Comparison on modelling the relative risk estimation: Bayesian study

The estimation of the disease incidents was previously analyzed using a classical approach. However, this approach features large outlying relative risks and considered as misleading due to several major problems. Some approaches such as the hierarchical Bayesian method have been adopted in the literature in order to overcome these problems. The purpose of this study is to compare between hierarchical Bayesian models that improve the relative risk estimation. The focus lies on examining the performance of different sets of densities via monitoring the history graphs, estimating the potential scale reduction factors and conducting sensitivity analysis for different choice of prior information. The best model fit is accomplished by conducting a goodness of fit test. The study is applied on Scotland lip cancer data set. The results show that for models with large number of parameters, more iteration is needed to achieve the convergence. The study also shows that diagnostic test and sensitivity analysis are important to decide about the stability and the the influence of the choice of the prior densities. The DIC results were in line with the previous results and provide a good method of comparison

Geometric inequalities via a symmetric differential operator defined by quantum calculus in the open unit disk

The present investigation covenants with the concept of quantum calculus besides the convolution operation to impose a comprehensive symmetric q-differential operator defining new classes of analytic functions. We study the geometric representations with applications. The applications deliberated to indicate the certainty of resolutions of a category of symmetric differential equations type Briot-Bouquet

Evolution of spatial correlation of mean diameter : a case study of trees in natural dipterocarp forest.

Problem statement: Spatial modeling has many applications in various fields like agriculture, meteorology, forestry and it takes into consideration the spatial correlation structures. In the field of forestry the growth rate, in particular, the diameter of trees is usually an important parameter. The growth rate of trees in a forest is likely to be influenced by various factors like nutrients, fertility of soil, sunshine and rainfall. In this study, we investigated the spatial correlation of the mean diameter of trees in the natural Dipterocarp forest in Gunung Tebu forest reserve, Terengganu, Malaysia. Approach: The diameters were measured using the diameter tape and the unit of measurement is in centimeters (cm). The main sampling unit was 1 ha plot of 100 by 100 m located approximately in the centre of each treatment block. Within the 1 ha sample plot, the quadrants (20 by 20 m) were numbered consecutively from 1-25 and in the outer 16 quadrants; all trees having a diameter at breast height over bark (dbh) of 15.0 cm or more are individually numbered, tagged and enumerated. Using the rook's and queen's neighborhood structure, we computed the Moran's spatial correlation coefficient for the mean diameter of trees in each quadrant for the years 1975 up to 1986. Results: We found that there was a negative spatial correlation among the mean diameter of trees in the 16 quadrants (cases) of the natural Dipterocarp forest in Gunung Tebu forest reserve, Terengganu at α level 0.10. Conclusion/Recommendations: The existence of negative spatial correlation indicated that there was competition among the trees in Dipterocarp forest as a result of tree growth over time which was affected by species, size, age and other environmental factors. Further research will concentrate on the spatial modeling of diameter of trees for the years where negative correlation was found

Posterior predictive scimulation Checks for hierarchical Bayesian Modelling

Problem statement: Assessing the plausibility of a posited model is always fundamental in order to evaluate and examine its performance. Such assessment is essential in the field of Bayesian data analysis. A Bayesian analysis can be very misleading when the model is far from plausible. Thus, any Bayesian analysis should include an evaluation method to find out whether the posited model should be excluded because it fails to provide a reasonable summary of the data at hand. Such evaluation method is referred as the posterior predictive checks. Approach: In this study we review the use of the posterior predictive simulation. We propose a simulation study to evaluate and examine the adequacy of three mixed effect hierarchical Bayesian models, namely IVM, CVM and GSM. These models include different sources of variability and used to examine the trend of the relative risk associated with the disease spread in lattice grid. The evaluation is achieved by proposing different graphical and numerical posterior predictive checks to compare features of the observed data to the same features of replicate data generated under each model. The proposed method is illustrated by analyzing the well-known data set of the lip cancer in Scotland. Results: The graphical and the numerical results suggested that the model which includes all sources of variability (GSM) had the most similar value for both original and predicted samples, as compared to the other models. Thus, it was concluded that the GSM is the most appropriate model which could fit the data well. Conclusion: The method used for assessing model fitness will provide guidance for practitioners to select an adequate hierarchical Bayesian model that expect to fit the data well

Dynamical system of the growth of COVID-19 with controller

Recently, various studied were presented to describe the population dynamic of covid-19. In this effort, we aim to introduce a different vitalization of the growth by using a controller term. Our method is based on the concept of conformable calculus, which involves this term. We investigate a system of coupled differential equations, which contains the dynamics of the diffusion among infected and asymptomatic characters. Strong control is considered due to the social separation. The result is consequently associated with a macroscopic law for the population. This dynamic system is useful to recognize the behavior of the growth rate of the infection and to confirm if its control is correctly functioning. A unique solution is studied under self-mapping properties. The periodicity of the solution is examined by using integral control and the optimal control is discussed in the sequel

On the Connection Problem for Painlevé Differential Equation in View of Geometric Function Theory

Asymptotic analysis is a branch of mathematical analysis that describes the limiting behavior of the function. This behavior appears when we study the solution of differential equations analytically. The recent work deals with a special class of third type of Painlevé differential equation (PV). Our aim is to find asymptotic, symmetric univalent solution of this class in a symmetric domain with respect to the real axis. As a result that the most important problem in the asymptotic expansion is the connections bound (coefficients bound), we introduce a study of this problem