(0,∞) ∫ Rp̃ f(Y | β⋆,D, τ, σ )π(D, τ, σ)dβ⋆dτdDdσ , where P = {D : D is a q×q positive definite matrix}.Without creating confusion we suppress the subscripts for the integration spaces below. Further let Σ = ZCZ + σI, where Z = (Z, Z) and Cq̃×q̃ = diag(D, . . . ,D, τIr−2) with q̃ = mq + r − 2. Note this Z is not the one originally defined in Section 2.2. For convenience, we do not change the notati...

Microarrays have become increasingly common in biological and medical research. They enable the simultaneous study of thousands of genes and provide gene expression information on a whole genome level. A major goal of microarray experiments is to determine which genes are differentially expressed between samples. A mixed model approach using the Johnson’s system of distributions and Baye’s form...

the  main  assumptions  in  liner  mixed  model  are normality  and  independency  of  random  effect component.   unfortunately,   these   two  assumptions   might   be  unrealistic   in  some   situations. therefore, in this paper, we will discuss about the analysis of bayesian analysis of non-normal and non-independent mixed model using skew-normal/independent distributions, and finally, thi...

this paper proposes a new mathematical model for the integrated procurement-production-distribution problem of a fuzzy mixed integer linear programming (fmilp) type. considering the uncertainty in real problems, a number of parameters such as demand, capacity, and cost where their values are not available or known precisely, have been considered as trapezoidal fuzzy numbers. to solve fuzzy mixe...

Estimation in generalized linear mixed models for non-Gaussian longitudinal data is often based on maximum likelihood theory, which assumes that the underlying probability model is correctly specified. It is known that the results obtained from these models are not always robust against misspecification of the random-effects structure. Therefore, diagnostic tools for the detection of this missp...

in this work the effect of electrolytes on hydrate formation was investigated. to do so, a new model was used in predicting the hydrate formation conditions in presence of both single and mixed electrolyte solutions. the new model is based on the van der waals - platteeuw hydrate equation of state. in order to evaluate the values for the activity of water in electrolyte solutions the simplified...

this paper presents a simple methodology for cost estimation of a near optimal heat exchanger network, which comprises mixed materials of construction. intraditional pinch technology and mathematical programming it is usually assumed that all heat exchangers in a network obey a single cost model. this implies that all heat exchangers  in a network are of the same type and use the same materials...

with the growth in customers’ demand diversification, mixed-model u-lines (mmul) have acquired increasing importance in the area of assembly systems. there are generally two different approaches in the literature for balancing such systems. some researchers believe that since the types of models can be very diverse, a balancing approach without simultaneously sequencing of models will not yield...