Henderson's mixed model equations system is generally required in a Gibbs sampling application. In two previous studies, we proposed two indirect solving approaches that give dominance values in an animal model context with no need to process all this system. The first one does not require D-1 and the second is based on processing the additive animal model residuals. In the present work, we show that these two methods can be handled iteratively. Since the Bayesian approach is now a widely used tool in estimation of genetic parameters, the main part of this work is devoted to a Gibbs sampling application that can be accelerated by means of the aforementioned indirect solving methods. Three replicates of a population data set are simulated in the paper to compare the applications and estimates. This shows effectively that the estimates given by implementing a Gibbs sampler with each of the two suggested solving methods are obtained with less computational time and are comparable to those given by considering the integral system, particularly when priors are more weighted.
This study presents a new approach to obtain dominance estimates without using the full Henderson?s mixed model equations (MMEs) related to an additive plus dominance animal model. This reduction could decrease substantially the computing time and hence its cost. In contrast to a procedure that we proposed before, the method developed in this paper does not require D?1 and provides best linear unbiased prediction (BLUP) of genetic values that is close to that given by processing the full MMEs. In the previous study, we also elaborated an algorithm (denoted ?-REML) in order to approximate restricted maximum likelihood estimation of variance components via the expectation maximization (EM) algorithm. The ?-REML algorithm has been modified to be adapted to our new resolution approach. Through a numerical example, we show that there is a good agreement between REML-(EM), ?-REML and modified ?-REML estimates and that the latter algorithm is more efficient than our first proposition in terms of computing time and memory conservation.
Sjogren's syndrome (SjS) is chronic autoimmune disease manifested by the loss of saliva and/or tear secretion by salivary and/or lacrimal glands, respectively. The pathogenesis of the disease remains elusive, perhaps due to the multiple triggers of the disease. However, substantial advances have been made in attempting to resolve the complexity of SjS using both animal models and human subjects. The primary objectives of this review are to provide a better understanding of the disease processes with major emphasis on the use of mouse models, how genetic predisposition plays a role in the natural history of the disease, as well as a presentation of new findings pertaining to the role of TH1, TH2, and TH17 cells in the pathogenesis of SjS.
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