Approximating faces of marginal polytopes in discrete hierarchical fashions
Authors: Nanwei Wang, Johannes Rauh, Hélène Massam
Abstract: The existence of the utmost likelihood estimate in hierarchical loglinear fashions is crucial to the reliability of inference for this model. Determining whether or not or not the estimate exists is the same as discovering whether or not or not the enough statistics vector t belongs to the boundary of the marginal polytope of the model. The dimension of the smallest face Ft containing t determines the dimension of the lowered model which must be considered for correct inference. For higher-dimensional points, it is not potential to compute Ft exactly. Massam and Wang (2015) found an outer approximation to Ft using a set of sub-models of the distinctive model. This paper refines the methodology to hunt out an outer approximation and devises a model new methodology to hunt out an inside approximation. The inner approximation is given not in relation to a face of the marginal polytope, nonetheless in relation to a subset of the vertices of Ft. Understanding Ft exactly signifies which cell potentialities have most likelihood estimates equal to 0. When Ft cannot be obtained exactly, we’ll use, first, the outer approximation F2 to chop again the dimension of the problem and, then, the interior approximation F1 to accumulate applicable estimates of cell potentialities corresponding to parts of F1 and improve the estimates of the remaining potentialities corresponding to parts in F2∖F1. Using every real-world and simulated data, we illustrate our outcomes, and current that our methodology scales to extreme dimensions.
