For an interest parameterψ(θ) the Bayesian method eliminates the nuisance parameterλ(θ) by integrating with respect to a conditional prior for λ given ψ. This conditional prior may be difficult to specify in both the subjective and objective Bayesian contexts. We propose the use of results from likelihood theory that give highly accurate third order determinations of various marginal distributi...

We present novel understandings of the Gamma-Poisson (GaP) model, a probabilistic matrix factorization model for count data. We show that GaP can be rewritten free of the score/activation matrix. This gives us new insights about the estimation of the topic/dictionary matrix by maximum marginal likelihood estimation. In particular, this explains the robustness of this estimator to over-specified...

Subjective opinions generalize probability distributions by including degrees of uncertainty which reflect lack of confidence in the probabilities. This paper describes a method for computing the joint subjective opinion of two variables which can be generalized to a method for computing joint subjective opinions over multiple variables in a subjective Bayesian network. We show how the joint op...

Given an undirected graph g or hypergraph 'H model for a given set of variables V , we introduce two marginalization operators for obtaining the undirected graph YA or hy­ pergraph 'HA associated with a given subset A c V such that the marginal distribution of A factorizes according to YA or 'HA, respec­ tively. Finally, we illustrate the method by its application to some practical examples. Wi...

We propose a two component graphical chain model, the discrete regression distribution, in which a set of categorical (or discrete) random variables is modeled as a response to a set of categorical and continuous covariates. We examine necessary and sufficient conditions for a discrete regression distribution to be described by a given graph. The discrete regression formulation is extended to a...

Given an undirected graph G or hypergraph potential H model for a given set of variables V, we introduce two marginalization operators for obtaining the undirected graph GA or hypergraph HA associated with a given subset A V such that the marginal distribution of A factorizes according to GA or HA, respectively. Finally, we illustrate the method by its application to some practical examples. Wi...

West Greenland has had multiple episodes of human colonization and cultural transitions over the past 4,500 y. However, the explanations for these large-scale human migrations are varied, including climatic factors, resistance to adaptation, economic marginalization, mercantile exploration, and hostile neighborhood interactions. Evaluating the potential role of climate change is complicated by ...

Given a set of possible models (e.g., Bayesian network structures) and a data sample, in the unsupervised model selection problem the task is to choose the most accurate model with respect to the domain joint probabil­ ity distribution. In contrast to this, in su­ pervised model selection it is a priori known that the chosen model will be used in the future for prediction tasks involving more "...

This paper tests competing hypotheses on the relationship between marginalization and participation in undeclared work. The ‘marginalization’ thesis views work as conducted primarily by marginalized populations among which young, unemployed economically fragile people dominate. A ‘reinforcement’ argues that is disproportionately those declared jobs thus economy reinforces, rather than reduces, ...

Structured settlement underwriting is the underwriting of medically impaired lives for the purchase of an annuity to fund the settlement. Other than risk assessment, structured settlement (SS) underwriting has little in common with traditional life insurance underwriting. Most noteworthy of these differences is the relative lack of actuarial data on which to base decisions about mortality and t...