification on the estimation of regression parameters. The application of the multivariate Gauss-Hermite quadrature method in the conjunction of measurement error and misclassification problems is further highlighted with real-world data based on a multilevel study of contraceptive methods used by women in Bangladesh.

In this paper, we consider a general Linear model where missing data may occur in response and covariate variables. We propose a new test based on Ramsy's test to identify goodness of fit for general Linear model with missing data. We show that under the null hypothesis, our test functions for complete case analysis follow a Fisher distribution and the other test function used for analysis with available data converges in distribution to Quasi-Fisher distribution. Furthermore, we compare proposed test functions by using some simulation studies. Also, we apply our methods in analyzing a real data set.

In recent years, some researches have been done on simultaneous monitoring of multivariate process mean vector and covariance matrix. However, the effect of measurement error, which exists in many practical applications, on the performance of these control charts is not well studied. In this paper, the effect of measurement error with Linearly increasing variance on the performance of ELR control chart for simultaneous monitoring of multivariate process mean vector and covariance matrix is investigated. The multiple measurement approach is also extended to reduce this effect. Also, the performance of the proposed multiple measurement approach is evaluated in terms of average run length (ARL) and standard deviation run length (SDRL). Finally, the application of the proposed monitoring method is illustrated by a real data in manufacturing industry.

This paper introduces a model to make decision on the maintenance of a mechanical component subject to condition monitoring. A stochastic model is used to determine what maintenance action should be taken at a monitoring check and the follow up inspection times. The condition of component has a stochastic relation with measurements. A new state space model is developed and used, to predict the hazard rate and condition monitoring measurements, to indirectly asses the hazard rate of the system. The Proportional covariate model (PCM) which was proposed by Yong Sun (2004) was also used to develop the model. The known Kalman Filter was employed to derive the probability of the conditional hazard rate, which is predicted and updated for condition monitoring. The maintenance is being performed based on the estimated hazard rate so that the desired level of reliability is achieved, in a cost effective approach. This approach is validated by using the experimental data obtained from gearboxes which ran and failed on the Mechanical Diagnostic Test Bed (MDTB) at the Penn State University Applied Research Laboratory.

In this article, an approach for fitting a fuzzy Linear regression model based on support vectors is presentedwhen the response variable, model parameters and errors are considered as fuzzy numbers.In this method, the objective function is based on the sum of the absolute values ​​of the distances of the hypothetical points to the non-parallel border hyperplanes. The presented model has good robustness to the presence of outlier data. The proposed model has been compared with some other models based on three goodness of fit indices.

Semiparametric Linear mixed measurement error models are extensions of Linear mixed measurement error models to include a nonparametric function of some covariate. They have been found to be useful in both cross-sectional and longitudinal studies. In this paper first we propose a penalized corrected likelihood approach to estimate the parametric component in semiparametric Linear mixed measurement error model and then using the case deletion and subject deletion analysis we survey the influence diagnostics in such models. Finally, the performance of our influence diagnostics methods are illustrated through a simulated example and a real data set.

Directional felling of trees plays a key role in reducing of damages to forest residual trees and can also facilitate skidding. The aim of this study was to present a practical Linear model for estimation of tree falling direction error in an uneven-aged mixed stand in northern forests of Iran. To conduct the study a number of 95 trees of four species Fagus orientalis lipsky, Carpinus betulus L., Alnus subcordata and Acer platanoides were randomly selected, and assumed felling direction were marked on the trunk of these trees. The trees were felled by experienced chainsaw operators, and the differences between the assumed and actual direction were measured as the felling error. The results showed that among the 12 effective factors, the elements of foot slope, diameter at the breast height (DBH), horizontal and vertical angles and area of the backcut surface (HABS, VABS, BA), vertical angle and area of undercut surface (VAUS, UA) were significantly correlated with the felling error; the determination coefficient (R2) of the presented Linear model was 52.0 % (P<0.01). Among the model factors, DBH, VABS, and HABS had the three most pronounced impacts on felling error.

Walnut has a high economic value because of the good quality of wood and fruits. So this species has been harvested since many years ago till today and has been introduced as a protected species. The performance of Juglans regia increases in wet years, but reduces in dry years, hence paying attention to physiological and morphological parameters in order to identify the genomic regions related to drought resistant is important for breeding programs in walnut. In this study, genetic diversity by SSR markers has been evaluated. Also, the association of used primers with physiological and morphological traits were analyzed before and after drought stress. 10 SSR primer pairs generated 53 alleles in 62 walnut seedlings. All locies showed significant difference (p£0.01) from the Hardy-Weinberg. Dendrogram of the Neighbour-Joining method showed that 62 walnut seedlings divided to four main groups. Analyses of population structure by Structure 2.3.1 software identified two sub populations (k=2). Based on association mapping analysis, by using MLM (mixed liner model) method, transpiration, conductance and photosynthesis have been controlled by WGA9 and WGA69 locies in normal condition. In stress condition WGA1 loci showed relationship with CO2 concentration that was covered %75 of variations of this trait. The results of this study can be used in breeding programs of Juglans regia to identify drought resistant varieties.