where u ∼ N(0, G) and 2 ∼ N(0, R) with u and 2 independent. This model can be interpreted as Y |β, u ∼ N(Xβ+Zu,R), u ∼ N(0, G), yielding (on integrating out u) the marginal model Y |β ∼ N(Xβ,ZGZ + R). Let V = ZGZ + R. Then the maximum penalized likelihood estimates of β and u given G and R are given by θ̂ = [ β̂ û ] = (CTR−1C + B)−1CTR−1y (A.2) where C = [X Z] and B is the block diagonal matrix w...

Longitudinal studies, where data are repeatedly collected on one subject over a period, are common in medical research. When effect of a time-varying exposure on an outcome of interest is measured at different time points, standard statistical methods fail to give robust estimate in the presence of time-dependent confounders. There is alternative method avoid, that is, inverse probability weigh...

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In this study we present a marginal mixture model for discovering probabilistic motifs in categorical sequences. The proposed method is based on a general framework for developing, extending and marginalizing expressive motif models that encapsulates spatial information. Two alternative schemes for constructing expressive models are described, the extend and the marginal approach. The EM algori...

We provide an existence proof for Generalized Marginal Cost Pricing with given tax-subsidy rules. The novelty is that our approach allows for economic environments where all the generalized marginal cost pricing equilibria are inefficient in the aggregate. An example is recalled in order to suggest how non-pathological these environments are. Journal of Economic Literature Classification Number...

Abstract In this paper, we introduce the notion of a marginal tube, which is hypersurface foliated by surfaces. It generalises marginally trapped tube and several notions black hole horizons, for example trapping isolated dynamical etc. We prove that if every spacelike section surface, then null. There no assumption on topology tube. To it, study geometry surfaces in four-dimensional spacetime ...

We extend the calculable analytic approach to marginal deformations recently developed in open bosonic string field theory to open superstring field theory formulated by Berkovits. We construct analytic solutions to all orders in the deformation parameter when operator products made of the marginal operator and the associated superconformal primary field are regular.

statement of the problem: although all-ceramic restorations are broadly used, there is a lack of information concerning how their fit is affected by fabrication procedure and marginal configuration. purpose: the purpose of this study was to evaluate the marginal fit of zirconia cad/cam ceramic crowns before and after porcelain firing. the influence of finish line configuration on the marginal f...

The joint asymptotic distributions of the marginal quantiles and quantile functions in samples from a p-variate population are derived. Of particular interest is the joint asymptotic distribution of the marginal sample medians, on the basis of which tests of significance for population medians are developed. Methods of estimating unknown nuisance parameters are discussed. The approach is comple...