@MISC{Dellaportas_asimulation, author = {Petros Dellaportas and Dimitris Karlis}, title = {A Simulation Approach to Hierarchical Models}, year = {} }

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Abstract

We deal with general mixture models of the form m(x) = R \Theta f(x j `)g(`)d`, where g(`) and m(x) are called mixing and mixed or compound densities respectively, and ` is called the mixing parameter. The usual statistical application of these models emerges when we have data x i ; i = 1; : : : ; n with densities f(x i j ` i ) for given ` i , and the ` i are independent with common density g(`). Then, the marginal density of any x i is m(x). These models are often called hierarchical models due to the ordered structure of the data and parameter distributions. Interest lies mainly in the estimation of the unit-specific parameters ` i , but an interesting problem is also the smooth reconstruction of m(x) which can also be viewed as the marginal density of the data. For a certain well known class of densities f(x j `), we present a samplebased approach to reconstruct g(`). The idea is based on the fact that at least for the class of densities we consider, the moments of g(`) can be d...